c 2011 Sanjit Krishnan Kaul ALL RIGHTS RESERVED

Transcription

1 c 2011 Sanjit Krishnan Kaul ALL RIGHTS RESERVED

2 PROPAGATION AND DELAY-OPTIMAL SAFETY MESSAGING IN VEHICULAR NETWORKS BY SANJIT KRISHNAN KAUL A dissertation submitted to the Graduate School New Brunswick Rutgers, The State University of New Jersey in partial fulfillment of the requirements for the degree of Doctor of Philosophy Graduate Program in Electrical and Computer Engineering Written under the direction of Prof. Marco Gruteser and approved by New Brunswick, New Jersey October, 2011

3 ABSTRACT OF THE DISSERTATION Propagation and Delay-Optimal Safety Messaging in Vehicular Networks by Sanjit Krishnan Kaul Dissertation Director: Prof. Marco Gruteser Vehicles that talk to each other are expected to unleash a broad spectrum of applications that will make road travel safer, faster, efficient and more entertaining. We study safety messaging, which enables applications that provide different levels of driver assistance to improve on-road safety, for different vehicular network scenarios. Initial deployments of safety applications in vehicles are expected to be sparse with support for event-driven messaging over a few wireless hops, for example, a car broadcasting messages when in distress. We propose GeoMAC, a protocol that exploits spatial diversity of forwarder nodes, and a geo-backoff mechanism to resolve contention between them, and achieves message delivery with smaller latency and jitter, and greater reliability. Eventually, all on-road vehicles will broadcast their state information, such as location and velocity, many times a second. Each vehicle s state must be received in a timely manner and be refreshed periodically at all other vehicles of interest. The network objective of minimizing the system age, which we define, is then explored for single and multi-hop networks. For single-hop networks we assume a carrier-sense-multiple-access (CSMA) based sharing of the wireless medium. We show that the minimum system age cannot be achieved in networks through pure MAC techniques. We propose, and evaluate on ORBIT, an application broadcast rate adaptation algorithm that allows nodes to locally adapt their messaging rate to ii

4 keep the system age to a minimum. Next, we explore the benefits of a multi-hop wireless connectivity for a given physical network of on-road vehicles, when nodes can piggyback other nodes states. The system age optimization is formulated for arbitrary network graphs and round robin schedules. We show that, under certain conditions, significant improvements in system age may be obtained. For tree topologies, an algorithm that gives schedules that minimize system age is proposed. We end our study on messaging with an empirical evaluation of how enabling location prediction can help reduce rate of messaging and hence channel congestion. Finally, we measure and model the effect of a car s own geometry, antenna placement, and of other cars in vicinity, on the vehicle-to-vehicle link and the network. iii

5 Acknowledgements First and foremost I would like to thank my advisor Prof. Marco Gruteser. I am thankful that he took me in as his student, sponsored my graduate studies and even today puts in a lot of time and effort in making all what I send to him better and more valuable. I am greatful for his immense patience with my ineptness and many a below par updates. I am a better researcher today thanks to his efforts and continued guidance. I also thank him for giving me the freedom and allowing me time to pursue research directions of my choosing. Thank you Marco! I thoroughly enjoyed my collaboration with Prof. Roy Yates. I thank Roy for his guidance, sharing of wisdom, his advice, his patience, and his painstaking efforts towards making my write-ups simpler and better. Someday I hope to draw a figure or write a document that will satisfy his high standards. I take inspiration from seeing him work out stuff on paper and on the white board. Hopefully, I will never forget the importance of putting pen to paper! Finally, I would like to thank him for attending student talks and asking questions that have often clarified my own understanding. I thank Dr. Larry Greenstein for teaching me about wireless channels and life and research in general. I thank him for his immense patience over many years of very small, half-baked, many times useless, and always delayed updates from my end. He has been very kind and supportive all through my time in grad school. I thank Ivan for being very helpful, friendly and approachable, right from my first day in WINLAB. I thank him for always managing to find time. I cannot stop being amazed by his energy levels, know-how and uncanny ability to stay updated with the latest. I would like to thank Prof. Dipankar Raychaudhuri, Prof. Wade Trappe and Dr. Rich Howard for having spared their time whenever I approached them. I thank Dr. John Kenney for agreeing to be on my thesis committee. I also thank him for two years of interesting collaboration and also suggesting the topic of application layer rate iv

6 control, which is now an important contribution of my thesis. Prof. Predrag Spasojevic has been very kind and friendly to me during my stay at WINLAB. I thank him for his help with my job search and also thank him for his, once in a while, friendly and light-hearted reminders that there is more to life than grad school. I thank Prof. Sophocles Orfanidis and Prof. Narayan Mandayam for their teaching. I thank Madhur and Gautam for their invaluable help with vehicle-to-vehicle measurements. Also, Chandru, Hari, Gayatree, Ashwin and Pravin were very kind to loan their cars and at times their time for the experiments. I was lucky to be in the company of some wonderful people at WINLAB and Rutgers. Specifically, I would like to acknowledge Madhur, Chandru, Kishore, Sachin, Joy, Jassi, Hitesh, Suhas, Roystein, Aditya, Sailesh, Pandurang, Sangho, Pravin, Ayaka, Gautam, James, Tam, Bin, Gayathri, Haris, Mesut, Baik, Narayanan, Ashwin, Shweta and Arati. I would also like to thank Kishore for many good years of collaboration starting from my very first semester, helping with my job search and always finding the time to help. I thank James for my very enjoyable dabbling in real analysis and mathematics in general for a couple of summers. Mesut and Haris have always offered to help, even when they were very busy with their own deadlines. I thank them both. Special thanks to Gayathri for sharing all the information she had collected with me, making my job search much easier. I have also enjoyed many a chat with her about life and goals (only during much needed coffee breaks, of course). I would also like to thank Shweta, Arati and Suhas for helping with my job search. I would like to acknowledge the cops who added intrigue, including a late night call to my advisor, and humor, to the vehicular channel measurements. Many thanks to the WINLAB secretaries. In person, I troubled Noreen and Elaine the most. They have been very kind and always very helpful. Finally, thanks to the many people of the past and present whose works and insights I have enjoyed and benefited from. v

7 Dedication To my parents and grandfather for a terrific upbringing. To all those who instilled in me the importance of asking questions. vi

8 Table of Contents Abstract Acknowledgements Dedication ii iv vi List of Tables xii List of Figures xiii 1. Introduction Towards Hands-Off, Feet-Off, Brains-Off Driving [1] Dedicated Short Range Communications Multiple Access in Vehicular Networks Vehicle-to-Vehicle Wireless Propagation Contributions to Safety Messaging Event Messaging in Sparse Networks Periodic Safety Messaging System Age Minimizing Age in a Single-Hop Network Is Multi-Hop better than Single-Hop? Age Optimal Piggybacking Intelligently Reducing the State Dissemination Rate Contributions to Vehicle-to-Vehicle Channel Modeling Effect of Car on Antenna Patterns Vehicle-to-Vehicle Channel Over a Short Range Layout vii

9 2. GeoMAC: Geo-Backoff based Co-operative MAC Introduction Geo-cooperative MAC Protocol Timing Geobackoff Protocol Implementation Evaluation Framework Simulation Setup Results Spatial vs Temporal diversity GeoMAC vs AODV and GPSR Packet Delivery Rate Receiver Diversity Delay Performance Related Work Conclusions Limitations and Observations Minimizing Age of Information in Vehicular Networks Introduction System Model and Objective Delays in an MAC system Information Age and Throughput Minimizing Information Age in a CSMA System Simulation Setup Results Rate Control Algorithm Algorithm Evaluation Evaluation on the ORBIT testbed viii

10 3.5. Limitations and a Few Observations Related Work Conclusions On Piggybacking in Vehicular Networks: Can Multi-Hop better Single-Hop? Introduction Related Work System Model Piggybacking Modeling the Network as a graph Optimization over a Graph Loose upper bound on age Fully-Connected Network vs. Piggybacking A Single Lane Network Scaling of Age Generalization to multi-lane Simulation Results Conclusions Age Optimal State Dissemination with Piggybacking Introduction System Model Piggybacking over Unreliable Links Example of Graph Optimization Optimization over a Tree Schedule Optimization on a Tree Gains from using an optimal schedule for an example tree network An Example Platoon network Related Work Conclusions ix

11 6. On Predicting and Compressing Vehicular GPS Traces Introduction Assumptions and approach Prediction Compression DP Polynomial Interpolation (PI) Distance-Time Trajectory Data Results Prediction Prediction gains for different polynomial degrees and number of known actual locations Gains using LPP Benefits of road information Speeds and distances at which prediction gains were obtained Compression Related Work Conclusions Effect of Antenna Placement and Cars on Vehicle-to-Vehicle Links Introduction Background and Related Work Experimental Methodology Hardware and Software Configuration Open Space Baseline Parking Lot and Freeway Experiments Experimental Results Effect of Car Geometry on Antenna Patterns x

12 Effect of Car Geometry on Communication Link Effect on Communication Link in Freeway Scenario Effects of Antenna Placement in LOS and Dynamic Multi-path Environment Diversity Gains Effects of Antenna Placement on Vehicular Protocol Design Discussion Conclusions Vehicle-to-Vehicle Short Range Channel Modeling Introduction Measurement Methodology and Scenarios Experiment Setup Model and Evaluation Error in Gain Prediction Performance Prediction using the Model Quantifying Diversity Gains Related Work Conclusions Appendix A. Derivation of System Age A.1. Random Transmitter Selection A.2. Round Robin A.3. Round Robin with Omniscient TX and Piggybacking Appendix B. Proof of Theorem References xi

13 List of Tables 1.1. Offered load for different sized car networks. The cars in each others communication and/or interference range Simulation Parameters Default Experimental Parameters used Simulation results Demonstrating the model s efficacy in predicting performance of a system that uses quantized power control to achieve a target BER of10 4. For eachm, the top row is the mean and the bottom row is the maximum of the absolute difference in percentiles of the logarithm of achieved BERs, when using measured and estimated gains Antenna diversity gains (in db) for antenna separations of0.5 and1 m Scenario A model parameters. The parameters are continued in Table Scenario A model parameters Scenario B model parameters Scenario C model parameters Scenario D model parameters Scenario E model parameters Scenario F model parameters Scenario G model parameters Scenario H model parameters Scenario I model parameters xii

14 List of Figures 1.1. An example road network. The intersection of New Jersey Turnpike and the Garden State Parkway is shown. There is a third, narrow roadway at the very top, which we ignore in our analysis. Map retrieved from maps.google.com The throughput S achieved over a range of probabilities p by p-persistent CSMA for different offered loads G. The best throughput achieved S is close to the offered load G for light loads. The difference increases as the load increases. Both S andgare measured in number of messages per transmission slot Vehicular Channel Measurements and Setup Protocol Timing assuming back-off is resumed after VACK-TIMEOUT PER Trace used for simulation Spatial vs. Temporal Diversity gains Number of Packets Received (TXDiv) Packet Transmission Delay (TXDiv). Note that the y-axis is omitted from for plot clarity Packet Transmission Jitter (TXDiv) AODV delay CDF vs. GeoMAC (TXDiv) Vehicle u generates its state at instants shown by arrows with triangular heads. Vehicle v receives a generated state packet at the next instant marked by diamond shaped heads. An erroneous reception is marked by a cross. The age of u s information accumulates with time until it is reset to the time elapsed between state generation and reception (t 1 andt 2 in figure). The average age uv is given by the area under the curve normalized by the interval of observation xiii

15 3.2. Application at a node generates packets that are queued into a queue of size m. The packet at the head of the queue, numbered 1, awaits 0 or more backoff slots before its transmission starts A four lane road network with cars placed very close to each other to simulate a high density environment System age as a function of broadcast periodicity for LO (dashed lines) and FIFO (solid lines) assuming a queue size of m = 2. Selected W0 = 15, 500, W = For W0 = 3772 we also show age form = 4. The circles markers show different cases for CW 15, the squares CW 500 and the diamonds show CW Variation of with period for different CW sizes Variation of for different sized car networks. The minimum system ages are 0.02, 0.05, 0.1 and 0.15 seconds for 50, 100, 200 and 400 node networks, achieved at T of 0.03,0.05,0.1 and 0.25 seconds respectively Effect of selection of β on rate control. 400 nodes, start period of 0.03 s and length of interval is2s Effect of selection of interval on rate control. Start period of 0.01 s, 400 nodes, β = ORBIT Experiment. Measurement interval is 5 s and β = 1.1. The max difference between the shown percentiles is The left y-axis is in log-scale. The dashed staircase at the top shows number of nodes in network. The three other curves starting from top are the 90 th percentile of the set {ˆ v } of local estimates ˆ v at all nodes v, the system age ˆ calculated offline and the 25 th percentile of {ˆ v } A k-connected m-lane network. Each rectangle encloses a group of nodes that are connected to each other Suggested schedule for a k-connected single lane network. Nodes that receive when 3+k transmits are boxed lane,N = 50 cars each lane. The boxed data points are where the age is minimized. The corresponding k is 10, 12 and 18 for q = 3 db, 9 db and 20 db respectively. From (4.24), optimal x is 0.2, 0.23 and 0.39 respectively, which corresponds to a k of 10, 11.5 and 19.5 respectively xiv

16 lane, N = 100 cars each lane. The dashed lines plot ages averaged over schedules that are randomly chosen permutations of nodes. The solid lines assume the schedule described in Section 4.6. The lines correspond to a fixed q db, given by the legend. The y-axis (log-scale) shows age assuming1hz of bandwidth. An age of sec corresponds to0.012 sec in a10 MHz system An Example Graph An Example Tree Illustration of Algorithm 2. (a) The given tree with its edges labeled (the parenthesis) by number of nodes on either side of the edge cut. (b) Direct edge from smaller cut set to larger. Node 1 emerges root. (c) T 9 : The original tree network rooted at 1. Labels of leaf nodes contain theirl/c ratio to the right of the :. The nodes 3,4,5and8only transit their own information, (h+s) slots, and each have c = N 2n = 9 2 = 7. Thus for each of theml/c = (h+s)/7. (d)t 5 : Obtained when all the leaves int 9 have been merged into their respective parents. The order of their merging is unimportant as they all have the same l/c ratio. Merged node (8 7) has a l/c = (2h+10s)/5, as 8 transmits over h + s slots and 7 (a non-leaf in the original tree) over h + 9s slots. Also, for (8 7), c = c 7 = N 4 = 5. (e) T 4 : (8 7) and ( ) were the leaves in T 5, of which (8 7) had a smaller l/c ratio. Thus (8 7) is merged into 6. (f) T 3 : (8 7 6) in T 4 has the smallest l/c ratio and is merged into 9. (g) T 2 : Obtained from T 3. (h) T 1 : The optimal sequence is obtained from the label of the node and is the sequence 8,7,6,9,3,4,5,2,1. A variant of the above can be obtained by assuming h s and h + Ns h. The l/c ratio for ( ) and ( ) in T 3 is then the same. As a result3,4,5,2,8,7,6,9,1 is also an optimal sequence A network of three platoons. The edges are between cars that have communication links between them. Leader of the platoon is the rootrof the tree Prediction of location using GPS traces Percentage compression for coarse grained topologies Percentage compression for fine grained topologies Experiment scenario, hardware setup and placement of antennas xv

17 7.2. RSSI received at antenna (a) BD, FD, BP and (b) FP, RV, CC, compared to the antenna on a tripod Empirical PER, RSSI and the Two Ray model The Two-ray ground reflection model. The illustration is from [2]. The piecewise approximation is drawn at an offset for clarity [2] Empirical CDF plotted against exponential and gamma distributions CPPE comparison of antenna positions, Livingston parking lot experiment (section 7.3.3) Performance comparison of antennas at (a) WALMART and (b) WINLAB Diversity gains using MPRS. Comparison of the best single antenna with the combination of best 2, 3 and 4 antennas Measurement setup installed at the transmitter and receiver on the car Illustration of how a typical measurement scenario was executed. The three snapshots, separated by the dashed lines, are at different points in time. The start of each of the snapshots is shown Illustration of all measured scenarios FittingM = 2,3,4 sinusoid models to select scenarios Error in channel gain prediction (db) is shown on the y-axis. Distances are grouped in bins of 5 m and for each distance a box plot of prediction errors is shown xvi

18 1 Chapter 1 Introduction 1.1 Towards Hands-Off, Feet-Off, Brains-Off Driving [1] A world where vehicles drive themselves, with occupants safely ensconced and engrossed in more productive or pleasurable activity, is the holy grail of Intelligent Transportation Systems (ITS). In the United States, one of the earliest initiatives towards automated highways was the California PATH [3] program established in 1986 by the Institute of Transportation Studies of the University of California at Berkeley [4] and sponsored by the California Department of Transportation [5]. The first demonstration of an Automated Highway System (AHS) was conducted in August 1997 [1]. The motivation behind ITS is to improve driver safety by reducing accidents that occur due to driver error or due to slow human response to on-road events like braking, improving road utilization using techniques like vehicle platooning [6] to reduce inter-vehicle spacing on freeways and last but not the least improving fuel efficiency. On-road safety in such systems is improved by using electronic steering and control and sensors that measure parameters local to a vehicle like speed, acceleration, yaw rate, steering angle, location, and also its distance from and speed relative to adjacent vehicles. Another aspect of the automated system is that of communication between the different vehicles which allows orchestrating maneuvers like lane-change, sudden braking, and collision avoidance, safely and in cooperation with each other. In case of platooning, messages related to platoon management are also exchanged. Such inter-vehicle communication is enabled via messaging over the wireless channel. Before autonomous systems become reality, in the short term, the information collected from the sensors of a vehicle and that of vehicles within a few hundred meters can be used by driver assist applications. Note that the information collected over wireless is from vehicles that may or may not be in the vehicle s view. For example, the other vehicles of interest may not be in the field of view of a radar attached to the vehicle.

19 2 1.2 Dedicated Short Range Communications Vehicle-Infrastructure Integration (VII), a US Department of Transportation program and more recently named IntelliDrive SM [7] 1, was a follow up to the AHS project and was inspired by the allocation of 75 MHz of bandwidth in the 5.9 GHz band for ITS [8] by the FCC in October The spectrum was known as Dedicated Short Range Communications or DSRC, also used to refer to the body of standards defined for Intelligent Transportation Systems. A DSRC network will contain on-board units (OBU) in vehicles and road-side units (RSU) (infrastructure) and will involve a mix of vehicle-to-vehicle and vehicle-to/from-infrastructure communication. The band consists of a total of seven channels, one for control and six service channels, each of 10 MHz bandwidth. The IEEE p standard defines the DSRC PHY and MAC. The DSRC PHY is OFDM based and supports data rates of 3 27 Mbps over a 10 MHz channel. A transmit power of 1 W and a maximum EIRP of 30 W for emergency services is allowed [9]. The MAC is carrier sense multiple access based (CSMA). The DSRC system is expected to support messaging for a plethora of applications typically divided into the categories of safety applications and non-safety applications. Non-safety applications include tolling, traffic management and flow control, cooperative glare reduction and other infotainment applications. Safety applications may include, for example, intersection collision avoidance, requiring messages like traffic signal violation warning and stop sign violation warning, and a mix of messaging between vehicles and/or infrastructure. Others examples include curve speed warning and emergency electronic brake light [10]. Most safety applications need messaging with high update rates (1 10 Hz) and over a large communication range ( m) and have stringent latency requirements (100 msec). We will refer to all such time critical messaging as safety messaging. In this thesis we will focus on vehicle-to-vehicle aspects of a DSRC network, and will not assume availability of any infrastructure. We will quantify and model the effect of cars on the vehicle-to-vehicle wireless channel. We will also study delay/age (defined later) optimal techniques for networks of hundreds of vehicles to make the best use of the available wireless 1 The USDOT dropped the name IntelliDrive too. The project goals and website remain the same, however.

20 3 bandwidth to support safety applications. 1.3 Multiple Access in Vehicular Networks Carrier sense multiple access (CSMA) techniques are proposed for use in a DSRC network. CSMA is typically used by networks of distributed nodes to share access to a communication medium with minimal overheads, that is without any prior co-ordination or configuration. Nodes in the network attempt transmission of a packet arrival, if the medium is sensed idle, with a certain persistence probability p. Large networks of nodes with fairly small packet arrival rates benefit from such statistical access to the medium as no bandwidth is wasted on co-ordination. However, large packet arrival rates can lead to significant probabilities of more than one node transmitting at the same time causing packet transmissions to collide, which leads to erroneous packet reception. Road networks, with large number of lanes, can have hundreds of cars within a few hundred meters of road length. Consider the road network in Figure 1.1, which shows an intersection of the Garden State Parkway (GSP) and the New Jersey Turnpike. Consider a box 600 m long along the turnpike and a box300 m long along the GSP, both boxes centered around the shown intersection. The turnpike has a total of 12 lanes and the GSP has 6 10 lanes. Assuming 6 GSP lanes, the total number of cars in the area covered by the boxes can be up to 1200 cars, where we assumed a road length of10 m dedicated to each car. Further assume perfect, interference free, round-robin (RR) scheduling of such a network of cars, each broadcasting messages at 10 messages every second. Note that RR is optimal for this network of cars as each car has a message to transmit at a fixed periodicity. Let a message be 128 bytes in size and the physical layer (PHY) transmission rate be 6 Mbps. Define the slot length τ to be the transmission time of a message, which given the message size and PHY rate is µs. Further assume that each car must get a chance to transmit once every 100 msec. We have a total of 586 slots in the RR schedule. Table 1.1 shows the number of packets that need to be transmitted per slot so that all cars in the network can send their message once every 100 msec. Perfect scheduling can very easily schedule 400 cars but 800 cars cannot be all scheduled every 100 msec. Clearly, if the intersection in Figure 1.1 is packed with cars and

21 4 Figure 1.1: An example road network. The intersection of New Jersey Turnpike and the Garden State Parkway is shown. There is a third, narrow roadway at the very top, which we ignore in our analysis. Map retrieved from maps.google.com. if the cars are in either the communication and/or the interference range of each other, safety messages cannot be scheduled once every 100 msec for every car. Techniques that reduce the messaging rate (rate control) and/or reduce the range of cars (power control) are needed. Round robin scheduling is replaced by CSMA in reality, which even for an optimal persistence probability, is unable to match network throughput even for offered loads much smaller than 1 packet per transmission slot. Let G be the number of messages offered for transmission per transmission slot. We saw in Table 1.1 that for a 256 car network G = Figure 1.2 plots the throughput achieved by a p-persistent CSMA over p (0,1) for select G. Only for small G = 0.17, the throughput S = G. For G = 0.6 the maximum throughput is achieved at p = 0.5 and is S = , which is less than G by 22% (as a percentage of G). Even at optimalpcsma in general cannot achieves = G for largegas available bandwidth is wasted due to idle slots and collisions. It is worth noting that a large enoughg 1 may maximize throughput, that is gives = 1. However, safety messaging is delay sensitive and a largegwill lead to large queuing delays at nodes in the network. Thus, merely maximizing throughput maybe suboptimal, especially for large networks. For a CSMA network, throughput can be maximized and stability achieved by setting the

22 5 Number of cars G (Messages offered per message transmission slot) Table 1.1: Offered load for different sized car networks. The cars in each others communication and/or interference range. persistence probability optimally [11]. However, it requires nodes to have network wide feedback regarding whether a transmitted packet was received successfully or in collision. Typically, a node receives feedback only for the packets it has transmitted. Given the limited feedback the nodes in IEEE systems employ an exponential backoff mechanism to alleviate contention for the medium and ensure throughput stability [11]. A node expects receipt of an ACK packet in response to a successfully received packet. Absence of an ACK is assumed to imply erroneous reception due to a simultaneous transmission. The node increases its backoff window by twice, which is the same as reducing the average transmission attempt probability by half, when no ACK is received, before attempting retransmission of the packet. Safety messaging in vehicular networks, unlike most messaging in WiFi systems, is broadcast in nature and is not acknowledged at the MAC layer to avoid the possibility of a storm of acknowledgments. The lack of acknowledgments preempt the use of back-off window based broadcast contention reduction techniques in the standard and make congestion control, necessary to keep messaging delays small, even more challenging. 1.4 Vehicle-to-Vehicle Wireless Propagation Wireless propagation between vehicles is featured by transmit and receive antennas at similar heights, typically on the order of a meter above the ground. The communication takes place in the 5 GHz band. Communicating vehicles can experience scatter from the ground, stationary

23 6 0.6 G= Throughput S Persistence probability p Figure 1.2: The throughput S achieved over a range of probabilities p by p-persistent CSMA for different offered loads G. The best throughput achieved S is close to the offered load G for light loads. The difference increases as the load increases. Both S and G are measured in number of messages per transmission slot. and large structures like buildings, and smaller mobile vehicles in their vicinity. Wireless link conditions can change faster than a cellular link because of the presence of mobile scatterers and obstructors in the path between the transmitter and receiver. Capturing the channel characteristics under different vehicle densities and mobility patterns is challenging and important to design reliable PHY layer mechanisms. Last but not the least, it is essential to quantify the effect of the channel on the performance of applications of interest. 1.5 Contributions to Safety Messaging We next summarize the contributions made by this thesis to vehicular safety messaging. Safety messaging can be broadly categorized into event-driven and periodic. The thesis makes contributions to both event-driven and periodic messaging in vehicular networks. Techniques that enable delay/age (defined later) optimal message dissemination, which is desirable for safety messaging, are proposed and evaluated. While both require vehicles broadcasting to others, event-driven messaging is one-to-many while periodic messaging is many-to-many in nature.

24 Event Messaging in Sparse Networks Event-driven messages, for example vehicle in distress message or ambulance approaching message, target a certain geographic region (one or more vehicles) and involve a given vehicle broadcasting the message with a certain periodicity, in response to the said event. Such a message broadcast may travel over a few wireless hops. The message broadcast continues till the goal of the broadcast is accomplished, for example the car in distress receives necessary assistance. Initial deployments of safety messaging will involve relatively sparse deployments of DSRC radios, for example on emergency vehicles and limited percentage of private vehicles, and a support of select event-driven messages. We first study the dissemination of such messages and propose GeoMAC to enable broadcast of the messages within a bounded delay, which is a challenge under changing network/hop connectivity, which is typical in a vehicular network. GeoMAC benefits from the spatial diversity (more than one possible forwarder) inherent in vehicular networks to enable delay bounded delivery of the message. It resolves contention between multiple possible forwarders using a distributed geo-backoff mechanism. We show that GeoMAC out performs proposed protocols like AODV and GPSR with respect to average message delivery delay and jitter Periodic Safety Messaging Vehicular networks will eventually support periodic safety messaging by every on-road vehicle, with messages broadcast at 1 10 Hz. The safety messages will contain vehicle state as collected by various sensors attached to a vehicle, for example its GPS location, velocity, yaw rate, and brake light indicator. The messaging, unlike event-driven, is many-to-many. We study the delay optimal dissemination of such messages in large networks. We introduce the metric of system delay/system information age to capture the requirements of periodic safety messaging. The network optimization aims at minimizing the metric, which is equivalent to enabling the state information of vehicles in the network to be as fresh as possible, on an average, at other vehicles in the network.

25 8 System Age Let uv (t) be the stochastic process that describes the age of the state information of node/vehicle u at nodev at timet. Let uv = E[ uv (t)], which is the average age (expectation) ofu s state information at v. Let N be the number of nodes in the network 2. The system age is defined as = 1 N uv, (1.1) u v u wheren = N(N 1). Minimizing Age in a Single-Hop Network We consider fully connected networks, with error free wireless links, in which nodes use CSMA to broadcast state over the wireless medium. Large number of nodes in the network can lead to congestion and undesirable levels of packet collisions and hence large system age. We show, via simulations, that the system age is minimized at an optimal operating point that lies between the extremes of maximum throughput and minimum packet delay. Also that it cannot be achieved in networks through pure MAC techniques such as contention window adaptation. This motivates our design of a broadcast rate adaptation algorithm that provides congestion control above the MAC layer. It uses local decisions at nodes in the network to adapt their messaging rate to keep the system age to a minimum. Simulations and experiments with 300 ORBIT nodes show the efficacy of the algorithm at minimizing system age. In recent years several works [12 15] have looked at controlling congestion in vehicular networks to enable safety messaging. Unlike many related works that use power control to reduce the number of vehicles in range to alleviate congestion, we assume that all vehicles in range want to communicate with each other and then find the broadcast rate that minimizes age. Also, none of the related works, which are detailed in Section 3.6, use an average end-to-end application delay based metric, which we capture in the form of the system age metric. 2 The network must be connected but need not be fully-connected.

26 9 Is Multi-Hop better than Single-Hop? We next ask that if for a given physical road network of vehicles we had the freedom to engineer a wireless network of our choice, what wireless network connectivity would minimize the system age. Given that safety applications require all cars in the region of interest to know each others state information, the chosen network connectivity must ensure that there exists a path between any two nodes in the network. That is the chosen network must be a connected graph. Also, nodes may have to piggyback/relay other nodes states. While almost all work on safety messaging assumes a CSMA based access control, we assume that all nodes are scheduled in a round robin manner. This allows interference free scheduling of nodes, eliminates penalties suffered due to the randomized mode of transmitter selection in CSMA, and makes analysis more tractable. The assumption is rewarding in that it exposes the mechanisms that lead to accumulation of system age over a chosen network connectivity. The system age optimization is defined for arbitrary network graphs. We show that a multihop network with piggybacking can in fact lead to a much smaller system age than a fully connected network of on-road vehicles. For a fastest relay heuristic based round robin schedule over an idealized multi-lane road network, we show that there exists a notion of an optimally connected graph, whose connectivity is independent of the size of the network and that the system age is of the order of the number of nodes in the network. Related works (Section 4.2) include [16], which is probably the closest to ours in that it asks whether multi-hop broadcasting is better than single-hop (fully-connected graph) or viceversa. The authors conclude that single-hop broadcasting is better when it comes to the age of received beacon information, however. The different conclusions may be explained by the authors creating a multi-hop network by reducing the transmit power instead of increase the rate (bits/sec/hz), as we do in our work, to create a multi-hop network. Age Optimal Piggybacking Encouraged by the gains achievable via engineering a multi-hop network, we investigate piggybacking in greater detail. We show that piggybacking is not a fix for unreliable messaging, assuming a reasonable link error probability 0 < ǫ < 0.5. That is piggybacking is a useful

27 10 strategy only when nodes want to communicate beyond their coverage range. The system age optimization is derived for tree graphs. An algorithm that gives optimal schedules that minimize system age is proposed for tree topologies and gains obtained when using an optimal schedule instead of random permutations are demonstrated for a platoon of vehicles. Intelligently Reducing the State Dissemination Rate One approach to address the problem of MAC congestion in large networks is to reduce the frequency of state update messages. We explore the possibility of the same via-a-vis a vehicle s location, when the movements of a vehicle can be predicted by nearby vehicles. We study how predictable vehicular locations are, given a Global Positioning System trace of a vehicle s recent path. We empirically evaluate the performance of linear and higher degree polynomial prediction algorithms using about 2500 vehicle traces collected under urban and highway driving conditions. Other works that use prediction to reduce the rate at which messages are broadcast include [17, 18]. However, no prior works carry out a detailed empirical evaluation of achievable gains when using prediction over real GPS traces. 1.6 Contributions to Vehicle-to-Vehicle Channel Modeling Effect of Car on Antenna Patterns This work studies the effect of a car s geometry and antenna placement on the vehicle-tovehicle link performance. The experiments use roof- and in-vehicle mounted omni-directional antennas and IEEE a radios operating in the 5 GHz band. We quantify the sensitivity of the radio reception performance to antenna placement and its effect on protocol design. We also quantify the alleviation of distortion in antenna patterns when using multiple antennas with different placements. The related works are detailed in Section Vehicle-to-Vehicle Channel Over a Short Range We measure and model the effect of vehicles in vicinity on the vehicle to vehicle channel, with a maximum distance of about 50 m between the transmitter and receiver. About 20 controlled

28 11 scenarios, a total of up to 6 cars, that represent traffic movement in a 1 4 lane road network are measured. The aim is to provide fairly simple parametric models that can be used to evaluate communication schemes between vehicles. We show the efficacy of the proposed multi-sinusoid models in estimating the performance of a communications system in terms of estimated signal power and also in terms of BER achieved for various QAM constellations and quantized power control. We also note the performance improvements when using two antennas and coherent combining. The related works are detailed in Section Layout In Chapter 2 we describe and evaluate GeoMAC for event messaging in sparse networks. We then look at networks of large number of nodes and application layer rate control in CSMA networks to minimize system age in Chapter 3. This is followed by formulating the system age for a general connected graph and answering the question of what is better, multi-hop or single-hop broadcast of safety messages, in Chapter 4. In Chapter 5 we look at age optimal schedules and describe an algorithm that returns an optimal schedule for a tree network. Chapter 6 explores the possible reduction in messaging rates when we allow vehicles to predict other vehicles locations. In Chapter 7 we evaluate the effect of antenna placement and car geometry on the vehicle-to-vehicle channel. Chapter 8 extends the study to short range vehicle-to-vehicle channels. The reader, having read this chapter, can read all chapters other than Chapter 5 without knowledge of the preceding chapters. Chapter 5 refers to a section in Chapter 4.

29 12 Chapter 2 GeoMAC: Geo-Backoff based Co-operative MAC 2.1 Introduction Vehicle-to-vehicle communication enables safety assistance, traffic improvement, customer service and infotainment applications. This chapter focuses on event-driven safety messaging in relatively sparse networks. To be effective, such messaging requires low latency and highly reliable vehicle-to-vehicle communication protocols. High mobility results in a highly time-varying wireless channel [19]. Sample RSSI measurements obtained with a nodes on a freeway-like stretch of US-1, with a moving transmitter and stationary receiver besides the road are shown in Fig. 2.1a. Measurements show up to 10 db RSSI changes every few hundred milliseconds likely due to shadowing from obstructions. Note that the observed temporal coherence in fading is about 100 ms during dips in signal, which would lead to significant delays for protocols solely based on ARQ schemes such as Stop-and-Wait [11]. If a packet is lost due to a reduction in received signal strength, the following MAC retries are also likely to fail until the signal strength has recovered. Ad hoc routing protocols, can also increase reliability by forwarding the message over an alternate path. Protocols such as AODV [20] or DSR [21], however, can efficiently adjust routes only on larger time scales they incur significant route discovery overhead when routes change every 100 ms. This work addresses the challenge of reliable communication in a highly time-varying channel through the GeoMAC protocol, which exploits the broadcast nature of the wireless medium to achieve spatial diversity. It uses receiver diversity, meaning that any of the nodes that can decode a transmitted message can opportunistically forward it towards the destination. Forwarders are selected in distributed manner via a geographic backoff (geobackoff), that assigns the highest priority to nodes with the smallest Euclidean distance to the destination node. This

30 13 allows forwarding with only an approximate knowledge of node density, no detailed monitoring of channel state or neighbor positions is necessary. It assumes, however, that nodes know their own position, for example through the Global Positioning System. If a transmission fails to achieve any forward progress (i.e., reach a node closer to the destination), the protocol can use cooperative ARQ by opportunistically retransmitting messages from the next closest node, rather than the original forwarder. Opportunistically choosing different forwarders and retransmitters increases spatial diversity and can circumvent delays imposed by temporal coherence of the channel. The remainder of this chapter is organized as follows. In Sec 2.2 we detail the protocol s design and follow it with implementation in Sec 2.3. Sec 2.4 describes the trace-driven simulation setup to evaluate spatial diversity gains in a vehicular scenario and compare the GeoMAC protocol with standard routing protocols. The results in Sec 2.5 show that spatial diversity can provide additional gains over temporal diversity and that the GeoMAC protocol reduces delays especially with regard to outliers. Related work is discussed in Sec 2.6. We conclude with a summary of results and discussion of limitations and other observations in Sec Geo-cooperative MAC The key challenge to exploiting spatial diversity in highly mobile networks is the efficient selection of the next transmitter, if direct transmission to the destination failed. This distributed decision making is enabled via a geobackoff, in which the backoff interval increases with a node s Euclidean distance from the destination. The sender includes the destination node s geographic position in the packet header, which allows each node to calculate its backoff interval independently. This assumes that each car monitors its own position (e.g., via the Global Positioning System). It also assumes that vehicles share these coordinates with potential communication partners, for example via periodic beacons. For an example of geographic forwarder selection, consider Figure 2.1c, where the source (S) transmits a message that is received by nodes (1), (2) and (3) but not by the intended destination (D). Node (3) will calculate the shortest geobackoff and first forward the message, because it is closest to the destination position. Beyond this opportunistic forwarding, spatial diversity is also exploited by co-operative ARQ

31 14 wherein (2) would retransmit the message if node (3) s forwarding fails. The nature of this back-off scheme allows additional nodes to dynamically participate in forwarding whenever they have overheard a transmission, no explicit joining procedure or route setup is necessary Protocol Timing Figure 2.2 shows GeoMAC s timing diagram for the same example 1. When nodes1 3 receive the packet, they start their geobackoff timers. On expiration of node 3 s timer the node forwards the DATA frame. On receipt of the first bit of the DATA frame, the co-operating forwarders 1 and 2 suspend their back-off timers for the transmission duration and an additional VACK- TIMEOUT. If no VACK is received after the VACK-TIMEOUT, the forwarders resume their backoff timers (a variation where forwarders restart timers is also possible). Now node 4, which has successfully overheard the transmission from node 3, transmits the message that is acknowledged by a VACK from the destination Geobackoff The geobackoff must efficiently map geographic distance to backoff intervals, which minimize the chance for collisions without imposing unnecessary delays. Assume that the minimum time-granularity that can be supported at the Physical layer is the slot timet s. Further, letd n m be the distance of a cooperative forwarder node n from the destination. The node n then sets its backoff timer to dn δ t s, which is rounded to the next integral multiple of t s, where δ is the expected minimum spatial separation between any two forwarders given the current vehicle density (e.g., for a very congested single lane road a δ of 5 m may be reasonable). δ could be estimated based on overhearing periodic beacon transmissions 2. 1 A more complete discussion of issues involved and probable solutions is in Section We ignore the difference in propagation delay to different forwarders as for typical PHY implementations, the slot time t s is much greater than the propagation delay even at the transmission powers considered in vehicular networks.

32 Protocol Implementation GeoMAC is implemented as a Click [22] router element, which can be used in the ns2 [23] network simulator through the nsclick [24] framework. 3. For ease of prototyping, GeoMAC is based on parts of the ns MAC implementation all packets are transmitted using MAC broadcast (hence MAC retries are disabled). To be able to suspend backoff while other transmissions are underway, the implementation monitors the MAC state. Since the GeoMAC is implemented in the click framework, while packet transmissions are simulated through ns2, the implementation needs to account for additional processing times used for communicating state between click and ns2. In particular if the MAC is in a receiving state, GeoMAC must defer any current transmissions by this PROCESSING TIME. We empirically determined this time to transfer a message received in ns2 to GeoMAC to be330 us. The timeslot is set to t s = DIFS + PROCESSING TIME 4. VACK TIMEOUT includes the processing time needed at the destination to start sending a VACK and an additional amount to account for the MAC DIFS, yielding DIFS + PROCESSING TIME. Assuming negligible propagation time, the first bit of a VACK must reach the waiting forwarders within a VACK TIMEOUT. DIFS is set to40 us. Re-transmission of a packet by a forwarding node is supported, in case spatial diversity fails to forward a packet 5. A forwarder sets its re-transmission timer if no VACK is received from DST after itself and other forwarders closer to DST have forwarded the packet at least once. The re-transmission timer is currently set to VACK TIMEOUT, a forwarder waits for one more forwarder to forward a message before resorting to re-transmission. Re-transmissions are currently not implemented at SRC. 3 We chose a click implementation because it will later allow us to run it in an actual Linux system, say emulated over implementation 4 The large timeslot value is because GeoMAC currently interfaces with PHY via We use only two forwarders for GeoMAC evaluation and so allow for re-transmission. Its requirement in vehicular networks, where we typically will have more than just two forwarders, needs evaluation

33 Evaluation Framework To study feasibility of the GeoMAC scheme, the evaluation compares GeoMAC s performance with the AODV and GPSR routing protocols on the IEEE MAC in terms of delay, jitter, and packet delivery rate using trace-driven ns2 simulations. We also first evaluate achievable spatial diversity gains in our simulations scenario by comparing three basic forwarding schemes without routing overhead. In scheme fixed-forwarder-retransmit (FixFWReTX), a packet is retransmitted by SRC until successfully received by a constant pre-selected forwarder, emulating the standard MAC. In scheme blind-forwarder-selection-retransmit (BlindReTX), the destination is switched between the two forwarders before each retransmission of a packet. Switches occur blindly without any knowledge of channel state. Finally, the Spatial Diversity scheme broadcasts each (re-)transmission to both forwarders. AODV is an on-demand routing protocol that looks for a route, when one to a packet destination is unknown. Routes over which no data is transmitted over a period of time are expired. It maintains only a single route to a destination. GPSR uses the position of nodes to make forwarding decisions. It uses greedy forwarding (maximize spatial progress) and perimeter mode when there are no nodes, closer to destination, in range MAC level retry failures and neighbor expiry timers are used to remove nodes from neighbor lists. It may maintain more than one route to a destination Simulation Setup The simulations consider a four node linear topology, in a 400 ms snapshot scenario where significant changes in channel state occur but geographic movement of the nodes is small (< 15 m) compared to the node density. We therefore keep the node positions that GeoMAC observes stationary, at relative positions (0,0) for the source (SRC), (0,100) for forwarder 1 (FW1), (0,200) for forwarder 2 (FW2), and (0,300) for the destination (DST). We configure the GeoMAC parameter δ to 100 m, the optimal value for this configuration. Further, the simulations use a 1 Mbps PHY rate 6, MAC with default parameters (CWMIN=31, CWMAX=1024) and without RTS/CTS. The data traffic is CBR at 10 packets/sec. A total of 6 affects only the packet transmission time as the channel is emulated by traces as explained later

34 ,512 byte, packets are sent during a simulation run( 1200 repetitions of the snapshot). Channels are emulated by replaying traces from an automotive experiment that measured packet reception rates on a freeway-like segment of U.S. Route 1. Each vehicle carried a roof-mounted, 7 dbi dipole, antenna connected to Atheros 5212, a radios. A moving vehicle (TX-Car), traversing a path, shown by a yellow line in Fig 2.1b, of the US-1 freeway, passed two stationary vehicles (Car1 and Car2 in figure) parked in lots adjacent to the road on opposite sides while broadcasting 500 packets per second. The stationary vehicles record traces of packet reception. To evaluate spatial diversity gains possible under favorable conditions, we selected a 400 ms snapshot, representative of regions in the trace where both vehicles receive packets, but channel to neither is very reliable (for the snapshot the packet error rates are 58.71% and 45.77%). Figure 2.3 shows the selected snapshot. Each dot in the time-series corresponds to a received packet. As the table indicates, out of the total 201 transmitted, 53 packets were not received by both vehicles. 168 packets ( 76% of total transmission) were received by at least one vehicle. We modified ns2 to interpret these packet traces instead of using one of the default propagation models. The trace is played at the rate of reading a new packet, i.e., a new channel condition, every 2 msec. If the packet in the trace was received the channel indicator is set to receive, otherwise to drop. Whenever a packet is transmitted in the simulation scenario, it will check the current channel indicator for the channel between source of the packet and each possible receiver to determine which nodes should receive the packet. The trace is repeated as many times as required over a simulation time. The four node topology is subjected to two different sets of channel assumptions, one where the lossy channels lie between the forwarders and the destination and one where the lossy channels lie between the source and the forwarders. The forwarders always have perfect channels between each other and SRC and DST are outside each other s communication range. TXDiv: The channel between FW1 and DST is emulated by the trace Car1 in Figure 2.3. Car2 emulates the channel between the FW2 and DST. Channels between the SRC and the forwarders are assumed perfect. A packet always arrives at both forwarders but may not be received at the destination after forwarding, allowing evaluation of transmit diversity (TXDiv) to the DST.

35 18 RXDiv: The channels between the SRC and forwarders are emulated by the traces Car1 and Car2 while the channels between the forwarders and the DST are assumed perfect. The scheme allows evaluation of receiver diversity (RXDiv) for transmissions from the SRC. 2.5 Results Spatial vs Temporal diversity We first demonstrate the gains that can be obtained by exploiting spatial diversity over two other prototype schemes in the RXDiv case 7. Using the described simulation setup, we measure the number of transmissions (i.e., first transmission of a packet plus all retransmissions from same or other nodes) necessary to successfully deliver the packet to one of the forwarders. Figure 2.4 shows the cumulative distribution function of the number of transmissions necessary for successful delivery of each packet under three basic forwarding schemes. Note that for scheme FixFWReTX we include a curve for each forwarder, because the scheme does not automatically use both, and performance is very dependent on the chosen forwarder. When the pre-selected forwarder is FW1, less than 40% of packets are received successfully on first attempt. For FW2, around 55% of packets are delivered by a single transmission. More than 20% and8% of the packets need more than4transmissions and the maximum number of transmissions is > 16 (simulations were limited to max 15 re-transmissions) and 10 for FW1 and FW2, respectively. Scheme BlindReTX closely tracks the performance of the better forwarder under scheme FixFWReTX, its switching strategy automatically settles on the better forwarder to use without the need for it to be pre-configured. The spatial diversity scheme, however, improves packet reception rate further, to 75% and 90% with just one and two transmissions, respectively. This represents a gain of two retransmissions over scheme FixFWReTX using the better FW2 and a gain of 6 transmissions over scheme FixFWReTX using FW1. The maximum transmissions that any packet requires is6compared to10 or > 16 for scheme FixFWReTX. This result indicates that potential exists in vehicular communications for exploiting spatial reuse, especially with receive diversity. It can significantly improve delay for a given reliability 7 The gains for TXDiv are similar and are omitted for brevity

36 19 and vice-versa, in certain vehicular communication situations GeoMAC vs AODV and GPSR The evaluation presented above, ignores the requirement of a protocol to gather information about available forwarders, forwarder selection and last but not the least, co-ordination between the forwarders(to avoid collisions and multiple forwardings of a packet). We next compare the ns-2 implementations of our proposed protocol GeoMAC, AODV and GPSR, that account for this protocol overhead for TXDiv and RXDiv. Packet Delivery Rate Routing overhead is very sensitive to the maximum number of retransmissions configured in the MAC, since fewer frame retransmissions lead to more route change overhead due to more packet errors reaching the routing layer. We therefore compare results dependent on the total number of transmissions permitted, which for AODV and GPSR corresponds to the number of MAC transmissions of a packet by a forwarder. However, it puts no limit on the number of times a packet is re-routed by SRC (for example GPSR may try to re-route a packet via another neighbor which amounts to multiple transmissions of a packet by SRC). Since GeoMAC also includes cooperative ARQ, we define the number of transmissions as the maximum cumulative number of transmissions over all forwarders. Since the topology contains two forwarders, 2 is the minimum transmission limit for GeoMAC. As another example, a value of 4 corresponds to the default 2 possible forwardings and one more forwarding by each of the forwarders. Figure 2.5 shows packet reception rate (out of 4990 transmitted) for different maximum number of transmissions settings (NumTrans) in the TXDiv case. It shows sizeable gains from exploiting only spatial diversity in GeoMAC, (N umt rans = 2). GeoMAC delivers 71% of the packets as against 10% by AODV and GPSR for NumTrans = 1 and 45% by AODV and 20% by GPSR for NumTrans = 2. AODV does much better than GPSR, especially for a smaller NumTrans, because it adjusts to route breaks, due to a bad channel to a currently

37 20 selected forwarder, more dynamically than GPSR 8. As expected packet delivery rate increases with higher NumTrans, which reduces route changes and puts the onus of packet delivery on the MAC which allows exploitation of temporal diversity in the channel. GeoMAC achieves 100% packet delivery atnumtrans = 8. AODV comes close to100% atnumtrans = 12. GPSR performs slightly worse than AODV. Note that the routing protocols with NumTrans limited to 1 fall significantly short compared to the packet delivery rate the basic scheme FixFWReTX achieved without any retransmissions. We attribute this to routing overhead. Receiver Diversity For RXDiv, the lack of a re-transmission mechanism at SRC in the current implementation of GeoMAC, restricts its NumTrans to a value of 2. 9 The efficacy of using spatial diversity is further brought out by packet reception gains of 40% at NumTrans = 2 for GeoMAC (not shown), over AODV and GPSR. Delay Performance Figure 2.6 plots the average delays for packets successfully received by DST, for TXDiv. Figure 2.7 plots the corresponding jitter, which is measured as the standard deviation of the delay. The delay for AODV and GPSR is split into routing-related (Rt) and non-routing related (Non-Rt) ( MAC back-off, retry and packet transmission and propagation). GeoMAC has no routing overheads and the delays incurred are due to the Geo-based back-off, VACK TIMEOUT, retransmission timers and transmission and propagation. Figures 2.6 and 2.7 contain a red line which marks the mean delay and jitter assuming an ideal forwarding MAC. This ideal mechanism exploits all available good channel opportunities via either FW1 or FW2. In case of TXDiv, it knows channels between forwarders and the DST in advance and can schedule a transmission via a forwarder to ensure that the DST receives the 8 For the selected GPSR beacon rate of once per second 9 Under RXDiv, GeoMAC will be able to deliver a packet as long as at least one FWD has a good channel to the SRC, else the packet will be dropped. The retransmission mechanism at the forwarders won t be used as the channels from them to the DST are perfect.

38 21 packet at the earliest possible good channel opportunity. The only delays suffered, other than waiting for a good channel opportunity, are transmission and propagation delays. For TXDiv, the mean delay and jitter for the ideal MAC are msec and msec, respectively. AODV leads to a maximum delay of msec for NumTrans = 1 and a minimum delay of 17.1 msec for NumTrans = 18. For smaller NumTrans, the large delays are routing related, 96.5% for NumTrans = 1 and 42% for NumTrans = 6. The jitter values, Figure 2.7, are considerably higher fornumtrans <= 10. Increased NumTrans leads to less routing delay and jitter, as channel conditions that would have lead to breaks in routes (and hence additional routing requests) are now alleviated by MAC retries. The re-routing overheads, seen for small NumTrans, also correspond to low packet delivery rates (Figure 2.5). Dynamic routing by AODV seems incapable of adjusting routes fast enough to keep track of changing channel conditions. GPSR, unlike AODV, doesn t look for routes dynamically. It routes via neighboring nodes, whose information it has via beacon packets that are exchanged periodically. Lack of dynamic routing leads to less packets delivered for the selected beacon rate as seen earlier. However, it also leads to less routing, small delay and jitter on the delivered packets. GeoMAC precludes the need for dynamic routing by exploiting spatial diversity. It keeps delay and jitter small by incorporating forwarder selection at the MAC layer. Figure 2.8 compares the jitter performance of AODV for minimum mean delay and Geo- MAC for TXDiv for NumTrans = 2,6,8. AODV, even at 18 NumTrans for which AODV s mean delay is the smallest, has a much larger spread in delay than GeoMAC. ForNumTrans = 8 (where all packets are successfully delivered) the maximum delays are 44.2 msec, while with AODV (at18 NumTrans)144 packets ( 3% of received) are received with delays greater than 50 msecs and the maximum observed delay is 300 msec 10. For smaller NumTrans of 2,4, or 6 AODV requires more than50 ms for24.48%,11.69% and 6.21% of packets, respectively. The delay and jitter performance for RXDiv are similar to TXDiv for AODV and GeoMAC. GPSR, however, shows increase in jitter with increasing NumTrans, which is because in RXDiv the channels between SRC and the forwarders, unlike in TXDiv, are lossy. 10 Figure 2.8 plots the AODV CDF for values up to 160 msec only

39 22 Overall, GeoMAC achieves high packet delivery rates with the lowest delay. In particular, its delay shows significantly fewer outliers than by adding spatial diversity at the routing layer. 2.6 Related Work The use of geographic position for routing was first suggested in the 1980s [25] for stationary packet radio networks. Imielinski and colleagues pioneered location as an addressing mechanism for the mobile Internet [26]. Research has progressed towards using geographic information in routing for wireless ad hoc and sensor networks [27 32]. Similarly multicast protocols that serve all nodes in a geographic region [33,34] have been developed. These protocols focus more on sparse scenarios with routing around voids in the communication network as a main challenge. In [35] the authors propose the ExOR protocol which uses opportunistic routing under which paths are chosen dynamically on a per path basis. In [36] a contention based forwarding scheme is proposed. It selects the next hop through a distributed contention process based on the actual geographic position of each node. The mechanism bears similarities to the geobackoff part of our protocol but is implemented above the MAC layer and the schemes differ in their goal. Whereas contention-based forwarding seeks to reduce or eliminate location beacon messages, GeoMAC aims at exploiting spatial diversity for increased reliability. In [37] the authors propose position and map based forwarding and geocasting for vehicular networks. Gains are obtained in the highly mobile vehicular scenarios as no route creation is required. In our work we use location to carry out position based forwarding and also to exploit spatial diversity, enabling packet forwarding with minimum delays and high delivery probability. 2.7 Conclusions We presented GeoMAC, a MAC-based protocol that exploits spatial diversity, inherent in a vehicular channel. Forwarder selection for transmission over the next hop is enabled in a distributed manner via geobackoff, which selects forwarders in decreasing order of spatial progress. It also uses a cooperative ARQ mechanism. We conclude that Spatial diversity with just two forwarders (NumTrans=2 for GeoMAC) can provide packet delivery of 20% on first transmission and of 25 50% when considering full AODV and

40 23 GPSR routing overheads ( with two MAC retries). GeoMAC lead to minimal mean delays and very low jitter in comparison to AODV. Mean AODV delays for 1 NumTrans 8 range from msec as against a mean of msec for GeoMAC (all NumTrans values). Further, AODV shows jitter values of msec as against a jitter of msec for GeoMAC. The high jitter and delay values are due to routing overheads under fast changing channel conditions. In general, both AODV and GPSR show better packet delivery, delay and jitter performance as number of MAC retries increases, putting the onus of packet delivery on the MAC layer. We show that a MAC exploiting spatial diversity performs better than a retry-based MAC, which transmits over the best available channel. The GeoMAC spatial diversity gains are likely to improve further, if more than two forwarders are available, which is likely in many vehicular network scenarios Limitations and Observations This preliminary protocol design raises several questions. First, the protocol must adapt the value of the δ parameter to vehicle density. The optimal value could be derived from neighbor information collected via periodic beacons or from overheard data packets. Second, it must handle concurrent transmission between multiple source-destination pairs. The current design may lead to too many collisions. This could be achieved by incorporating a random component into backoff choices. A single forwarder may also have to keep track of multiple geobackoff timers. Finally, the protocol should suppress unnecessary transmissions if multiple forwarders are not within range of each other. The current protocol may lead to redundant or colliding transmissions. One approach may be specifying a forwarding region, to exclude extraneous nodes outside this region from the forwarding process. It could also restrict the number of co-operative transmissions of a DATA packet.

41 RSSI Time (sec) (a) Sample SNR fluctuations on vehicle-to-vehicle communication link in freeway environment (b) US-I, two receivers and a transmitter, RSSI and PER measurement setup (c) Source (S) sends message for destination (D). Radios 1, 2 and 3 are prospective forwarders. Figure 2.1: Vehicular Channel Measurements and Setup

42 25 Figure 2.2: Protocol Timing assuming back-off is resumed after VACK-TIMEOUT Packet based Channel Trace Packet Reception Indicator Car1/Car2 Dropped Received Dropped Received car1 car Time (msec) Figure 2.3: PER Trace used for simulation.

43 26 1 Empirical CDF 0.8 CDF Spatial Diversity FixFWReTX (FW1) FixFWReTX (FW2) BlindReTX Dropped No. of Transmissions before successful reception, unless dropped Figure 2.4: Spatial vs. Temporal Diversity gains. 100 Percentage Packets Rcvd AODV GPSR GeoMAC No. Of Transmissions Figure 2.5: Number of Packets Received (TXDiv)

44 27 Mean Delay (msec) AODV Non Rt AODV Rt GPSR Non Rt GPSR Rt GeoMAC Ideal No. Of Transmissions Figure 2.6: Packet Transmission Delay (TXDiv). Note that the y-axis is omitted from for plot clarity Jitter (msec) Log Scale AODV GPSR GeoMAC Ideal No. Of Transmissions Figure 2.7: Packet Transmission Jitter (TXDiv)

45 28 1 AODV vs GeoMAC Delay Distribution Comparison 0.8 CDF AODV Total No. Of Transmissions = GeoMAC Total No. Of Transmissions = 8 GeoMAC Total No. Of Transmissions = 6 GeoMAC Total No. Of Transmissions = Delay (msec) Figure 2.8: AODV delay CDF vs. GeoMAC (TXDiv)

46 29 Chapter 3 Minimizing Age of Information in Vehicular Networks 3.1 Introduction There is a new class of emerging applications that require nodes to periodically share their time critical status information with nearby nodes. Perhaps the most prominent examples are found in vehicular networks, where each vehicle shares its position and other vehicle dynamics with nearby vehicles to improve on-road safety. Though these applications use broadcast as their dissemination mechanism, their QoS requirements are far more stringent [10] than the typical use case for broadcast, traditionally, beaconing for announcing presence or non-critical information. For many new applications broadcasting is the dominant form of messaging. In vehicular networks, an entire band of 10 MHz is reserved solely for safety applications that broadcast their messages [9]. Likely high node densities make it important to have broadcast congestion control mechanisms [38] so that the applications can achieve desirable performance. Vehicular network clusters may be spread over hundreds of meters and have hundreds of participating vehicles. A vehicle s state must be received by other vehicles at a sufficiently high rate so that, at any given time, it is recent enough for use by their on-board safety applications. The large numbers of vehicles possible in vehicular network clusters create the potential for congestion, even when only periodic status messages are sent. Most earlier work has looked at metrics that capture only selected aspects of the problem, like packet error rate and clear channel assessment (e.g., [12, 13, 15]). There is earlier work [39 41] that uses explicit feedback messages like the RTS/CTS exchange to detect congestion, and carry out PHY or source rate adaptation or TCP congestion control in wireless networks. In [42], a satellite broadcasts to terminals to reduce rate on detection of congestion. More recent work [43], perhaps the most directly related, provides control strategies in vehicular networks to maximize the average broadcast rate at which packets are received by a vehicle from its neighbors. The analysis

47 30 assumes a saturated load (MAC always has a packet to transmit) and does not consider queuing delays. We are not aware of any work, however, that addresses the vehicular broadcast problem from a more comprehensive perspective, including queuing delays, delays from packet losses, and delays inherent in the selected application messaging rate. In this work, we use a system age metric to capture these issues. System information age is the average end-to-end (application-to-application) delay observed in any vehicle s state within a certain cluster of nodes. We first show that to minimize information age the source rate of status messages needs to be adapted to an optimal operating point, which changes with node density. We then show through simulations that this operating point cannot be achieved through MAC layer contention window adaptation in an MAC. This motivates a broadcast source rate adaptation algorithm that operates above the MAC layer. Given the broadcast nature of the messaging, senders do not immediately receive feedback on sent messages. Instead they infer feedback from the status messages received from other nodes. Our proposed algorithm relies entirely on local calculation of the system age metric and node broadcast periods, based on these received packets. In summary, our specific contributions include: Quantitatively showing that minimizing the system age cannot be achieved by maximizing throughput in a practical system and that the minimum age at any given contention window (CW) size is achieved at an application messaging rate such that the offered load is much smaller than when saturated. Arguing that in systems with tail-drop FIFO queues rate control for broadcasts needs to be provided above the MAC layer. Via simulation we confirm the presence of a unique common period at which system age is minimized and propose a distributed algorithm that relies on local information alone to achieve the minimum. Simulations and also experiments with 300 ORBIT testbed nodes show the efficacy of the algorithm. The chapter is organized as follows. In Sections and 3.3 we show how the system age may be minimized and motivate rate control. The rate control algorithm is described and

48 31 Figure 3.1: Vehicle u generates its state at instants shown by arrows with triangular heads. Vehicle v receives a generated state packet at the next instant marked by diamond shaped heads. An erroneous reception is marked by a cross. The age of u s information accumulates with time until it is reset to the time elapsed between state generation and reception (t 1 andt 2 in figure). The average age uv is given by the area under the curve normalized by the interval of observation. evaluated in Section 3.4. In Section 3.5 we discuss current limitations and how the proposed technique can complement others. In Section 3.6 we describe the related works and conclude in Section 3.7. Next we define our system model. 3.2 System Model and Objective We consider a network of vehicles that communicate with each other using an based CSMA mechanism for channel access. Also, we assume that the clocks of all vehicles in the network are synchronized using, for example, GPS devices. Every vehicle executes an application that generates packets at a periodicity of T sec for broadcast. The packet contains the vehicle s state information, for example, location and velocity, and the time it was generated and also the period T (used by rate control). Let t uv be the age of the state information of vehicleuat vehiclev at timet. A vehicle always has its current information. Thus, t uu = 0. At vehicles{v u}, the state information ofuages during the time between any two successfully received broadcasts from u. Also, the age of any received information is the time that elapses between its generation and successful reception (see Figure 3.1). Over the time interval of interest T, let uv be the average age of u s information at v. Thus uv = (1/ T ) T t uvdt.

49 32 Figure 3.2: Application at a node generates packets that are queued into a queue of sizem. The packet at the head of the queue, numbered 1, awaits 0 or more backoff slots before its transmission starts. Let V denote the network of vehicles and let N = V. We define system age as = 1 N uv (3.1) u V v u wheren = N(N 1). The system objective is to minimize the system age Delays in an MAC system Here we summarize an system and the delays experienced by packets in it. A more thorough summary can be found in [44]. Packets generated by the state broadcast application at a node arrive at its link layer, where they are queued for transmission if the queue is not full, else they are dropped. Figure 3.2 shows the link layer consisting of a FIFO queue of lengthm. Packets are transmitted over the wireless medium using the CSMA backoff mechanism, where in on receipt of a packet, if the channel is busy, the CSMA MAC at the node selects the number of slots to backoff (backoff counter) from a discrete uniform distribution over the interval [0, W0 1], where W0 is the contention window (CW) size. The broadcast nature of the packets implies that the receivers do not explicitly acknowledge having received a packet transmission. This precludes the use of an exponential backoff mechanism and the contention window size stays fixed at the chosen W0 for broadcast applications. Let the length of an idle slot be σ s (equal to a PHY layer slot, 13 µs in the p standard). Since counter decrements take place only during idle slots, the average time a packet spends waiting is a function of the average slot lengtht, that is the average time that the MAC stays in a given state, described by the backoff stage and the value of the counter. Let a packet

50 33 transmission/collision occupy an average of L slots (includes data payload, header and other delays like that of DIFS, SIFS and ACK (on unicast)). ThusT = p I σ+(1 p I )Lσ, wherep I is the probability that the medium is idle (no transmissions). Let the CSMA MAC have a packet ready for transmission (head of queue) with probability q. A larger q implies a higher message rate, smaller broadcast period T. When q = 1, we say that the MAC is in saturation, that is it always has a packet to transmit. A broadcast packet at the head of the queue will wait an average of(w0 1)/2 slots before being transmitted, if the channel is busy, else it will begin transmission (we included DIFS in the average transmission time). Let T s be the average service time for a packet generated by the application, that is the average time elapsed between a packet arrival into the queue and the end of its transmission. We have,t s = T w +T b +T x, wheret w is the average time a packet spends in the queue before arriving at the head, T b is the average time spent by the packet at the head waiting for backoff to end, andt x is the sum of the propagation delay (negligible) and the transmission delay (size of the packet divided by the PHY layer rate (bps)). Further,T b = (1 p I )T(W0 1)/2, where we assumed that the counter is selected independently of the slot size Information Age and Throughput To put the concept of information age into perspective, let us consider how it relates to throughput and queuing delay for a simplified network containing a queue into which the application sends packets. The service time of a packet is T s, after which it is received. In our network, throughput can be increased by reducing the broadcast period T. Does increasing throughput minimize information age? Consider first a lightly loaded network, where the service time is well below the broadcast period, i.e., T s << T, and thus the queue is always empty when a new packet is generated (the waiting time T w = 0). In this case the average information age is = T s +T/2, wheret s is negligible. Thus, it is clear that reducingt will lead to a lower information age. The service time in general, however, is also dependent on T, since the network load affects queuing delays. This will become particularly noticeable when the network becomes more heavily loaded (smaller T ). In fact, classic networking theory based on M/M/1 models

51 34 with infinite queues tells us that queuing delays rise sharply as throughput approaches its maximum [45]. Beyond a certain optimal operating point, these delays will substantially increase the service time T s and thereby increase the information age. Conversely, delay is minimized as the throughput approaches zero. However, this would make T, and hence the system age, very large. Thus, information age is minimized neither by solely maximizing throughput nor by solely minimizing packet delay. Instead information age reaches its minimum at an optimal operating point between these two extremes, akin to how the power of the network can be maximized in classic network theory. Our system differs in a number of subtleties from this classic model. The interaction of MAC contention and queuing policies with finite queues with information age is more intricate. We will study this next through simulations. 3.3 Minimizing Information Age in a CSMA System Is there an effective MAC layer solution for minimizing information age in a CSMA system? Given our insight that information age is minimized at an optimal operating point where throughput is high and queuing delays are low, we now consider several MAC layer strategies in a CSMA system for reaching this operating point. In particular, we will investigate (i) whether the contention mechanisms could provide congestion control necessary for minimizing information age and (ii) whether minimizing the queue size can effectively avoid the queuing delays, so that the problem of minimizing information age is reduced to maximizing throughput. We investigate contention mechanisms because in a CSMA multiuser access system, the information age problem is further complicated by the effect of load on packet loss rates. Higher load also results in increased collisions during transmissions, which would lead to a higher information age. In fact, even throughput cannot be maximized by merely increasing source rate. Instead CSMA uses a contention window mechanism that seeks to achieve the optimal operating point. We will investigate whether similar mechanisms also minimize information age. With respect to queuing, it is clear that smaller transmission queue sizes reduce queuing

52 35 Figure 3.3: A four lane road network with cars placed very close to each other to simulate a high density environment. delay and therefore improve information age at higher load. In the class of status information sharing applications that this paper considers, there is actually little value in buffering outdated information for transmission. Can the queuing delays be avoided simply by configuring the MAC with small buffer/queue sizes? Or, would it be worth redesigning the hardware to eliminate queues for such status messages altogether. Since the affect of these issues on information age is quite intricate, we resort to simulations to shed light on these questions Simulation Setup We use the Network Simulator (version 2.33) 1, with PHY layer extensions by Chen et al. [46]. The extensions provide an implementation of the a/p physical layer and handle capture and packet decoding criteria as in the standards. For our simulations we use the p standard, which has been proposed to support messaging between vehicles [9]. All simulations use a four lane network illustrated in Figure 3.3. The placement of vehicles is chosen to simulate as high as possible wireless medium congestion levels for the two dimensional road network. The physical grid shape ensures that effects like capture seen in simulations are similar to those expected in real road networks. Mobility is not considered and we assume that over the few seconds that the rate control takes to converge (see Section 3.4.1) the wireless connectivity of the vehicles under consideration is more or less the same. The MAC in the simulator does not 1

53 36 Pathloss Exponent 2.0 Frame capture thresholds Transmit Power PHY Rate 10 db 1 W 6 Mbps Number of cars 400 Receive Sensitivity Application Payload Size 99 dbm 300 bytes Table 3.1: Simulation Parameters transmit any periodic management messages. Table 3.1 lists default values for various parameters used. The application generates broadcast packets/messages at the configured periodicity plus a small random offset to ensure that packet generation at the different nodes is not synchronized. The packet is sent to the link layer of the ns-2 simulation stack. The minimum queue size supported is 1 packet. The queue will hold at least one packet when another one is awaiting completion of backoff and transmission (Packet 1 in Figure 3.2). In general, a queue size of k in ns-2 corresponds tom = k+1 in Figure 3.2. All cars/nodes/vehicles are in communication range of each other. When calculating the system delay in the simulations we average over discrete time instants. We calculate uv = 1/n n i=1 (t i T u (t i )), where T u (t i ) is at time t i, the time at which the state information of u last received by v was generated. The difference t i T u (t i ) is the instantaneous age of u s information at v at t i. The number of time samples n is chosen large enough to sample age at a large enough rate. The system age is then obtained as in Equation (3.1). To address the contention mechanism question, we consider different contention window sizes in our simulation. We know from Bianchi [44] that the system throughput of a saturated based network can be maximized when the contention window size W0 is set to its optimal value W, which depends on the number of nodes in the network. We will therefore conduct simulations with standard contention window sizes and with W for our network.

54 37 At a PHY rate of 6 Mbps, an application payload size of 300 bytes and overheads like packet headers and DIFS = 2 σ + SIFS, where σ is the PHY layer slot length [47], we get W = 3772 slots for N = 400 nodes. 2 Such an inordinately large contention window setting is not possible in current implementations. We consider it here to understand whether it would be worth enabling in future implementations. To address the queuing question, we will introduce a hypothetical system, which we will call the Latest state Out (LO) system, that eliminates queuing delays. Whenever a packet transmission opportunity arises, it fills the packet with the latest available state information. In other words, the age of information in the packet, if received successfully, is equal to its transmission time T x. We compare this system with standard FIFO tail-drop queuing system as used in implementation we are aware of. We refer to this system in short as FIFO. Here, the state information in a packet is not updated after it is generated by the application and queued. We will investigate, however, whether the affect of queuing delays on system age can be virtually eliminated by using small queues Results Strategies that can minimize system age for Latest Out and FIFO systems: Figure 3.4 shows system age as a function of the broadcast period T in a network of 400 cars. It compares a Latest Out (LO) system with a FIFO system for queue sizes of m = 2 and m = 4 and contention window sizes of 15, 500 and the Bianchi s throughput-optimal contention window size of Note that system age in a LO system does not depend on the queue size as in it the state is updated at the last moment. The results shows that the Latest Out system generally tends to achieve lower system age than the FIFO system, but a FIFO system with minimal queue size and well-chosen broadcast period can achieve a similarly low system age. Also, in the Latest Out system, using the optimal contention window size of3772 and small broadcasting periods leads to system age that is very close to the minimum achieved ( 0.15 s) by any of the plotted configurations. This means that setting the contention window to its 2 For a single stage back-off system that the backoff application uses, the optimal value CW size under saturated load conditions is W = N 2T c/σ [44], wheren is the number of nodes in the network,t c is the average packet collision time and σ is the PHY layer slot length, which is 13 µs for p.

55 38 (sec) LO, CW 15 LO, CW 500 LO, CW 3772 FIFO m=2, CW 15 FIFO m=2, CW 500 FIFO m=2, CW 3772 FIFO m=4, CW Broadcast Period (sec) Figure 3.4: System age as a function of broadcast periodicity for LO (dashed lines) and FIFO (solid lines) assuming a queue size of m = 2. Selected W0 = 15, 500, W = For W0 = 3772 we also show age for m = 4. The circles markers show different cases for CW 15, the squares CW 500 and the diamonds show CW throughput-optimal value and saturating the MAC is a strategy to minimize system age when using Latest Out. The above is clearly not true for a FIFO system, however. For large CW sizes of 500 and 3772, and small periods, a significantly greater system age is observed even for the smallest size FIFO, that ism = 2. Also, as expected system age increases with queue size. Increasing the queue size by 2 to m = 4 increased the age for saturated loads by about twice. Saturating the load under Latest Out, and setting the CW size to optimal, is equivalent to delivering the latest state information as fast as possible. For Latest Out, unlike FIFO, maximizing the throughput is equivalent to minimizing the system age. Alternatively, the minimum system age may also be achieved at smaller CW sizes and large values of the period T. This holds true for both Latest Out and FIFO with queue size m = 2 systems and is seen in Figure 3.4 for CW sizes of 15 and 500 that achieve the minimum age at a period of 0.25 s, for Latest Out and FIFO. Unlike the former strategy, this one requires adapting the period to minimize the system age. Latest Out will require hardware changes to current implementations. The hardware

56 39 (sec) CW 15 CW 50 CW 100 CW 500 CW Broadcast Period (sec) Figure 3.5: Variation of with period for different CW sizes. will need the ability to fill a packet with fresh state just before transmission. Also, support for the optimal contention window size for varied sized networks adds further complexity. This motivates designing a rate control mechanism, which, when using FIFO, can find the period that minimizes system age. For rest of the paper we assume a FIFO queue of size m = 2 and look at how the achieved system age can be minimized. A contention window adaption based strategy for reducing age is unsuitable: The typical use case for an system has been unicast applications, where a given packet generated by an application needs to be delivered. In dense networks, where there are a large number of users contending for the channel to transmit their packet, packet delivery rates can be improved by increasing the CW size, as it reduces the probability of collisions. In our application a given packet is not so important, because holding it for too long will only make it stale. Figure 3.5 shows why a strategy that changes the CW size in response to a congested channel is unsuitable to make smaller. At small periods T, increasing CW size from 15 to 500 or 15 to 50 reduces the age. However, increasing it from 50 to 100 makes it worse. CW sizes of 500 and 50 alleviate the collision probability significantly, such that they do better than 15 at the small T, but for their larger queuing delays. On the other hand CW size of 100 does not reduce the collisions enough and adds to the queuing delays seen at CW size 50. Finally,

57 40 (sec) Contention Window Size is Cars 100 Cars 200 Cars 400 Cars Broadcast Period (sec) Figure 3.6: Variation of for different sized car networks. The minimum system ages are 0.02, 0.05, 0.1 and 0.15 seconds for 50, 100, 200 and 400 node networks, achieved at T of 0.03, 0.05, 0.1 and 0.25 seconds respectively. contrary to behavior at small T, at large T, larger CW sizes can make delay worse because of larger queue wait times. Note that the minimum age achievable at CW size of 3772 is 0.22 s instead of the0.15 s for smaller CW sizes, where the minimums are att far from saturation, at T = 0.3 s and T = 0.25 s respectively. Age of information seen by all nodes is close to the optimal (fairness): In Figure 3.5, for CW size of15 and3772, for eacht we plot a bar the end points of which denote the minimum and the maximum uv (age of u s information at v) calculated over all nodes in the network. As T reduces, the length of the bar increases significantly for CW size 15. This is a result of physical layer capture, which allows larger rates of packet delivery between close by nodes than those that are farther apart. For the large CW size of3772, collisions are less probable and the benefits of capture are very limited. However, the unfairness is negligible even for the small CW size at and around the period at which the system delay is minimized (0.25 s for size 15 and0.3 s for size3772). The observation holds true for similar sized networks and implies that when operating at the period corresponding to the minimum age, links between all node pairs u andv can achieve an age close to minimum system age. In what follows, all our evaluation will be for a CW size of 15, which is proposed for use in the p MAC and is the default for broadcast applications in WiFi standards like

58 41 Algorithm 1 Update Broadcast Period at Nodev. Require: T v (broadcast period at node v), TR (average of periods calculated at node), ˆ v (current estimate of system age at v), ˆ v (past estimate of system age at v), Λ (action), β (factor),δ s (maximum allowed broadcast period spread). Ensure: Updated value of T v, the period at nodev. 1: if T R T v > δ s then 2: T v = T R 3: Λ = INCR{/*Forcing nodes to believe they took the same action. Setting to DECR is fine too.*/} 4: else 5: if ˆ v > 2 T R then 6: Λ = INCR{/*Implicitly assuming congestion*/} 7: else if ˆ v > ˆ v then 8: Λ = Λ c {/*Reverse action. Take complement*/} 9: end if 10: if (Λ == INCR) then 11: T v = βt v. 12: else 13: T v = T v /β. 14: end if 15: end if 16: return T v a/b/g, and a queue size of m = 2. The existence of a unique period that minimizes system age, Latest Out being impractical, and the lack of a simple CW based adaption strategy as shown earlier, motivates application layer rate control: In Figure 3.6 we plot for networks of size 50,100,200,400, CW size of W0 = 15, and m = 2, the system age with the message period T set the same at all nodes. As is seen in the figure and also Figures 3.4 and 3.5 (different queue and CW sizes), is minimized at a period, typically, to the right of where saturation occurs for larger CW sizes, and to the left of periods that leave the wireless medium very lightly loaded. The existence of a minimum motivates designing of a rate control algorithm that can achieve it in a distributed manner. Intuitively, a minimum must exist at a period larger or equal to the one that saturates the load offered to the CSMA MAC. 3.4 Rate Control Algorithm We require an algorithm that runs on a node and continuously adapts its broadcast period

59 42 to minimize the system age of the network. Our proposed algorithm is invoked locally and asynchronously at each node, once every pre-defined interval, and uses the node s local estimate of the system age to either increase or decrease its broadcast period. The chosen action is the same as the one chosen during its last invocation if the current estimate of system age is less than the last one. Conversely, if the system age increases, the action is reversed. We now describe the details of how local estimates are calculated, the implementation and evaluation of the algorithm. Assume that a node v s broadcast contains its state information, the time the information was generated and the broadcast periodt v set at the node s application. Lack of global information: The exact calculation of system age, given in Equation (3.1), requires knowledge of ij for all vehicles pairs in the network. A given vehiclev can, however, only estimate a subset of the terms ij, where j = v, based on the broadcasts it receives from the other vehicles. Let v = (1/(N 1)) i v iv, where N is number of nodes in the network, and let ˆ v be the estimate of v calculated by v at the end of a Measurement Interval (interval for short). Let R be the set of nodes v receives packets from during the measurement interval. The node uses the broadcasts it receives during the interval to calculate ˆ v = (1/ R ) ˆ i R iv, where ˆ iv is the average age of i s information at v calculated over the interval, as described in Section 3.2. All information and estimates calculated are discarded at the end of an interval. Node v also calculates the average T R of the broadcast periods of nodes in R received in the nodes broadcasts. The intervals need not be synchronized across the nodes in the network. We now describe the algorithm s actions. Keeping the spread of broadcast periods chosen at nodes limited: The spread at a node v is given by T R T v. If the spread is greater than δ s, the node s period is set to T R. If the spreads 3 are not limited, the system age is seen in simulations to converge to a value other than its minimum. Note that the existence of a unique minimum system age was assuming a common broadcast period for all nodes in the network. It is not clear that the same will hold true when nodes are allowed to choose from a broad range of periods. Choosing a very small δ s, however, can be detrimental and lead to the algorithm at a node setting its period T v = T R 3 We used aδ s of 1/2( T R) for T R < 0.1 and0.05 for larger T R in experiments and simulations.

60 43 at the end of every interval, halting descent towards the minimum. Increase period blindly, if medium congested: If the algorithm determines that ˆ v > 2 T R, it assumes that the medium is congested 4 and increases the period irrespective of the result of the action taken at the end of the previous interval. The motivation behind the step is that if the age is greater than twice the period then the age must be achievable at a much larger period. Remember that if the medium is not congested, say ift s T (see Section 3.2.2), then the average achievable age is T/2. Approaching the minimum, choosing the descent direction: A node invokes Algorithm 1 at the end of its current interval. Let ˆ v be the estimate of v calculated in the previous interval. The algorithm needs to decide whether the current periodt v must be increased (action Λ = INCR) or decreased (Λ = DECR), given ˆ v, ˆ v and the action it had taken at the end of the previous interval. The choice the algorithm makes over successive intervals must take the system age closer to its minimum value. The algorithm, however, has no knowledge of whether, for the given network, the minimum is approached by increasing or decreasing the current T v. Based on its local information it repeats the action at the end of the previous interval if ˆ v < ˆ v, else it performs the opposite, that is increase the period if it had earlier been decreased and vice-versa. The factor β > 1 by which the period must be increased or decreased is an input parameter and, as we will show later, its selection is a trade-off between speed and accuracy of convergence Algorithm Evaluation We show the effect of the parameters β and length of the interval on the algorithm s performance, followed by an evaluation of the algorithm using a large number of simulations, and experiments on the ORBIT grid. The average system age ˆ = (1/N) N v=1 ˆ v and the average period selected by nodes at the end of an interval T = (1/N) N v=1 T v are calculated offline at the end of every interval for evaluation. Effect ofβ: In Figure 3.7 the length of interval is set to2sand400 nodes start broadcasting with a period of0.03 s (medium is very congested). Forβ = 1.2, the algorithm achieves system 4 Ideally, this should be supported by an indication from another mechanism (e.g., the PHY), so that very large packet error rates are not confused with congestion.

61 44 ˆ (sec) β=1.05 β=1.1 β= Time (sec) T (sec) β=1.05 β=1.1 β= Time(sec) Figure 3.7: Effect of selection of β on rate control. 400 nodes, start period of 0.03 s and length of interval is2s. age ˆ < 0.2 s (top sub-plot) within 20 s. The minimum achievable, see Figure 3.6, is 0.17 s. However, ˆ sees large fluctuations as time progresses. The bottom sub-plot shows T, and is also more jagged as a result of different nodes v selecting more varied periods than when β is smaller. For the setting of β = 1.1, ˆ v crosses 0.2 s at about 40 s and stays smooth and below for most of the 200 s of the simulation. Note that in 40 s, T goes from 0.03 to 0.2, which is an order of magnitude larger. Convergence time for larger start periods, shown later, is much smaller. The value of β = 1.05 takes much longer than 40 s but is not much better than β = 1.1 in following the minimum age. We find that in general β = 1.1 has desirable convergence performance. Effect of length of interval: In Figure 3.8, we look at interval lengths of 2,5,10 seconds for β = 1.2. The 400 nodes start broadcasting with an initial period of 0.01 s. From the plot we see that the initial estimated for an interval length of 2 s, is 0.3 s instead of the 0.5 s obtained for interval lengths of 5 s and 10 s. The difference in averages is because for the smaller interval, a node v does not receive sufficient packets from other nodes to accurately calculate their local estimate ˆ v. In general the interval length may need increasing to obtain accurate estimates in larger networks for a given periodt, or for smallert in a given network. The inaccurate estimates can lead to nodes choosing different Λ v, leading to different selected

62 45 ˆ (sec) 0.5 2s 5s 10s Time (sec) T (sec) 0.2 2s 5s 10s Time (sec) Figure 3.8: Effect of selection of interval on rate control. Start period of0.01 s, 400 nodes, β = 1.2. periods T v and less smooth convergence. Note the jagged nature of the curves corresponding to an interval length of 2 s. A smaller interval will get the network closer to the optimal age faster, however. In the figure, for the interval of 2 s, ˆ first goes below 0.2 s at about 20 s into the experiment. It takes> 100 s for the interval of 10 s. Note that forcing a node v to increase its period (see Algorithm 1) whenever ˆ v > 2 T R (the smooth descent in ˆ for time< 30 s and interval length of2sin plot), makes the algorithm more robust to such averaging related errors and takes the system closer to the minimum age quickly. This is because as long as the nodes satisfy the condition the exact value of ˆ v at v is unimportant. Quality of convergence: We ran the rate control algorithm with start periods selected randomly over the range of (0.03,0.5) seconds for a network of 400 cars. A total of 124 simulations were run, out of which about 100 had a common initial period set at each vehicle, while for the remaining each vehicle randomly and independently selected a start period, at the beginning of simulation, from the interval above. For β = 1.1 and interval of 2 s, the median time it took for ˆ to go below 0.2 s was 4 s, the mean was about 8 s. From that instant to the end of simulation, a total of 200 s long, 95% of the nodes observed 0.16 ˆ v 0.18, which is very close to the minimum achievable (0.17 s) as seen in Figure 3.6. Similar simulations for 200 node networks also saw good convergence.

63 Evaluation on the ORBIT testbed The ORBIT grid [48] is a 400 node, 800 radio grid that hosts Atheros and Intel radios and allows for emulation of real world wireless network experiments. The 400 nodes occupy a 20 m x 20 m area and hence provide an excellent platform for testing network algorithms for high density networks. Experiment setup on ORBIT: We evaluate our algorithm using 298 nodes, all containing the Atheros chipset AR The chipset supports the802.11a standard, which though not the same as p, is suitable for evaluating our rate control algorithm as we are only interested in MAC broadcasting and CSMA aspects of a. We use the Atheros Linux Wireless driver ath5k 6, which we modify to disable beaconing, reduce the buffer space (queue size) to the minimum possible, increase the maximum number of allowed STAs to512 and set the CW size to a fixed value of 15. The default transmit power of the cards is about 20 dbm and PHY layer rate is fixed at 6 Mbps (default for broadcast), and so all the nodes are in communication range of each other. We set the frequency to 5.22 GHz. The grid is an environment of much greater node density than the road network we used for simulations and may lead to different capture and collision characteristics than those we observe in simulation. However, the change in system age with broadcast period was similar in character. The state application is run as a UDP broadcast application and, for the results shown in Figure 3.9, uses β = 1.1 and an interval of 5 s. We used settings of β = 1.2, and intervals of 2 and 10 s too. While an interval of 2 s seemed too short for getting an average delay estimate on the grid (probably because of the high density of nodes), convergence was observed for the other settings. The Network Time Protocol is used to synchronize the clocks at the nodes. Evaluation of results: The dotted staircase at the top of Figure 3.9 plots the number of nodes, shown on the axis to the right, that were a part of the network at a given time. At the beginning, t = 0, we have 298 nodes, 63 of which (about 3 rows on the grid) are switched off at t = 250 s. The nodes in the network are reduced every 300 s. At t = 1520 s only 50 nodes remain in the network. At t = 0 all nodes have their broadcast periodicities set to 0.05 s

64 47 ˆ (sec) No. of Cars 90pct( uv ) 25 pct( uv ) No. of Cars Time (sec) Figure 3.9: ORBIT Experiment. Measurement interval is 5 s and β = 1.1. The max difference between the shown percentiles is The left y-axis is in log-scale. The dashed staircase at the top shows number of nodes in network. The three other curves starting from top are the 90 th percentile of the set {ˆ v } of local estimates ˆ v at all nodesv, the system age ˆ calculated offline and the25 th percentile of {ˆ v }. The start period of 0.05 s and 300 nodes leads to a large system age of 0.5 s at the beginning of the experiment as shown in Figure 3.9. The nodes, however, soon start descending to a smaller system age of 0.13 s. After every instant at which cars leave the network, the remaining nodes converge to a smaller system age, at around which they stay till the next change in the network. The spikes in age that coincide with cars leaving the network are observed in the interval during which the cars leave. This is because, the remaining cars expect the cars that left to be a part of the network, but do not receive any packets from them. In the interval that follows fewer cars remain and the system age begins to descend. At the end of the experiment the50 car network achieves an age of0.02 s (close to optimal) in contrast to the0.13 s the298 nodes at the beginning had converged to. 3.5 Limitations and a Few Observations The system age metric assumes that all vehicles interested in each others state know of each others presence. Even though different nodes may see different average information age from a given vehicle, the average system age estimated by them must be similar. This will be true

65 48 if the nodes are in communication range of each other. However, this may not hold true in the presence of interference due to hidden nodes. As a result, groups of nodes in the network may not decode messages from all nodes of interest, assume that the network is smaller than it is, estimate a smaller system age and converge to a smaller broadcast period. To avoid the same may require the nodes to add to their messages, less frequently than their state information, their neighborhood information, encoding the approximate region over which they hear nodes and the number of nodes they hear from the region. This way, even if nodes cannot decode from all nodes they want to listen to, they can know of the nodes presence from other nodes messages and account for them in their estimate of the system age. On Power Control: Under large offered loads, power control can alleviate congestion by limiting the communication range of vehicles and hence the channel load. Limiting the range may disallow communication between vehicles interested in each others state. Rate control will reduce load by reducing messaging rates while allowing vehicles to communicate. Rate control may operate in conjunction with a power control algorithm. In the absence of power control and a very large number of cars, the rate control algorithm will push the broadcast period at the nodes to close to a very large value, a highly undesirable scenario. Once the size of network is chosen, the rate control algorithm can then minimize the system age seen by nodes in the network. Other congestion control strategies: TCP congestion control uses multiplicative decrease when a packet delivery fails and multiplies its CW size by2. The strategies are agnostic to network size and application requirements, however, and simply respond to packet errors. Packet error rate (PER) at a given broadcast periodt is a function of number of nodesn in the network and any PER thresholds chosen to varyt would need to be a function ofn. Also, one would need to know a priori the PER corresponding to minimum system age for all possible N. Same holds true vis-a-vis packet delay based thresholds.

66 Related Work Controlling congestion in the DSRC channel used to convey vehicle-to-vehicle safety messages has been the subject of several papers in recent years [12 15]. The authors of [12] use transmit power as the primary control. The power is computed locally at each sender in an approximation of a global max-min fair allocation, based on the location of the other vehicles within the sender s range. Transmit power is also the principal means of controlling congestion in [13]. In that paper the control is a linear function, within minimum and maximum power constraints, of the channel load, as measured by the Clear Channel Assessment (CCA) function defined in [49]. Message transmission opportunities are also chosen advisedly, using a concept that the same authors explore in more detail in [14]. In that paper the transmit events are chosen statistically as a function of CCA, perceived packet error ratio (PER), and vehicle dynamics, in an attempt to control a receiver s modeling error and to use the channel efficiently. In [15] a vehicle transmits safety messages at a rate that is adapted as a function of the local CCA and the CCA measured by neighboring vehicles. In [50] beaconing rate is adapted based on estimated channel capacity and message priority. The goal is delay sensitive distribution of traffic information to optimize routing of vehicles. In [51] the authors look at the effect of beaconing rates on channel load and the accuracy of the estimated position at beacon recipients. However, none of the above works use an average end-to-end application delay based metric. In [43] the authors provide broadcast congestion control strategies in vehicular networks to maximize the average rate at which packets are received by a vehicle from its neighbors, assuming a Rayleigh faded channel. However, the analysis does not include queuing delays. In [52] the authors propose congestion control by prioritizing messages based on their deadline, in vehicular networks. In [17], the authors propose prediction and efficient messaging to keep the number of transmitted messages in a vehicular network to a minimum. A protocol that improves broadcast reliability in networks is proposed in [53]. The protocol uses the collision avoidance of and RTS/CTS and NACK frames for reliable delivery of broadcasts. Rate and congestion control has been studied extensively in ad-hoc and sensor networks. In [40] the authors propose a rate control algorithm for wireless sensor networks that uses

67 50 knowledge of available capacity and allocates rates to flows so that they achieve a lexicographic max-min fair optimum. In [54] the nodes send back-pressure messages once they detect congestion so that the senders can throttle their sending rate. In [55] the authors propose contention window adaptation to enable the different flows in an ad-hoc network to achieve delay guarantees. They assume that there is enough capacity to support all flows, however. A survey on the work on congestion control in the internet, which is dominated by TCP traffic, can be found in [56]. In [42] the authors propose congestion control for the Satellite MAC, where on detection on congestion the satellite broadcasts to ground terminals to reduce their rate. 3.7 Conclusions We looked at the problem of congestion control in large wireless networks where nodes periodically broadcast time-critical information. Specifically: We introduced the system age metric to capture in an end-to-end manner the timeliness requirements of new applications that periodically broadcast their information. We show that, given limitations of current hardware, minimizing age cannot be achieved by maximizing throughput. This precludes the use of a saturated messaging load at the optimal contention window size, for a network to achieve the minimum age in a practical setting. Instead one wants to choose a small CW, a small queue size and a larget (larger than periods that lead to a saturated load). Changing CW sizes is used in CSMA networks to achieve better packet delivery, for example. We show that a simple CW adaptation that chooses to either increase or decrease CW size to reduce the system age is unsuitable. The above observations and the presence of a unique broadcast period at which system age is minimized motivated the design of an application layer rate control algorithm. The algorithm is fully distributed, uses the local estimate of the system age at each node. It achieves fast convergence, a median time of 4 s over many simulations. It is shown not

68 51 only to settle well around the system age, once achieved, for extended periods of time, but also has an ability to adapt quickly to changes in network size.

69 52 Chapter 4 On Piggybacking in Vehicular Networks: Can Multi-Hop better Single-Hop? 4.1 Introduction Our work is motivated by applications of safety messaging in vehicular networks. Most safety applications, proposed in DSRC [57], involve periodic broadcast of their state information, for example location, possibly as often as 10 times a second, to other vehicles that may be hundreds of meters away. Prior work has looked at techniques like repetition [58 60] and congestion control [61, 62] to improve broadcast reliability of state information in such networks, which use carrier sense multiple access (CSMA) mechanisms specified by DSRC. We explore the state dissemination problem in large networks at a more fundamental level. We capture the stringent delay requirements of these applications using the system age metric, Equation (4.1), which is the average age (over time) of any node s state at any other node. We then ask what wireless network connectivity would minimize the system age for given a physical road network of vehicles. Given that safety applications require all cars in the region of interest to know each others state information, the chosen network connectivity must lead to a connected graph, that is it must ensure that there exists a path between any two vehicles in the network. Also, nodes may have to piggyback/relay other nodes states. While almost all work on safety messaging assumes a CSMA based access control, we assume that all nodes are scheduled in a round robin manner. It allows interference free scheduling of nodes, eliminates penalties suffered due to the randomized mode of transmitter selection in CSMA, and makes analysis more tractable. This helps expose the mechanisms that lead to accumulation of system age over a chosen network connectivity. This allows us to arrive at theoretical insights, to the best of our knowledge, hitherto unpublished in the area of safety

70 53 messaging. The paper organization and its contributions are as follows. Sections 4.2 summarizes related works. Section 4.3 describes the system model. Section 4.4 derives the system age metric for a connected graph, which is followed by Section 4.5 that motivates piggybacking. In Section 4.6, for a heuristic based round robin schedule over a multi-lane road network, we show that there exists an optimally connected (multi-hop) graph, whose connectivity is independent of the size of the network. Also that the system age grows as the number of nodes in a large network, which is the same rate of growth for a fully-connected (single-hop) network. Section 4.7 shows the significant reductions in the achieved system age as a result of the above and the larger achievable wireless link rates by a node s transmission in a multi-hop network. We end with a summary of our work in Section Related Work CSMA is the chosen MAC mechanism for vehicle-to-vehicle networks. It can lead to significant packet collision rates in large networks with large offered loads. In [61] congestion control is achieved by power control with the goal of keeping the channel load seen at all nodes under a certain threshold. The authors of [62] propose mechanisms that control the channel load using much smaller overheads. Improving broadcast reliability via repetition has been explored in [58 60]. In [59] use network coding to reduce the bandwidth penalty of repetition. Piggybacking to improve reception rates, and hence reduce delays, was proposed in [58]. Beacons with earlier deadlines and/or those that are received from a farther transmitter are prioritized for piggybacking. In [60], the authors evaluate and compare six different repetition schemes to improve packet reception. In [17] the authors use linear predictive coding and other efficient messaging techniques to better use the available network bandwidth. Interference free scheduling of adjacent cells of vehicles using existing cellular infrastructure is proposed in [63] to perform alert dissemination within bounded delay. Our work is not the first to look at piggybacking in vehicular networks. In [58], the authors use piggybacking as a form of repetition coding to improve broadcast reliability, which they

71 54 define as packet reception rates. The work in [16] is probably the closest to ours in that it asks whether multi-hop broadcasting is better than single-hop (fully-connected graph) or vice-versa. The authors conclude that single-hop broadcasting is better when it comes to the age of received beacon information, however. Our claim is that a multi-hop network with piggybacking can in fact lead to a much smaller system age than a fully connected network of on-road vehicles. The different conclusions may be explained by the authors creating a multi-hop network by reducing the transmit power. In our work, we fix the transmit power, and increase the rate (bits/sec/hz) to create a multi-hop network. 4.3 System Model We consider a slotted transmission system with slot length τ. Let ij (t), denoted as t ij for notational brevity, be the age of node i s information at node j at the end of slot t. Measured in slots, i.e., the age is the number of slots old the state information of node i is at node j. Thus, t ii = 0. Let the length of transmission of node i be l i slots, assuming that it ends at t, for any node j that decodes the transmission, t ij = l i. After k slots without another transmission by i, t+k ij = k +l i. Let uv = E[ t uv] denote the average age of node u s information at node v. There are a total of N nodes and for each node u, the other N 1 nodes in {v : v u} have old information of nodeu, which leads to a total ofn = N(N 1) unique age terms. The system age is obtained by averaging over then age terms, and is defined by = 1 N uv. (4.1) u v u Piggybacking A packet transmitted by any node i consists of at least node i s state information and a header, which includes all overheads such as for authentication, link and physical layer headers. Define τ s = sτ andτ h = hτ, that is a node s state information occupiessslots while the header occupies h slots. It is often the case that the transmission time τ s required for the state information of one node is much smaller compared to the time τ h occupied by the packet overheads. For

72 55 example, the IEEE [64] standard for vehicular networks uses the ECDSA algorithm for supporting the authentication mechanism. A payload (contains state information) size of 53 bytes together with a certificate and a signature could lead to a packet size of up to 262 bytes [65]. A node may piggyback the state information of other nodes in its own transmission. The header does not change as a result of piggybacking and occupies h slots. Let s say that the node piggybacks the information of k 1 other nodes in the network. The packet contains k nodes state information. The total transmission time of the packet will be h+ks slots. This piggybacking may provide timely updates but comes at the expense of additional slots used for the packet transmission. 4.4 Modeling the Network as a graph Consider a network of nodes described by its connectivity graph G = (V,E), where the set V is the set of all nodes in the network and the set E consists of edges between nodes. The set of all possible directed edges between nodes in G is denoted by E. We assume that G is a connected graph, that is there exists a path between any two nodes in the graph. Further, only nodes connected by an edge can successfully decode each others transmissions. The implication is that the system employs coding such that reliable communication has a sharp threshold behavior; nodes within communication range of a transmitter decode packets perfectly while nodes beyond range discard the transmission. The number of nodes in the network isn = V. LetP denote the set of unordered pairs of nodes in the network and P be the set of ordered pairs of nodes. A pair of nodes may or may not be connected. We denote an ordered pair of nodes by [u,v] and an unordered pair by (u,v). We have [u,v] P and (u,v) P. If the pair is connected we use the notation [i k,j k ] and (i k,j k ) for ordered and unordered respectively. The ordered and connected pair [i k,j k ] E and also denotes the directed edge from i k j k, while the pair (i k,j k ) E and denotes the undirected edge between them. The subscript k is to index the pair and will be dropped when referring to one or any such pair. The ordered pair [u,v] will be connected by a path consisting of a sequence of directed edges ([i 1 = u,j 1 ],[i 2 = j 1,j 2 ],...,[i k = j k 1,j k = v]). When it is convenient we will denote

73 56 such a path by(u,i 2,...,i k,v). We are interested in round robin schedules over nodes in V that minimize the system age. The nodes may choose to piggyback the information of zero or more other nodes to achieve the minimum. They, however, always send their own information during their transmission turn. For any node k, let 0 p k < N be the number of other nodes information it piggybacks. Therefore, the length of transmission of node k is l k = h+(p k +1)s slots. The total number of slots in the round robin schedule is therefore given by L = k V l k. (4.2) Deciding on a schedule K for the nodes involves choosing the ordering of the nodes and the information that each node piggybacks. Consider the pair of nodes i and j such that (i,j) E. Let node i end its packet transmission at the end of slot t. The transmission is decoded by j at the end of the slot. The age of i s information at j at the end of slot t, t ij, is the length of the packet transmission by i. Thus t ij = l i. Further, t+1 ij = l i +1 and t+s ij = l i +s, where s = 2,...,L 1. The next transmission ofiends in slott+l, which is a round robin cycle afteri s previous transmission. We have t+l ij = l i, which marks the start of a repeat of the above sequence of ages. Thus, the age, averaged over a round robin cycle, is where ij = E[ t ij] = 1 L L 1 t+s ij = R +l i, (4.3) s=0 R = L 1. (4.4) 2 The age ij has two components,l i, which we will call the transmission delay and R, which we will call the round robin delay. While l i depends on the length of i s transmission, and therefore on the number of other nodes state information i piggybacks, R is a consequence of the round robin nature of the scheduling, which restricts a node to transmitting once every L slots. Clearly, both l i and R depend on the chosen schedule.

74 57 We define ρ uv as the schedule delay between any two nodes u and v. Let node u begin its transmission in slot t u. Let the next scheduled transmission of node v start in slot t v. Then, ρ uv = t v t u. Also, let d uv be the age of node u s information when it is forwarded by node v (age at the start of node v s transmission). We refer to d uv as the relay age of node u by v. Note that the relay aged ij = ρ ij for the connected node pair (i,j) E. Now consider the node pair u and v, where (u,v) / E. In this case when v transmits, it may not have received the latest update fromu. Thusd uv ρ uv. LetP uv be the set of directed paths starting at u and ending at v in the graph G. The paths P uv are those that can relay 1 u s information to v. Let one such path be p uv P uv. The path p uv = (u,i 2,...,i k,v). The length of the path is p uv = k. Consider the flow of u s information along the path p uv to v. The flow starts with u s transmission, followed by the transmissions of the nodes i 2,i 3,...,i k, all of whom by assumption will piggybacku s information. The information of nodeu, before it is received by node v, suffers delays that accrue over the length of transmissions of nodes u and i n, where 1 < n k, and the scheduling delays between them. Since [i k,v] E, v receives what u had transmitted at the end of the transmission by i k. It is worthy of note that the delays do not include the scheduling delay betweeni k andv. Also that the scheduling delay between i n 1 and i n, 1 n k, includes the length of transmission l n 1 of node n 1. The sum of these scheduling delays isd uik, which is the age ofu s information that is relayed byi k. Next we will express the age of u s information received by v as a sum of d uik and the length of transmission of nodei k. Nodei 2 is scheduledρ ui2 slots afteru,i 3 is scheduledρ i2 i 3 slots afteri 2 and so on. Let p uv be the subpath fromu = i 1 toi k, which lies within p uv. Thus p uv = p uv [i k,v] = (u,i 2,...,i k ). (4.5) Also, as discussed earlier, d uik = [i,j] p uv ρ ij. Further, to emphasize that i k is a function of u and v and a certain path p uv between them, define d p uv = d uik. Similarly, define l p uv = l ik. The number of slots before v = j k receives u s transmission, which is also the age of u s 1 Whether a path relays or not, in a given schedule, also depends on the piggybacking of information by the nodes in the path.

75 58 information when received byv, is then d p uv + l p uv. The age of information of node u at node v, however, depends on the minimum delay path for a given schedule K. Let p uv P uv be the minimum delay path. Once v has received u s information viap uv, the same information received later via other paths inp uv is ignored byv, as it does not update the information of nodeuat nodev. Let s say that node v receives u s state update at the end of slot t. Thus, t uv = Further, t+l uv = d p uv + l p uv. d p uv + l p uv +l, l L 1. Finally, after an L slot round robin cycle, t+l uv = d p uv + l p uv. Thus the average age of u s information at v is uv = 1 L N 1 l=0 t+l p uv = R + d uv + l uv. p (4.6) The age uv is specific to schedule K as it is a function of the path p uv. Further, since for a connected node pair i andj, ρ ij = d ij, we can rewrite d p uv in terms of relayed ages giving d p uv = [i,j] p uv ρ ij = [i,j] p uv d ij. (4.7) Rewriting d p uv in Equation (4.6), we obtain uv = R + [i,j] p uv d ij + l p uv. (4.8) The first term is the round robin delay R, the second term is an accumulation of scheduling delays and the last term is the transmission delay on the last hop of the path, at the end of which v receives u s information. Comparing the delays with those incurred between a connected pair i andj, we see that the round robin delay is suffered byuandv too. Also the delay l p uv incurred over the last hop corresponds to the transmission delay incurred between a pair of nodes i and j over the only transmission, the one by i, as between the pair i and j are0, as d p ij = 0. l p ij = l i. Lastly, the schedule delays suffered

76 Optimization over a Graph The system age (4.1) is a function of the schedule K and graph G. We denote it as (G,K). Using Equations (4.1), (4.3) and (4.8), (G,K) = R + S + L, (4.9) where R = (L 1)/2, (4.10) S = 1 d ij = 1 d ij, N N (4.11) L = 1 N [u,v] P [i,j] p uv [u,v] P lp uv = 1 N [u,v] P \ E [u,v] P \ E [i,j] p uv lp uv + 1 N [i,j] E l i. (4.12) System age, in Equation (4.9), is contributed to by the following interrelated quantities, the round robin delay R, the average scheduling delay S suffered by information, and the average last hop transmission delay L. None of the quantities are schedule independent. We want to find the schedulek that minimizes (G,K) for a giveng. The optimization can thus be defined as arg min (G,K). (4.13) K Loose upper bound on age An upper bound on system age, for any connected random graph and any schedule over it, can be obtained by assuming, unrealistically, that any ordered pair [u,v] P is connected by N 1 edges. Let D = S + L. Also assume that every node in the graph piggybacks all

77 60 other nodes information. Thus for any nodeu,l u = l max = h+ns. From (4.12) we obtain D = 1 N = 1 N = 1 N [u,v] P \ E [u,v] P \ E [u,v] P \ E lp uv + [i,j] p uv l max + [i,j] p uv d ij, (4.14) (N 1)l max, (4.15) (1+(N 2)(N 1))l max, (4.16) < (1+N 2 )l max, forn > 0, (4.17) N 2 h(1+ Ns ), for N 1. (4.18) h Equation (4.15) is obtained by setting d ij to its maximum possible value, which is a total of N 1 node transmissions of length l max slots each. Also, the last forwarder s transmission is l max slots long. We get (4.16) from (4.15) from our prior assumption that every [u,v] P is connected byn 1 edges and therefore p uv = N 2. The round robin delay, given by (4.4), can be bounded as follows. R = L 1 2 < L 2, (4.19) = (h+ns) N 2 = Nh 2 Ns (1+ ). (4.20) h From (4.9), (4.18) and (4.4) we obtain a bound on the system age = R + D (4.21) < max = Nh Ns (1+ 2 h )+N2 h(1+ Ns ). (4.22) h Therefore, the worst case system age max iso(n 3 ). IfNs/h 1, then the age increases as O(N 2 ).

78 61 Figure 4.1: A k-connected m-lane network. Each rectangle encloses a group of nodes that are connected to each other. 4.5 Fully-Connected Network vs. Piggybacking Assume that all vehicles transmit at a fixed transmit power. If all vehicles in our network choose a rate C such that two vehicles that have the smallest point-to-point link SNR are connected, then the network is a fully connected (single-hop) network. Choice of a larger rate (> C) will lead to a network in which not all nodes are connected to each other. In such a multi-hop network, some nodes will have to piggyback other nodes states, so that all nodes receive all other nodes state, which will lead to larger packet transmission sizes. However, a larger rate will imply a smaller transmission time than in the fully-connected case, for a given packet size. Piggybacking is beneficial when improvements in rate outdo the increases in packet size that piggybacking may cause. Next we ask, when for a given transmit power and physical network of nodes does transmitting at a rate which leads to a multi-hop network lead to a smaller system age? For exploratory purposes and given that the motivating application is vehicular, we first look at a single lane road network. 4.6 A Single Lane Network Figure 4.1 shows an example of am-lane road network, each lane consisting ofn cars, indexed 1 to N. A car u is connected to cars v in all m lanes, such that max(1,u k) v min(u+k,n), where the connectivity 1 k N. If k = N, the network is fully connected and cars can transmit their state to all other cars. When k < N, a car s state may need to be

79 62 Figure 4.2: Suggested schedule for a k-connected single lane network. Nodes that receive when 3 + k transmits are boxed. piggybacked by other cars to reach all cars in the network. For the purpose of this example, without loss of generality, we assume that k is even and N = k + nk, where n is an integer, n = (N/k 1) 0. We first look at the casem = 1, that is a single lane network. An example schedule for such a k-connected network of cars is illustrated in Figure 4.2. The construction of the schedule is motivated by the heuristic that a given car s state must take the smallest possible number of hops through the network to be received by all cars in the network. Not all cars states will satisfy the above requirement, however. Also we assume that, a node always piggybacks another node s state (as known to it) if any nodes connected to it have older state information about the other node. The schedule progresses along the arrows in Figure 4.2. For 1 e k, where e may be seen as the row index in the figure, car e + jk is followed by e + (j + 1)k for {e mod 3 = 0 j < n} and by e + (j 1)k for {e mod 2 = 0 j > 0}. Boundary conditions that occur at e mod 3 = 0,j = n and e mod 2 = 0,j = 0, lead to different following nodes as shown in the figure. Consider the node 3 + k. The node s transmission is received by all nodes boxed in the figure, a total of 2k nodes. The node 3 + k is followed by 3 + 2k in the schedule. The node 3+2k received node 3+k s transmission. It follows 3+k in the schedule and is connected to the set of nodes [3 + k,...,3 + 3k] of which the subset [3 + 2k + 1,...,3 + 3k] is not connected to3+k and hence did not receive3+k s transmission. Thus3+2k s transmission

80 63 will include its state information and will also piggyback node 3+k s information. Further, it will piggyback the states of those nodes, whose state is newer at its end than at one or more of nodes in the closed set [3+k,...,3+3k], for example the state of node2+3k. Accounting for the number of statesp u a nodeuwill piggyback, the length of transmission l u, defined in Section 4.4, can be obtained as follows for the selected schedule and any node u = e+jk. if e mod 3 = 0: 2j +2 j (0,n 1), 2n+1 j = n, if e mod 2 = 0: 2(n j)+1 l e+jk = if e = 1: 2j +1 e 2,j (0,n), j (0,n 1), (4.23) 2n j = n. if e = 2: 2n j = 0, 2(n j)+1 j (1,n). Define x = k/n, where 0 < x 1 is the normalized connectivity w.r.t. the fully connected network (k = N => x = 1). Using Equations (4.10), (4.11), (4.12) and (4.23), we obtain the system age = Hh + Ss, where H and S are given by Equations (4.25) and (4.26) respectively 2. Let s = βh, where β 0 is the ratio of the size of state information and the 2 We approximated the sum contribution of nodes in {e + jk e mod 2 = 0} {e + jk e = 2} to S (4.11) and L (4.12) by that of nodes in {e + jk e mod 3 = 0} {e + jk e = 3}, which upper bounds the former contribution, the difference between them being negligible. Also, later we will show that for the chosen schedule contributions of R (4.10) to dominate, and S, L can be ignored.

81 64 S = 2 N H = 2 N { N 2 (1 x) 3 3x + 5N2 (1 x) 2 4 [ N 2 (1 x) 4 + 5N2 (1 x) 3 3x 2 4x [ 47N(1 x) N + 1 [ N(1 x) 2 2 x 2Nx+ N2 x 2 + 5N(1 x) 2 + 7N2 x(1 x) N2 (1 x) 2 6 (1 x) x N(1 x)2 2x + 11N2 x(1 x) 4 + (1 x) ] +2 2x ] +Nx 2 + (1 x)2 2x 2 3N(1 x) } + N 2 2 5N(1 x)3 6x 2 (4.25) ] 33N(1 x)2 12x (4.26) header. For a fixed x, as N becomes large, can be approximated by = hn ( β 2 + (1 x)2 β 3xβ ). (4.24) x 2 The age is in slots, where a slot length was defined to be τ seconds in Section 4.3. Let q be the SNR 3 of the wireless link between the farthest nodes 1 and N. Assuming a path loss exponent of γ, the SNR between any two nodes k-hops away, for example nodes i and i + k, is q k = q((n 1)/k) γ qx γ. The capacity C k of the link between two such nodes is 0.5log 2 (1 + q k ) = 0.5log 2 (1 + qx γ ) bits/sec/hz. We make a simplifying assumption that all the nodes in the k-connected network transmit with rate C 4 k. The age in seconds is given by τ = τ = /C k. Equation (4.24) suggests that the x that minimizes age τ, that is the optimal normalized connectivityx = x for the single lane network and the chosen schedule is independent ofn. Also, it can be shown that increasingβ for a givenγ andq, increasesx. As β increases the optimal connectivity moves towards a fully-connected one. Vehicular networks can benefit from piggybacking as state dissemination typically involves a smallβ, for example β 0.25 in Section 4.3. The optimal x also increases when q is increased for a given γ and β. Lastly, for a givenβ andq, increasingγ reducesx. 3 We assume that the SNR is time-invariant. We show results over a wide range of SNR, however. 4 Note that otherwise, for large k > N/2, there will be nodes in the network that are less than k-hops away from any other node in the network. Such a node may therefore achieve a rate larger than C k. We will relax our assumption later in simulations.

82 Scaling of Age We will show that for the chosen schedule and a fixed x, the age increases as O(N), which is also the case for a fully-connected network. From (4.23), the maximum length of any node s transmission is 2n + 1 slots, which is O(n). Also, for any two nodes u and v, the age of u s information at v is the sum of relay delays along the fastest path between u and v and the length l v of v s transmission. From Figure 4.2, the maximum number of hops, and thus transmissions, any node s information needs to take before it is received by all other nodes is O(n). For example, node u = 3+(n/2)k and v = 3, is an example of a worst case pair. Node u s state is forwarded along the path p uv = (u,3+((n/2)+1)k,...,3+nk, 4+((n/2) 1)k,...,4,v). The corresponding sequence of relay delays is {1(n/2 times), n, 1(n/2 times)}, which is a total ofo(n) relay delays. Therefore the sum of the relay delays is of the order ofo(n) packet transmissions, each of which is O(n), as discussed above. Thus from (4.11) and (4.12), S is O(n 2 ) and L is O(n), as L is at worst a sum of N transmission lengths normalized by N and S is at worst a sum over O(n) relay delays for each of N pairs of nodes u and v, normalized by N. The last component of the system age is R L/2, where L is the sum of transmission lengths of all nodes and thus iso(nn). If we fix n, which is the same as fixing x as n 1/x, and increase N, for large enough N, the system age can be approximated by just its round robin component R. The O(N) scaling of age is the best achievable for a round-robin schedule and is the scaling obtained for a fully-connected network. The O(N) scaling together with choosing an optimal x leads to smaller system age than a fully-connected network for a range of SNR q, as we show later. Note from above that if we fixq andγ, for a givenxand the schedule in Figure 4.2, the age for a network of mn nodes in a single lane is m, where is the age for the single-lane network with N nodes. This explains why, as we noted from (4.24) too, the optimal normalized connectivity x is the same for a single lane network with mn nodes, wherem 1.

83 Generalization to multi-lane Consider a multi-lane road network, which is m > 1 in Figure 4.1. It has a total of mn cars. Further assume the schedule described next. It is a concatenation of the schedule in Figure 4.2 carried out for lanes 1,2,...,m one after the other. We argue that adding m lanes to the road network, for a given k and hence x = k/n (note N, not mn), leads to a similar S and L as for m = 1 and increases R by m times. The reason is that even with additional lanes, the state information of a node u takes the same number of transmissions to reach all nodes in the network (nownm). The fastest relay paths are still the same. Also, nodes piggyback the same information as they did for the single lane case. S, even for the m-lane network, scales as O(n 2 ), while L as O(n). If we have a single lane network with age 1 R (large N), for the same k, the multilane network will have a system age m = m R. Also, thex is the same for all m Simulation Results We carried out simulations for different sized road networks (N = 50,100, m = 1,4). We show that reductions of up to 70% in system age for large road networks may be achieved by piggybacking. We also verified (do not show for lack of space) the notion of an optimal connectivity that we derived in Section 4.6. The simulation setup, written using MATLAB, accepts a connectivity graph, physical positioning of nodes and a schedule of interest. It returns the achieved system age. Figure 4.3 shows the system age achieved for N = 50 and m = 4 when using the schedule described in Section The age is plotted w.r.t k, for SNRs q = 3,9and 20 db. We assume that all nodes in the network transmit at rate C = log 2 (1 + q) bits/sec/hz. In the figure we show that the optimal k, corresponding to x, obtained via simulation match very well with those given by (4.24). The simulations help us validate the theory in Section 4.6, which made assumptions of large N, to ensure that reductions in system age are obtained for network sizes of interest. We simulate the case where instead of all nodes transmitting at a common ratec as assumed during analysis, a node u transmits at a rate determined by the SNR of the link to the node farthest from it, which foru+k isuand/oru+2k. If the farthest node is at a distancetunits,

84 67 thenutransmits at a ratec u = log 2 (1+q((N 1)/t) γ ) bits/sec/hz. Such a rate selection can allow some nodes to transmit at rates> C fork > N/2 and thus yields the smallest achievable age for a given q. In practice nodes use a few discrete rates and typically a common rate when broadcasting, which lead to larger reductions in age than shown next. Figure 4.4 shows (all solid lines) the ages obtained for N = 100, m = 4 when using the schedule from Section 4.6. The ratio of size of state information to header is β = Each line corresponds to a differentq and plots ages obtained for differentk. The right mostk = 100 corresponds to a fully-connected network. The obtained ages are clearly smaller for k 20 than k = 100. Specifically, the reduction in achieved age (as a percentage of age for the fullyconnected case) is (66.75, 54.91, 42.35, 30.25, 19.6)% for q = ( 3, 0, 3, 6, 9) db respectively. Similar improvements were obtained for a network with N = 50 and m = 4 and selected q. This corroborates our earlier observation that for the chosen schedule, and a fixed x, the round robin delay R, which increases linearly in the total number of nodes in the network, is the most significant contributor to the system age. Also, the optimal normalized connectivity x is same for both networks. The dashed lines in the figure show the age obtained when the schedule is a randomly chosen permutation of the nodes in the network. Each age plotted is averaged over 10 random permutations. As is seen from the figure, piggybacking reduces age even when using random permutations. However, random schedules do worse than our chosen schedule. Age (sec) 2 x h=1600 bits,s=400 bits,γ=3 q=3db k (connectivity) Figure 4.3: 4-lane,N = 50 cars each lane. The boxed data points are where the age is minimized. The corresponding k is 10, 12 and 18 for q = 3 db, 9 db and 20 db respectively. From (4.24), optimal x is 0.2, 0.23 and 0.39 respectively, which corresponds to ak of 10, 11.5 and 19.5 respectively.

85 68 Age (10 4 sec) h=1600 bits,s=400 bits,γ=3 3dB k (connectivity) 100 Figure 4.4: 4-lane,N = 100 cars each lane. The dashed lines plot ages averaged over schedules that are randomly chosen permutations of nodes. The solid lines assume the schedule described in Section 4.6. The lines correspond to a fixed q db, given by the legend. The y-axis (log-scale) shows age assuming 1 Hz of bandwidth. An age of sec corresponds to0.012 sec in a10 MHz system. 4.8 Conclusions We proposed the metric of system age to capture the requirements of delay constrained messaging, of which safety messaging in vehicular networks is an example. An analytic formulation of the system age was derived for a connected graph. We define the normalized connectivity of a m-lane road network and use the system age formulation to show that the optimal normalized connectivity is invariant w.r.t. the number of nodes in the network for a fixed worst-case SNR q and path loss exponent γ. The result is shown for a schedule derived using the heuristic of engineering the fastest relay of a node s state to all other nodes. Via simulations we show that significant reductions in age may be obtained by configuring an optimally connected network with piggybacking. The increase in age for the chosen schedule increases as the number of nodes for any normalized connectivity x. This motivates spatial reuse to further reduce system age. Also, we are exploring gains achievable when node placements are more random than assumed in this work.

86 69 Chapter 5 Age Optimal State Dissemination with Piggybacking 5.1 Introduction This work is motivated by applications of safety messaging in vehicular networks. Vehicles periodically broadcast their state, for example location and velocity, possibly as often as 10 times a second, to other vehicles that may be hundreds of meters away. At each vehicle, the state information of other vehicles must satisfy stringent delay constraints. The problem in its generality is designing age optimal mechanisms that allow a network of N arbitrarily connected nodes to exchange their time varying state information. We want to minimize the system age, i.e., the average age of the known global state information, accrued over the N nodes. We consider specifically networks in which nodes can piggyback other nodes state information. We limit ourselves to round robin schedules and assume that nodes broadcast their state information to other nodes. We next distinguish our work from other time bound information dissemination mechanisms, for example gossip based mechanisms [66, 67] and reliable multicasting [68]. In gossip based algorithms, every transmission opportunity, a node chooses to communicate with a neighbor with a certain probability, which is chosen to minimize delay. The gossip may or may not code other nodes received information. In our work, we assume round robin schedules wherein nodes take turns to transmit their information in a known order. Multicasting involves a single transmitter, multiple recipients and relay nodes. In our network, all nodes play all the three roles. To exemplify the difference from delay optimal multicasting [69], consider a line network of nodes indexed (1,2,...,5), where node i can only communicate with nodei 1 andi+1. The schedule that is delay optimal if only node1was multicasting to the other nodes is clearly 1,2,3,4,5. This schedule, however, one can show

87 70 leads to the worst possible system age. The optimal schedule, which minimizes the system age for the graph, can be shown to be1,2,3,5,4. In Section 5.3 we explore link conditions under which piggybacking is beneficial. Earlier, in Section 4.4, we formulated the problem of age optimal state dissemination for arbitrary graphs. In Section 5.4 we show via a simple example how the framework can give interesting insights into age optimality. In Section 5.5 we use the formulation for an arbitrary graph to derive the system age for a general tree-graph. We then describe an algorithm of linear time complexity, which returns a provably optimal schedule in Section 5.6. Finally, the gains obtained on using an optimal schedule, for the example of a vehicle platoon, are evaluated in Section System Model The system model is as described in Section Piggybacking over Unreliable Links We start with a simpler model for a network of N nodes. We assume that the channel between any two nodes in the network is characterized by a link error rate of0 ǫ < 1. We next analyze three example state information dissemination schemes namely, Random Transmitter Selection (RTS), Round Robin (RR) and Round Robin with Omniscient transmitter and Piggybacking (RROP). In RTS, a node is randomly selected for transmission at the beginning of a slot. The probability of a node being selected is1/n. The selected node transmits just its own state information. In RR, all nodes follow an a priori fixed round robin schedule. Hence every node gets to transmit once inn slots. Like in RTS, nodes in RR do not piggyback any information. The scheme RROP has the nodes following a fixed round robin schedule, as in RR. However, the nodes are allowed to piggyback other nodes state information. Further we assume the presence of an omniscient genie that, at the beginning of a slot, provides the transmitter with the most recently transmitted state information of all other nodes in the network. The information from the genie is for the exclusive purpose of piggybacking and does not reduce the age of the state information of other nodes at the transmitter. The transmission of each node is thus

88 71 h+ns slots. Further assume that h s and h+ns h, that is, the header overheads are much larger than the state information and piggybacking of other nodes information causes a negligible increase in a node s packet transmission time. Given that in RROP we not only allow piggybacking with negligible increase in transmission time but also provide the transmitter with all the information it can ever piggyback, say if ǫ = 0, the system age achieved serves as a lower bound on achievable ages for all round robin schedules. The system age for the schemes can be derived to be 1 [ ] ǫ RTS = (h+s)n 1 ǫ +1, [ ǫ RR = (h+s)n 1 ǫ + 1 2N [ 1 RROP = (h+ns)n N ], ǫ 1 ǫ + 1 2N ]. (5.1) Comparing the ages for h + Ns h, it is clear that RROP has the smallest system age, followed by RR and RTS. The schemes RR and RTS pay a penalty for not piggybacking. The scheme RTS pays an age penalty over RR for having a random schedule. However, in all the schemes the system age increases as O(N), even for reasonable values for the packet error rate, say ǫ < 1/2. Piggybacking reduces age, but the rate of growth of the age is still linear inn, which is an artifact of the round robin scheduling of nodes. The average age suffered due to round robin dissemination of information in a fully connected network is (N +1)/2. We conclude that piggybacking is not a fix for unreliable messaging and that the real purpose of piggybacking is to convey the state of a node beyond the coverage range of that node. This further motivates us to model any network of nodes as a graph. Nodes that are connected via an edge in the graph have a link error rate of ǫ = 0 and those that are not connected have ǫ = 1. In practice, such links between a network of nodes can be obtained by using robust channel coding schemes. Note that we had derived the system age for a graph in Section The derivations are in Section A.

89 Example of Graph Optimization The graph optimization is given by Equation (4.13), which we derived in Section 4.3. Consider a graph containingn nodes, with nodes indexed1,2,...,n 1 connected to each other while node N is connected only to node N 1. A 5-node example is shown in Figure 5.1. In this graph, nodes in the set V = {1,2,...,N 2} need only transmit their own state information. Node N is a leaf and hence transmits only its own state information. Node N 1 will have to transmit all nodes states as it communicates the state of N to nodes in V and the states of nodes inv ton. The relay age of the state information of nodes inv, relayed by noden 1 to node N, is dependent on the chosen schedule as is the relay age of N, relayed by N 1 to the nodes in V. We want to minimize the system age and thus want to keep the cumulative contributions of the relay ages to a minimum. SinceN 1 is the only relay, lesser aging of the state information of nodes in V, before it is relayed, must come at the expense of the aging of N s state information and vice-versa. Armed with the above intuition we look at two possible schedules. The schedule1,2,...,n 2,N,N 1 in which noden immediately precedesn 1 and thus gets the fastest possible relay of its state to nodes inv and the schedule1,2,...,n 2,N 1,N where nodes inv benefit, however, at the expense of N. From the discussion above, for all i V, l i = l N = h + s and l N 1 = h + Ns. Before looking at the specific schedules, we derive the general expression of the system age for the network. From Equation (4.6), we obtain for u V, un = R +d u(n 1) +l N 1 and Nu = R +d N(N 1) +l N 1. For the remaining node pairs(i,j) E, ij is given by (4.3). Using Equation (4.1) and making the above substitutions

90 73 we obtain N = uv + [ ] u(n 1) + (N 1)u + [ un + Nu ] u V u V u V v V :v u + N 1,N + N,N 1 = (N 2)(N 3)( R +h+s)+(n 2)[( R +h+s)+( R +h+ns))] + [ ( R +d u(n 1) +h+ns) ] +(N 2)( R +d N(N 1) +h+ns) u V +( R +h+ns)+( R +h+s) = C +(N 2)d N(N 1) + u V d u(n 1), (5.2) wherec aggregates the terms that are the same in both the schedules. For the schedule1,...,n 2,N,N 1, we haved N(N 1) = (h+s), which is the length of N s transmission. Also, we have u V d u(n 1) = ( (N 1))(h+s) = (N 2)(N +1) (h+s). (5.3) 2 It follows from Equations (5.2) and (5.3) that N = C + (N 2)(N +3) (h+s). (5.4) 2 For the schedule1,2,...,n 2,N 1,N, we haved N(N 1) = (N 1)(h+s), which is the number of slots it takes node N and the nodes inv to transmit. Also, u V d u(n 1) = ( (N 2))(h+s) = (N 2)(N 1) (h+s). (5.5) 2 Let be the system age when the schedule is used. It follows from Equations (5.2) and (5.5) that N = C + 3(N 2)(N 1) (h+s). (5.6) 2 From Equations (5.4) and (5.6) it is clear that the former schedule is better for N > 3. For

91 74 Figure 5.1: An Example Graph. 1 < N 3, the schedules lead to the same system age. In general, from Equations (5.3) and (5.5), placing the leaf noden after the parent leads to an additional = (1/N)(N 2)(N 3)(h+s) slots of system age. The result that it is better to place the leaf just before its parent s transmission will hold in general for tree graphs, as we will show later in the chapter. 5.5 Optimization over a Tree For a tree-graph we will exploit the uniqueness of the path, and hence of the nodes that relay information, between any two nodes in a tree. Denote the set of leaf nodes of a treet(v,e) by L. A node u L transmits only its own state, as leaf nodes are connected to at most one other node. For example, leaf nodes 4, 5, 6 in Figure 5.2a cannot relay other nodes state. On the other hand, removal of a non-leaf node u partitions a tree into a collection of subtrees. Such a nodeumust forward the state of every nodev in one of these subtrees, since otherwise nodes in the other subtrees will not hear the state updates of node v. Hence a non-leaf node u forwards updates for all other nodes in the network. For example, node 2 in Figure 5.2a is connected to three subtrees in the shown tree T. Subtree T 1 that contains node 4, T 2 containing node 5 and subtree T 3 containing nodes 1, 3, and 6. Nodes in different subtrees receive information from each other via2 s transmission. For example, node5 T 2 receives information of node1 T 3 via 2 s transmission. Thus, the non-leaf node 2 transmits the information of all nodes in the

92 75 tree. The length of transmission of u is thus given by h+s if u L l u = h+ns otherwise. (5.7) Therefore, the length of the round robin schedule for any tree is L = L (h+s)+ L c (h+ns) = hn +s( L +N L c ), (5.8) highlighting clearly the slots occupied by headers and information. Clearly, for any node u, l u depends on the tree structure and is independent of the chosen schedule. Thus, for a tree the round robin delay R in (4.4) is schedule independent. Further for (u,v) / E, the last forwarder in the path p uv must be in L c as leaf nodes cannot forward. Thus for (u,v) / E, lp uv = h+ns. Substituting in (4.12), we can rewrite the average transmission delay for a tree as L = 1 N [u,v] P \ E (h+ns)+ [i,j] E:i L c (h+ns)+ [i,j] E:i L (h+s) = 1 {(h+s) L +(h+ns)(n L )}. (5.9) N The last equality is obtained by using L = {[i,j] E : i L} and thatn = L + {[u,v] P\ E} + {[i,j] E : i L c }. Also note that, while L for a general graph was schedule dependent, for a tree-graph it is schedule independent. Next we look at the average scheduling delay S for a tree. In a general graph, any two nodes u and v may be connected via more than one path. However, in a tree any two nodes u and v have a unique path between them, and so the minimum delay path p uv is independent of the chosen schedule. Let λ ij be the number of minimum delay paths that use [i,j] E for relay of information. Thus λ ij is the number of times the term d ij appears in Equation (4.11).

93 76 (a) An example tree with edges labeled by size of edge cuts. (b) Directing edges from smaller edge cut to a larger one. Figure 5.2: An Example Tree. For a tree it is independent of the schedule K. We define the indicator functioni ij (u,v) as, 1 if [i,j] p uv I ij (u,v) = 0 otherwise. (5.10) Rewriting S, given in Equation (4.11), for a treet, we get S = 1 N = 1 N [i,j] E [i,j] E d ij [u,v] P \ E d ij λ ij = 1 N I ij (u,v) (5.11) (i,j) E (λ ij d K ij +λ ji d K ji) (5.12) whered K ij is the relay age ofiby nodej in schedulek. Ani j cut will partition the tree into components T ij and T ji rooted at node i and node j respectively. For example, in Figure 5.2a T 31 = {3,6} and T 13 = {1,2,4,5}. Paths that use [i,j] must originate on a node in T ij and terminate in a node in T ji {j}. Let n ij = T ij. Further, T ji {j} = N n ij 1. For each nodeu T ij, a total ofn ij, there aren n ij 1 nodesv T ji {j}, to whom state of

94 77 u is relayed across link [i,j]. Thus, λ ij = n ij (N n ij 1). We now use the λ ij to construct a directed tree. Define set E λ as Eλ = {[i,j] E : λ ij > λ ji } {[i,j] E : λ ij = λ ji,i > j}. (5.13) Note that E λ = V = N 1, wherev is the set of edges in the treet. Note thatn ji +n ij = N. Thus, λ ji = (n ij 1)(N n ij ). Also, since nodes i and j are connected, d ij = ρ ij. It follows from the round robin nature of the scheduling that d ji = L d ij. Set c ij = N 2n ij. Also, note that [i,j] E + [u,v] P\ E = N. Making substitutions and rewriting Equation (5.12), we get S = 1 N [i,j] E λ L(N n ij )(n ij 1)+ 1 N [i,j] E λ c ij d K ij, (5.14) where the summation on the left is schedule independent while that on the right is a function of the relayed ages and hence of the schedule. The edges of any given tree can be directed and a root node selected by noting that the condition λ ij λ ji is equivalent to n ij n ji. Therefore for (i,j) E, [i,j] E λ if n ij < n ji. When N is even, the case n ij = n ji will occur for exactly one edge in T. Such an edge is directed from the node with the larger index to the one with the smaller index, thus ensuring that a unique root emerges. Consider the tree in Figure 5.2b, which is obtained by directing the edges in Figure 5.2a. In the treen 21 = n 12 and we choose to direct the edge from 2 to1. As a result the root is R = 1. Further, given edge [i,j] E λ, [i,j 1 ] E λ j 1 = j, that is there is only one directed edge that originates from i, and that the edge ends in j. We call j the parent of node i. Since a node has just one parent node, we can skip the j in d K ij, n ij and c ij, for a tree. Only one node, the root noder, in the tree does not have a parent. From Equations (4.9), (5.9) and (5.14), we can write the system age for a treet as (T,K) = R (T)+ L (T)+ c S(T)+ v S(T,K) (5.15)

95 78 where c S(T) = 1 N v S(T,K) = 1 N L(N n i )(n i 1) (5.16) [i,j] E λ c i d K i. (5.17) [i,j] E λ Only v S (T,K) is schedule dependent2. It is also the cost function that the optimization over K minimizes. Note thatc ij 0. Thus, the cost function v S (T,K) is a positive weighted sum of relay delay contributions of the set {[i,j] E λ }. The optimization problem is finding arg min K v S(T,K) = argmin c i d K i = argmin c i d K i (5.18) K [i,j] K E i R λ 5.6 Schedule Optimization on a Tree In general, any permutation of nodes of T = (V,E) is a valid round robin schedule. We are interested in a round robin schedule K that minimizes v S (T,K). We describe a graphical method to find the optimal schedule on a tree. This method depends on the merge functionµ(t,x) that merges a nodexin the rooted tree T with its parent and returns the resulting rooted tree T = µ(t,x) that is a copy of T, except node x is merged into its parent. Let p x be the parent of any node x. To exemplify the merge function, consider a treet with nodes {v 1,...,v n }, such that v k is the parent ofv j. The treet = µ(t,v j ) has the set of nodes {v 1,...,v j 1,v j+1,...,v k 1,v k+1,...,(v j v k )}. (5.19) The operator works on merged nodes too. If v i was originally a child of v j, it is a child of (v j v k ) in T. The merge µ(t,v i ) creates the merged node (v i v j v k ). In general, a node v may or may not be a merged node. The length of transmissionl v of a nodev is the total length T. 2 Superscript v in v S(T,K) to denote variable and c in c S(T) to denote constant part of S for a given tree

96 79 Algorithm 2 Obtaining an optimal schedule. Require: A rooted tree T N 1: fori = N to1do 2: L = argmin l v /c v v L(T i) {/*L(T i ) is the set of leaf nodes int i */} {/*Randomly choose an element from set L. Let selection be indexed k*/} 3: u = L(k) 4: T i 1 = µ(t i,u){/*concatenate selected node with parent*/} 5: end for 6: return T 1 of transmission, in slots, occupied by all nodes contained in v. We have l v = j v l j, where we used the node name to also denote the set of all nodes it contains. Note that when v is merged withp v, the resulting merged node is labeled by(v p v ), which denotes a concatenation of the labels of nodes v and p v. In a node v, let v 0 denote the common ancestor of the nodes contained inv. Ifv is a merged node thenv 0 is the right most node in its label. We now extend the definitions ofn v andc v for a merged nodev by definingn v = n v0 andc v = c v0. Also, note that the parent of the merged nodev is the parent of v 0. Thus,d v = d v0. Algorithm 2 starts with a tree T N = (V, E λ ), which is the given network of nodes. No node in the treet N is a merged node. Also, assume that the tree is rooted at noderand thatr is selected as in Section 5.5, ensuring thatc i 0 for alli {V R}. In an iterationk 1, the algorithm selects a leaf nodev of treet N (k 1) that has a minimum value ofl v /c v (l/c ratio). It then merges the node with its parent. As a result the tree T N k is obtained. Such iterations lead to a sequence of trees {T N,T N 1,...,T 1 }. The tree T 1 contains just a single node which is a merge of all the nodes in T N. We will verify that the sequence of nodes that constitutes its label is an optimal schedule that minimizes (T, K). An illustration of the algorithm for an example graph is shown in Figure 5.3. Root selection, which was discussed in Section 5.5, is also shown. Let Σ(T i ) be the set of all allowed sequences over the nodes in T i. The set contains all possible permutations of all the nodes in T i, under the constraint that the elements in a merged node always retain their relative order. Permutations treat merged nodes as single permutable entities. Also, note that a sequence and its circularly shifted versions are equivalent, as such

97 80 a shifted sequence leads to the same system age as the original one. The set of Σ(T i ) corresponding to the sequence of trees is {Σ(T N ),Σ(T N 1 ),...,Σ(T 1 )}. (5.20) Consider a sequences i Σ(T i ). One iteration of the algorithm on the tree will givet i 1. The sequence will be transformed into S i 1 Σ(T i 1 ). Assume that S i is circularly shifted such that nodep u is placed at the end of the sequence, that is in positioni. Further, assume that node u in T i was merged with its parent p u during the iteration. The corresponding transformation in the sequence from S i to S i 1 involves moving u (the child) from its position in S i to immediately beforep u (the parent) and then treating the two nodes as one merged node ins i 1. The merged node (u p u ) will have the positioni 1 ins i 1. We now state the result that an iteration of the algorithm never increases the system age. Theorem Given a tree T n obtained after N n steps of Algorithm 2 on a tree T N = (V,E). Assume an arbitrary schedule S n Σ(T n ). Generate T n 1 by carrying out a single iteration of Algorithm 2 on T n. The corresponding transformation from schedule S n to S n 1 satisfies (T n 1,S n 1 ) (T n,s n ). The proof of the theorem can be found in Section B. Consider any round robin schedule S N on T N. By definition, S N Σ(T N ). Transform the tree T N to T N 1 and use the same transformation on nodes in the sequence S N. At the end of i such transformations, S N i Σ(T N i ). The reason being that the set of merges (transformations) that gavet N i fromt N are the same as those that gaves N i froms N. For a given sequence of transformations,σ(t 1 ) is a singleton and unique set, which consists of just a node which is a merge of all nodes of T N. This, and that S i Σ(T i ), implies that for any start sequence S N, and a given sequence of transformations, we always end up with a unique sequence S 1, also given by the label of T 1. From Theorem 5.6.1, irrespective of a given random initial sequence S N, a transformation from S n+1 to S n for 1 n N, never increases the system age. Thus, since S 1 is unique, starting with an optimal sequences N must also lead tos 1, with no increase in resulting system age. Therefore,S 1 is optimal.

98 Gains from using an optimal schedule for an example tree network We evaluate the average age that is achieved when schedules are chosen at random, for an example network of vehicle platoons. The average age is then compared with the age obtained when an optimal schedule is chosen. Platooning involves forming groups of vehicles that move together [70]. It requires vehicles within a platoon to communicate with each other and also inter-platoon communication. Inter-platoon communication is between vehicles that have been elected as platoon leaders by vehicles in their platoon. Assume a network of k platoons. Each platoon has a leader and has a total of j vehicles. We assume that vehicles in a platoon are only connected to their platoon leader. Also, a platoon leader is only connected to leaders of adjacent platoons. The resulting tree network consists of N = kj nodes (vehicles). Assume that the k platoon leaders are indexed 1,2,...,k. An example platoon fork = 3 andj = 5 is shown in Figure 5.4. The system age is given by Equation (5.15). The number of leaf nodes in the platoon network is L = k(j 1) and the number of non-leaf nodes is L c = k. The length of the schedule is L = k(j 1)(h+s)+k(h+Ns). From Equation (4.12) we have, R = L 1. (5.21) 2 Now consider c S (T), see Equation (5.16). The platoon leader indexed (k + 1)/2 is a valid selection for the root R of the tree network. Also, note that within a platoon, the j 1 nonleader nodes are leaf nodes and hence for any such node i, n i = 1. Thus only the k leaders contribute non-zero terms to c S (T). Substituting N = kj and rewriting the summation over just the non-zero terms we obtain c S(T) = k 1 2 i=1 = 2 N L(kj n i )(n i 1) N k 1 + k i= k+3 2 L(kj n i )(n i 1) N 2 L(kj n i )(n i 1), (5.22) i=1

99 82 where we exploited the symmetry of placement of platoon leaders around the root node. Further, from Equation (5.9) we get L (T) = 1 N {(h+s)(j 1)k +(h+ns)(kj(kj 1) k(j 1))} = (h+ns) sk (j 1)(N 1) h+ns, (5.23) N where the approximation holds for large N. Further, assume that h >> s, h+ns h = 1, that is any packet transmission occupies a single slot and the overheads of piggybacking others states are negligible. Thus, L = N, L (T) = 1. Further, the platoon leader indexed i has n i = j +(i 1)j = ij, where node i has amongst its descendants j 1 other members of its own platoon, and the i 1 platoons indexed 1,2,...,i 1. Thus the subtree rooted at i is of sizeij. Substituting for n i, from (5.22) and (5.23) yields c S(T)+ L (T) = 1+ kj2 (k 2 1) 6(kj 1) 3k2 j +j 4(kj 1) + kj kj 1. (5.24) Next we evaluate v S, which is the value of v S for an optimal schedule. LetS i be any permutation of the non-leader nodes of platoon leader i. An optimal schedule is 3 S = {S 1,1,...,Sk 1, k 1 2 2,S k,k,......,sk+3, k ,Sk+1 2, k +1 }. (5.25) 2 Next we write v S assumings is the chosen schedule. v S = 2 N k 3 2 c i d i + k N i=1 j 1 c i d i i=1 + 1 N ck 1 dk N ck+3 2 dk+3. (5.26) 2 Note that c i = N 2n i = kj 2ij. Consider the right hand side of the above equation. The summation in the first term is contribution to the age of the platoon leaders indexed 1,2,(k 3 This schedule is optimal for anyh > 0 andh+s 1, as for the platoon network the ordering of thel/c ratios of the nodes is not affected by the relative lengths of h ands.

100 83 3)/2,(k + 5)/2,...,k. Any node i in the index set has d i = j. This is because adjacent platoon leaders are separated by j 1 non-leader nodes in the optimal schedule and all node transmissions occupy one slot. The third and the fourth terms are contributions of platoon leaders indexed (k 1)/2 and (k + 3)/2 respectively. Both the nodes have the root node, indexed(k+1)/2, as their parent. However, the node(k 1)/2 suffers a greater relay delay, as is seen ins. We haved (k 1)/2 = j(k+1)/2, as we have(k+1)/2 platoons scheduled before the root can relay node (k 1)/2 s information. Also, d (k+3)/2 = j. Finally, the second term in the equation is the contribution to age of all the non-leader nodes of all platoons. The set of relay delays of a single platoon s non-leaders is{1,2,...,j 1}. Making the substitutions, we get v S = 1 N 2 k 3 2 i=1 = kj2 3j +2 2(kj 1) j(kj 2ij)+j 2k +3 2 j 1 +k(kj 2) i=1 i j 2, (5.27) where the last approximation is true for largen. Let be the averaged over randomly selected schedules. = E[ R + L + c S + v S ]. For randomly selected schedules, the relay delay of any node in the network is uniformly distributed over (0,L) = (0,N = jk). The average relay delay is E[d i ] = jk/2. Since only v S is dependent on relay delays, we have = R + L + c S +E[ v S ]. E[ v S ] is given by v S = 1 N E 2 k 1 2 j 1 (kj 2ij)d i +k(kj 2) i=1 = 2k2 j 2 jk 2 6jk +j +4k 4(jk 1) i=1 d i kj 2. (5.28) An Example Platoon network Consider a network consisting of k = 5 platoons. We have = R + L + c S + v S and = R + L + c S + v S. The percentage improvement in the optimal schedule over the average, for k = 5, is 100(1 / ) 22%. For k = 10, the percent gains are about 17%. The gains obtained are mostly independent of j, the size of a platoon. The values above hold

101 84 for small platoon sizes of about20 vehicles to platoons that have hundreds of vehicles in them. For large N, from (5.27) and (5.28), v S / v S k = O(k). While the improvements obtained in the contribution of the schedule dependent v S are significant when using the optimal schedule, the over all gains in system age do not scale similarly because of the schedule independent components R, L and c S whose sum contributions to age increase as O(k2 ). The observation motivates engineering connectivity in a network of nodes, such that the schedule independent overheads are kept to a minimum, allowing larger gains in system age for largen. We are exploring the possibilities as a future extension to this work. 5.8 Related Work In the field of vehicular networks, mechanisms of reliable broadcast while keeping delays to a minimum have been proposed earlier. In [60], the authors evaluate and compare six different repetition schemes to improve packet reception that may suffer due to interference from other transmissions. In [71] the retransmissions are network coded, where coding of packets is guided by position information of involved cars. In [72] space division multiple access is used to allow for interference free scheduling of messages. Interference free scheduling of adjacent cells of vehicles using existing cellular infrastructure is proposed in [63]. The aim is alert dissemination within bounded delay. Piggybacking to improve reception rates, and hence lesser delays, was proposed in [58]. Two criteria are used to decide on which received beacons must be piggybacked. Beacons with earlier deadlines and/or those that are received from a farther transmitter get priority. In [73] propose a multi-channel approach, to support infotainment applications, when hotspots are available, together with time critical safety applications which use an ad-hoc network. RMDP, a hybrid FEC+ARQ protocol, for reliable multicast to potentially large sets of receivers is proposed in [68]. FEC is used in presence of large groups of receivers to minimize the need for feedback. In [74] the authors propose safety message dissemination using multicast trees. They propose an approach that creates a single group multicast tree independent of multicast sources for vehicular networks where a source may not be known in advance. Gossip based mechanisms have been proposed to disseminate messages to all nodes in a

102 85 network. In [66] the proposed protocol aims to disseminate rapidly amongst n nodes k n messages. Nodes send random linear combinations of messages they have. In [75] propose a gossip mechanism to improve multicast reliability in Mobile Ad-Hoc Networks. In [67] the authors analyze and design gossip mechanisms to facilitate distributed averaging over a network. 5.9 Conclusions We defined the problem of age optimal dissemination of time varying state information, between nodes in a network, under the assumption that the nodes can piggyback other nodes information and presented an algorithm that minimizes system age. Specifically, our contributions include: We show that piggybacking is not a fix for unreliable messaging and that its purpose is to convey the state of a node beyond the coverage range of that node. We derived the optimization problem of minimizing system age for an arbitrary treegraph under the constraint of round robin schedules. An algorithm, of time complexityo(n), that returns an optimal schedule for a given tree is proposed and its optimality proven. Gains obtainable in vehicular platoons were evaluated to be about 20% for networks containing 5 10 platoons. The gains do not vary much with the number of vehicles in a platoon.

103 86 (a) (b) (c) (d) (e) (f) (g) (h) Figure 5.3: Illustration of Algorithm 2. (a) The given tree with its edges labeled (the parenthesis) by number of nodes on either side of the edge cut. (b) Direct edge from smaller cut set to larger. Node 1 emerges root. (c) T 9 : The original tree network rooted at 1. Labels of leaf nodes contain their l/c ratio to the right of the :. The nodes 3, 4, 5 and 8 only transit their own information, (h+s) slots, and each have c = N 2n = 9 2 = 7. Thus for each of them l/c = (h+s)/7. (d) T 5 : Obtained when all the leaves int 9 have been merged into their respective parents. The order of their merging is unimportant as they all have the samel/c ratio. Merged node(87) has al/c = (2h+10s)/5, as8transmits overh+s slots and7(a non-leaf in the original tree) overh+9s slots. Also, for(87),c = c 7 = N 4 = 5. (e)t 4 : (8 7) and ( ) were the leaves in T 5, of which (8 7) had a smaller l/c ratio. Thus (8 7) is merged into6. (f)t 3 : (876) int 4 has the smallestl/c ratio and is merged into9. (g)t 2 : Obtained fromt 3. (h) T 1 : The optimal sequence is obtained from the label of the node and is the sequence8,7,6,9,3,4,5,2,1. A variant of the above can be obtained by assuming h s and h + Ns h. The l/c ratio for ( ) and ( ) in T 3 is then the same. As a result 3,4,5,2,8,7,6,9,1 is also an optimal sequence.

104 Figure 5.4: A network of three platoons. The edges are between cars that have communication links between them. Leader of the platoon is the root R of the tree. 87

105 88 Chapter 6 On Predicting and Compressing Vehicular GPS Traces 6.1 Introduction Vehicle-to-vehicle communications is expected to enable a broad spectrum of safety, traffic management, and infotainment applications [57]. Safety applications, in particular, require that vehicles share their positions and trajectory with other nearby vehicles. This is typically envisioned through periodic broadcasts of Global Positioning System (GPS) coordinates over a Dedicated Short Range Communications channel. It has been shown, however, that the wireless medium represents a bottleneck because it can saturate under dense automotive traffic conditions [76]. While many communications and networking techniques to increase capacity or use available capacity more efficiently have been investigated [63, 73], it is still not fully understood what communication load is necessary to convey vehicular movements in a local region. A typical assumption is that every vehicle needs to transmit positions updates with a frequency of 10 Hz to reliably communicate changes in vehicle movement to nearby cars. This update frequency is determined by the rate of change of vehicular positions, the reliability of the communication channel, and application latency requirements. Recent work has begun to study the required position update frequency in more detail and has demonstrated that vehicular movements can be quite predicable and thus lower transmission rates may be sufficient. If the receiver can predict the path of the transmitter for a certain duration, the transmitter only needs to send the next update when the receivers prediction becomes inaccurate. In [17] the authors implement such a scheme through predictive coding techniques with non-linear models to reduce the number of position updates transmitted from each vehicle. The evaluation uses a few sample location traces from highway and urban datasets. In [18] prediction is evaluated using traces from a traffic simulator. To our knowledge, however, there

106 89 does not exist in the literature a comprehensive study of how well automotive GPS traces can be predicted, for a range of traffic scenarios and driving conditions. A related question is quantifying the effectiveness of compression techniques for real-world GPS traces. The vehicular communications community is considering to include in vehicle s position update messages not just the most recent position update, but a trace of the n most recent positions. Compression techniques for location traces can therefore help reduce the payload size before transmission. To address these questions, this chapter studies the effectiveness of linear and higher degree polynomial prediction and compression schemes on an extensive set of about 2500 real-world vehicle trips obtained from both a highway and a city environment and with different GPS update frequencies. It concentrates on prediction techniques that do not require a model of vehicle movements. The key contributions are: We show that linear prediction based on the two most recent GPS updates outperforms more complex polynomial prediction techniques. We show that most predictions errors are caused by incorrect speed estimation, suggesting that using road maps to improve prediction will not yield significant benefits for vehicle traces sampled at high rates. We quantify compression gains and show that polynomial compression techniques can outperform the Douglas-Pecker (DP) algorithm [77] for compression of location traces. The remainder of the chapter is as follows. Section 6.2 describes the assumptions we make and the different approaches we evaluate. In section 6.3 we describe the GPS trace data that we use for evaluations. Section 6.4 presents the results. Related work is described in 6.5. We conclude with a summary of our contributions in section Assumptions and approach A trajectory/trace is defined as a sequence of one or more locations at points in increasing time. Let (x t,y t ) represent the location at time t. A trajectory or trace T(t) = {x t,y t : t = (t 0,t 1,...,t k ),t 0 < t 1 < < t k }. We define trace granularity as the time interval

107 90 between any two adjacent points in T(t) 1. The trace T(t) stripped of all time information is defined as the available road/path information (just thexy co-ordinates, not). Typically, at any given time, the location estimate required by a target application needs to be within a certain tolerance of the actual location. The maximum acceptable error is defined as the tolerance δ. At any given time t, it is required that (ˆx t x t ) 2 +(ŷ t y t ) 2 δ, where the left hand side of the equation is the Euclidean distance between the location (ˆx t,ŷ t ) as estimated by the application, and the actual location (x t,y t ) Prediction Location at a future time is predicted using a certain length of known actual locations, which precede it in time. The actual locations at any time are only available to an Observer, for example using a GPS device, and it disseminates (broadcasts) the actual locations in the form of a location update to other interested parties. When the prediction error at the interested parties using the last location update exceeds the tolerance, only then a new snapshot of actual locations is sent by the Observer. In the absence of prediction, location updates will need to be sent at the rate at which a new location is observed. Thus prediction reduces the rate at which the Observer needs to broadcast its location. As the Observer needs to know the prediction error at the interested parties, a prediction algorithm will have to run not only at the interested parties but also at the Observer. Prediction using polynomials: Polynomials of various degrees n can be fit to the known actual trace data, exactly or in the least-squares sense (fitting M + 1 > n points). M + 1 is the length of known actual locations. The known locations are used to calculate the coefficients, p 0,...,p n, of a polynomial p(t). The coefficients are two-dimensional vectors, (x and y coordinates as elements). p(t) = p 0 +p 1 (t t 0 )+p 2 (t t 0 ) 2 + +p n (t t 0 ) n (6.1) 1 The location co-ordinates could be the latitude and longitude or a point s co-ordinates in any other co-ordinate system, for example UTM, which specifies locations on earth as points on a 2-dimensional grid. The timest 0,t 1,... don t have to correspond to a fixed sampling rate. However, most GPS devices log time and location information at a fixed rate and hence a fixed.

108 91 The polynomial model thus obtained is used to predict (extrapolate) the location at a time in the future. We define linear polynomial prediction (LPP) as prediction that uses a line model (a polynomial of degreen = 1,M +1 >= 2). Prediction gains are defined as the reduction in the number of location updates required when using prediction. Specifically, for the evaluation in Section 6.4, the reduction is defined as the difference between the number of packets sent in absence of any prediction mechanism (one for each point in the GPS trace being evaluated) and the number of packets sent when prediction is used. The gains are shown as percentages of the total points in the trace. For a CSMA MAC, such as used in vehicular systems, the reduction in packets will imply equivalent reduction in channel access by the on-road vehicles and hence lesser contention for the wireless medium. The presented evaluation doesn t consider scenarios where a certain predictor (interested party) may not receive the sent actual locations. For example, a vehicle that enters a road network will not have location information that was broadcast earlier. When prediction is being used, the packets that update the network with the actual locations will contain more than one actual location. The additional locations will make a location update packet larger. However, given the authentication and other header overheads, the increase in packet size can be ignored for the number of actual locations assumed in the evaluation presented. Also, as will be clear in Section 6.4, a total of two actual locations from the past is most beneficial. In general, a predictor maybe aided by error corrections or may use prior noisy predictions to come up with a new one. It may also assume models for the process that is being predicted, as in typical Kalman filter based designs. In this work we assume that predictions are made only based on a certain length of actual locations that is known a priori to the predictor. For our study we assume the locations obtained from a GPS device to be the actual locations. We do not account for possible error in location logged by a GPS device Compression Compression involves representing a given trace T(t) by fewer points in (x,y,t) space, as long as the error in location estimated from the compressed trace, at any given time, is within

109 92 the tolerance δ of the actual. Under prediction only the current actual location and the past is known. Compression on the other hand has the entire trace information a priori. Compression achieved is defined as the difference in the points in the actual trace and its compressed version. Gains are shown as percentages of the total number of points in the trace evaluated. DP The Douglas-Peuker (DP) Algorithm approximates a trajectory by fewer lines. Given any two points in the trajectory, the algorithm tries to minimize the number of lines that connect the points, while ensuring that the error tolerance requirements are satisfied [77]. Polynomial Interpolation (PI) We use polynomial approximation of a car s trajectories. Let the functionsx(t) andy(t) represent respectively thexandy co-ordinates, of a trajectory, changing with time. In Equation 6.1,p k,k = 1,...,n are the polynomial coefficients, andp 0 is the value of the co-ordinate at timet 0. The number of co-ordinate points encoded by a polynomial approximation ism+1, wherem >= n. Letp x (t) andp y (t) be the polynomials approximatingx(t) and y(t) respectively, for t t 0. At any time t, (p x (t) x(t)) 2 +(p y (t) y(t)) 2 δ needs to be satisfied. The above condition is satisfied by ensuring that p x (t) x(t) δ 2 and p y (t) y(t) δ 2 are satisfied at all t. Distance-Time The Distance-Time (DT) algorithm first encodes the xy-part of the trace T(t) using minimum number of line segments. It then encodes the distance travelled along each of the line segments, using a line simplification approach (as in DP), as constant velocity segments.

110 Trajectory Data We evaluate aforementioned prediction and compression schemes using GPS traces collected by on-road vehicles. Specifically, we answer the following questions: What prediction gains are achieved for polynomial models of different degrees n and lengths of known actual locations M +1? How are the gains affected by the tolerance δ? How are prediction gains affected by trace granularity? Is a certain smaller than needed in a given environment, for example city or highway roads? By how much does knowing road information improve prediction? At what speeds do we get prediction gains and what distances can be predicted on average? How well do different schemes compress traces as a function of? The traces can be organized into three sets on the basis of the frequency at which the GPS information was logged. A set of34 traces recorded in and around a downtown in New Jersey were logged at5hz 2, i.e., = 0.2 s. The average speeds in the collected traces were less than 40 mph, i.e., about 60 km/h. The total trace length is about 30 hours. Another set of 134 traces, collected in New Jersey, by four drivers over their daily commutes, were logged at1hz, i.e., = 1 s 3. Finally, two sets of traces, one from20 cars driving over a4mile highway section in Oakland CA and the other from 100 cars going back and forth over a highway section were collected at a time granularity of 3 s. The two sets together are a total of about 2300 traces and more than 400 hours in time. 2 Garmin GPS 18 device was used 3 The Holux GPSlim236 GPS device was used

111 94 The GPS latitude and longitude are converted into Universal Transverse Mercator co-ordinates, UTM-x and UTM-y, for all evaluation that follows. 6.4 Results Prediction Prediction gains for different polynomial degrees and number of known actual locations Figure 6.1a shows the prediction gains obtained for δ = 0.5 m and varying degree n of the extrapolating polynomial 4. In the plot we choose M = n, where M +1 is the total number of known actual locations. For a fixed n, choosing M > n leads to lower prediction gains than M = n, however. Traces with = 0.2 s were chosen for the plot. The gains are the greatest for = 0.2 s (median of about 80% for M = n = 1) and fall considerably for granularities of 1 s and 3 s (not in plot) to a median of about 30% and 10% respectively. Also, for any, the combination of M = n = 1, i.e., linear extrapolation using two actual locations from the past, provides the maximum prediction gains. The gains, shown for n <= 4, reduce as the degree n increases. Last but not the least, the lack of gains at larger trace granularities, suggests a minimum rate at which location may need to be broadcast. Since these results show that LPP outperforms higher order polynomial prediction, the following results focus on LPP. Gains using LPP LPP achieves median gains of 80%, see Figure 6.1b, for δ = 0.5 m and traces with a time granularity of = 0.2 s, which were taken in a city environment (refer Section 6.3). Gains of 80% suggest that, with prediction, only a packet per second may be sent to update location, instead of a packet every0.2 s. The figure also shows the improvement in prediction gains, for LPP, obtained with increasing δ. Median gains for a tolerance of δ = 1 m are 6%,10% and15% higher than for δ = 0.5 m, for of 0.2, 1 and 3 s respectively. For tolerances greater than 1 m even higher prediction gains were observed. The improvements are most notable for the larger. For 4 The plot shows results for extrapolation done independently along(x,t) and(y,t). The basic trends are similar for joint (x, y, t) extrapolation.

112 95 Prediction using polynomials of different degrees, tol=0.5 Prediction gains (%) M=n 3 4 (a) Prediction Gains for polynomials of various degrees. 100 Linear Polynomial Prediction (M=n=1) Prediction Gains (%) {Granularity (sec), Tolerance} (b) Linear Polynomial Prediction Gains: x-axis first row is granularity s, 2nd row is tolerance δ m 100 Compressibility of xy trace % Compression Trace time granularity (sec) (c) Compressibility of xy-traces.

113 96 Increase in Prediction Gains (%) Mean vel. on successful prediction Prediction with and without road information (M=1) Slow, 0.2 Slow, 1.0 Slow, 3.0 Fast, 1.0 Fast, 3.0 {Vel, Granularity (sec)} (a) Improvements in prediction gains on using road information Mean velocity when prediction is successful (M=1) Slow, 0.2 Slow, 1.0 Slow, 3.0 Fast, 1.0 Fast, 3.0 {Vel, Granularity (sec)} (b) Successful prediction occurs at slower velocities (shown in mph). CDF of mean distance predicted sec (with Road Info) sec 3 sec sec (no Road Info) 1 sec 3 sec Mean Distance Predicted (m) (c) Distribution of mean distance predicted with and without road information. Figure 6.1: Prediction of location using GPS traces

114 97 = 1 s the gains at δ = 2.0 and δ = 4.0 were 67% and 77% respectively. For = 3 s they were31% and 48% respectively. Benefits of road information LPP implicitly assumes that the direction of motion and speed in the future are the same as the current known direction and speed, which are calculated from the known actual locations. Errors in prediction will therefore occur on a change of either or both and are more likely to occur for larger. Errors due to changing direction alone, can be eliminated if the predictor has access to road information (RI), which is the xy part of the actual future trace. We will show that road information is of very limited benefit in prediction. We define xy-compressibility of a trace as the reduction achieved in the number of straight lines that can approximate a given trace, considering only the xy-plane, i.e., we ignore the time co-ordinate of the trace. The greater the percentage compressibility, the lesser the number of straight lines required in proportion to the total in the uncompressed trace. Compressibility of a trace in xy provides a rough estimate of how well direction can be predicted, using LPP, along the trace. In the absence of changing speed, LPP over a trace should achieve prediction gains in the range of the trace s compressibility. This is because, at constant speed the errors in prediction will occur only when the road changes direction, i.e., at all those points in the trace where its compressed version adds a new line (or direction). Figure 6.1c shows the xy-compressibility of the traces, grouped by their granularity. A tolerance of δ = 0.5 m is assumed. The granularities of 0.2, 1 and3s have median compressibility of 94%, 64% and 52% respectively. The achieved prediction gains for δ = 0.5 m, Figure 6.1b, are 80%, 40% and 8% respectively. LPP unable to achieve prediction gains close to the xy-compressibility can be explained by its inability to predict changes in speed. Consider again = 1 s and δ = 0.5 m. The xy-compressibility is 64%, i.e., 36% of the trace has unpredictable changes in direction. If speed was constant, the presence of RI would lead to prediction gains of 100%, as RI would lead to a priori knowledge of all changes in direction. Figure 6.1a shows the improvement in prediction gains using LPP, when the predictor has RI. The increase in prediction gains is the difference between prediction gains when RI is

115 98 known and when it isn t. It is plotted for all granularities. Further, for each time granularity the traces are grouped by their mean speed 5. Speeds > 41 mph, about 65 km/h, is labelled as fast. The speeds 41 mph are labelled as slow 6. The improvement in prediction gains is a median of about 2.5% for = 0.2 s traces, smaller than that at of 1 and 3 s. The 0.2 s trace benefits very little from RI as it is already very close to xy-compressibility (94%) and could have benefited a maximum of6%. The gains being less by about3.5% may be attributed to changes in speed entangled with that of direction. For the case of = 3 s, prediction seems to be greatly impaired by lack of speed prediction. Although an improvement of 6.8% is seen at faster speeds, xy-compressibility of 52% suggests that an improvement of around 48% is possible in the absence of speed errors. Lastly, faster speeds benefit more from RI (as seen for = 1 and 3 s in Figure 6.1a). This can be explained by the more frequent changes in direction at faster speeds, which given the RI don t contribute to errors in prediction. To summarize, RI is of very little benefit at = 0.2 s. The benefits at of 1 and3s are greater. However, the prediction gains obtained are still limited due to speed prediction errors. Speeds and distances at which prediction gains were obtained Figure 6.1b shows the distribution of mean speeds over time intervals of successful prediction. Even for the traces with fast mean speed, the mean speed during successful prediction is in the slow range (medians are < 30 mph). Successful prediction at of 1 and 3 s is limited to slow speeds. Lastly, in Figure 6.1c we plot the cumulative distribution of the mean predicted distance 7 for the traces of different granularities. For = 0.2 s, 80% of the times (80 th percentile) the mean is 2 m. Road information changes the mean predicted distance by a negligible amount. The 80 th percentile improves by 8 m for traces with = 3 s and by 3.5 m for the traces with = 1 s. The median for = 3 s is less than that for traces with = 1 s, further evidence 5 Speed between two consecutive points in a trace is calculated as the distance between the points in the xy-plane divided by their separation in time. 6 The selection of 41 mph gives equal number of traces with fast and slow mean speeds. 7 The calculation of the mean assumes the predicted distance to be 0 when prediction along a trace fails.

116 99 that prediction gains for larger time granularity traces are impaired by speed prediction errors and the gains achieved are mostly at slow speeds. The increase in the payload of a location update packet is negligible on using LPP with M = n = 1. A network of cars that uses LPP will have to run as many predictors as the number of cars in the network. However, LPP involves extrapolating along a straight line and hence is computationally simple Compression We evaluate the percentage compression achieved using polynomial interpolation (PI), DP and DT algorithms (Section 6.2). The compression gains for coarse grained topologies are shown in Figure 6.2. The gains are evaluated over the traces collected at = 3 s (Section 6.3). The allowed error tolerance is fixed atδ = 0.5 m. In the plot we show gains on using DP, DT and PI using degrees of3and7. PI using degree7, achieves maximum gains (a median of about30%). The next best gains are achieved by DT, a median of about 25%. DP achieves a low of 15% gains. For coarse grained traces, evaluated over different tolerances, polynomials of degree 6-7 gave maximum compression gains. Figure 6.3 shows the compression gains achieved for the traces with = 0.2 s. DP and DT do equally well at compressing the traces, achieving median gains of about 85%. PI, especially using degree n > 3, achieves a tad lesser compression. Given the much greater time complexity of PI, it may not be preferred for compressing fine-grained traces. DT on the other hand does well compressing both fine and coarse grained traces. However, its time complexity is greater than DP. 6.5 Related Work Predictive coding is shown to reduce channel load in [17]. The authors a priori assume a Newtonian model for a vehicle. A Kalman filter update scheme with noiseless observations is used. Predictive coding gains are evaluated using two urban and one highway datasets. In [18] the authors use a Kalman filter estimator approach supported by a variable rate communication scheme to reduce the rate at which safety messages need to be sent.

117 Coarse Grained Trajectories % Compression Gains (DP,0.5,1) (PI,0.5,3) (PI,0.5,7) (DT,0.5,1) (Algorithm, Tolerance, Degree) Figure 6.2: Percentage compression for coarse grained topologies. % Compression Gains Fine Grained Trajectories (DP,0.5,1) (PI,0.5,3) (PI,0.5,7) (DT,0.5,1) (Algorithm, Tolerance, Degree) Figure 6.3: Percentage compression for fine grained topologies.

118 101 In our work we evaluate the predictability of location based on the availability of a certain length of trace of GPS coordinates from the past. The model used for prediction is extracted from the GPS trace. Studies, such as [60, 63, 73], suggest mechamisms at the medium access control (MAC) layer to support high offered load in vehicular networks, instead of coding at each node to reduce the offered load. Compression of spatio-temporal trajectories is studied in [77]. The compressed trajectories should be able to support different database query types. The Douglas-Pecker algorithm is compared with that of Haar wavelets method. In our work we compare the compression gains from Douglas-Pecker algorithm with polynomial interpolation for different trace granularities. An algorithm, that compresses trajectories in xy-plane and then uses line simplification to encode changes in velocity is also compared to DP and polynomial interpolation. 6.6 Conclusions We compared polynomial based schemes for the prediction and compression of GPS trajectories. The schemes were evaluated over a large GPS trace data set of about2500 traces, collected in urban and highway environments. Different GPS trace time granularities were evaluated. Specifically, we conclude Linear polynomial prediction using two most recently known locations, gives the maximum prediction gains. A location update rate of 1 Hz may suffice for vehicles on city roads. GPS traces collected with mean velocities of < 40 mph, and trace granularity of 0.2 s show a high predictability of 80%. Road information has very limited benefit for prediction in city conditions when predicting a 0.2 s trace granularity. At granularities of 1 s and 3 s road information is beneficial, however the additional gains achieved are much lower than expected from xy-compressibility.

119 102 At time granularities of 1 s and 3 s prediction is only successful at low speeds. Traces collected in highway conditions, with mean speeds > 40 mph, showed prediction gains only during stretches when mean speeds were< 30 mph. We compare compression obtained using polynomial interpolation (PI), a distance-time (DT) approach, and Douglas-Pecker (DP). DT performs well across granularities. It does better than PI for the traces at 0.2 s granularity. It performs better than DP by a median of 10% for traces with granularities of1and3s.

120 103 Chapter 7 Effect of Antenna Placement and Cars on Vehicle-to-Vehicle Links 7.1 Introduction Advances in vehicle-to-vehicle communication enable novel safety, driver information, and entertainment applications. Safety applications such as an extended electronic brake light or intersection collision avoidance promise to reduce vehicle accidents by transmitting warning messages to notify cars and their drivers of dangerous situations. To be effective, these applications require low latency and highly reliable vehicle-to-vehicle communication protocols. The development of coding, automatic repeat request, and cooperative retransmission schemes to achieve high reliability all require a detailed understanding of radio propagation. Antenna design for Wireless Access in Vehicular Environment / Dedicated Short Range Communication (WAVE/DSRC) systems is constrained by practical limitations on antenna height and placement, leading to different propagation environments than those found in well studied cellular systems [78], for example. WAVE radios may be packaged in small units for inside windshield mounting, near the rearview mirror, to accelerate deployment. 1 Longer term designs for new vehicles are likely integrated into the car roof but will need to minimize antenna height to protect against vandalism and other damage. Since it is difficult to apply known propagation models to this environment, it is important to empirically characterize the vehicleto-vehicle channel and how different mounting positions affect V2V communications. To inform protocol development for VANETs, prior research has focused on measuring propagation and packet loss patterns(e.g., [79 81]) in different roadway and urban environments. These measurements were conducted with a single antenna mounting position and the simulation models based on these measurements all assume omnidirectional propagation from 1 Several electronic toll collection systems such as EZPass in the New York metro area already use this mounting position for tags.

121 104 each vehicle. Other, prior work in the antenna design community has shown, however, that for the 900 MHz and 2 GHz band [82] [83] [84] achieving omnidirectional propagation with roof-mounted antennas is a non-trivial task. Moreover, these studies show that results vary with the frequency band thus, it remains unclear how Dedicated Short Range Communications at 5.9 GHz are affected by such effects. A unique aspect of vehicle-to-vehicle communication links is the presence of electrically large scatterers in close vicinity. The effect of surrounding vehicles on a link, in typical onroad scenarios, is of significance, especially in the absence of Line of Sight and large static structures. This chapter addresses these challenges by quantifying IEEE a performance using a vehicular testbed with 5 antennas mounted on the rooftop and one inside-windshield position. These a results provide a useful data point for the IEEE p standard under development. Although, our experiments focus on characterizing single link performance the results have direct implications for ad hoc network MAC protocol design. Specifically, key contributions include: Identifying that based communication systems in the 5 GHz band with roofmounted antennas are significantly affected by the car geometry. We characterize the effect on antenna patterns and measure up to 15 db received signal strength differences depending on the angle of arrival in an open space environment under line-of-sight conditions. Results specific to this were earlier presented by the authors in [85]. Confirming that these received signal strength difference are also reflected in significant packet error rate variations over different angle of arrivals and that packet error rates between one stationary vehicle and one moving vehicle fit the two-ray ground reflection model. Showing that signal strength measurements in a freeway environment between two cars following each other may not be well described by a Rician model or a frequently assumed two-ray model. The distribution of received power values is shown to fit the Rayleigh model even in the presence of a few vehicles in the vicinity of the link. Showing that the effect of car geometry can be alleviated through careful choice of the

122 105 mounting position (center mount) or through antenna diversity. The use of multiple antennas also provides improved receiver performance. These multi-radio diversity gains through selecting among multiple antennas and radios are higher than expected even in an LOS environment due to the effect of vehicle geometry. Results specific to this were first presented in [85]. The remainder of this chapter is structured as follows. The next section briefly discusses prior work in empirical channel modeling studies and antenna design. Section 7.3 describes our vehicular testbed and data collection procedures. Section 7.4 describes the results and explores the effect of antenna placements on directionality, effect of vehicle (car) geometry and gains from using more than one antenna. We then show from experiments and via simulation the effect of cars on the communication link, in typical on-road scenarios. Lastly, we discuss protocol design issues in Section 7.6 before concluding in Section Background and Related Work The IEEE p draft standard [9] adapts the IEEE a MAC and PHY to provide increased robustness in an outdoor, high-speed vehicular environment. It is designed to operate at 5.9 GHz and for most applications, it uses transmission powers of up to 2 W Equivalent Isotropically Radiated Power (EIRP). It also allows for EIRP as high as30 W for critical applications like public safety, to enable LOS transmissions up to a distance of1000 m. Despite the use of these high transmission powers, obstructions from roadside features and larger vehicles are expected to affect communication system performance. Since the maximum transmission power is governed by FCC regulations, this motivates research to improve reliability at the antenna and protocol layers. As we pointed out earlier, antenna design for vehicular networks is constrained by vehicle height and deployment considerations. Thus, we expect a range of different designs to emerge. For example, the DSRC community currently considers antenna mounts on the side-mirror, on the rear-center rooftop, and on the windshield inside the vehicle, to name a few. This motivates our work, in which we explore the performance characteristics of different antenna options and discuss their potential impact on protocol design. In [86, 87], the authors emphasize the importance of detailed simulation models to describe

123 106 the wireless channel and point out how changes in these models can affect relative performance of higher-layer protocols. The results of existing measurement studies from indoor environments (e.g., [88, 89] or stationary outdoor mesh networks (e.g., [90]), are not directly applicable to vehicle-to-vehicle communications due to difference in antenna type, height, mounting, rate of change in environment, for example. Thus, several studies have concentrated on short-range vehicle-to-vehicle communications. Using based systems, transport layer throughput and packet loss measurements were conducted by Wu and colleagues [91] for vehicle-to-vehicle and vehicle-to-roadside communications, by Hui and in [81,92] with a special emphasis on multi-hop routing over vehicles, and by Ott and Kutscher [93] for vehicle-to-roadside communications. These studies characterize throughput, latency, and packet loss at the transport layer, they do not characterize propagation effects and antenna dependencies using devices. Channel models for Vehicle-to-Vehicle (V2V) communication were built using empirically measured data by Taliwal and colleagues [80] and for the 60 GHz band in [94]. These studies concentrate on identifying the communication range and on channel modeling and do not address the effects of antenna placement or vehicle orientation on system performance. In [95] measurements in the 5 GHz band, centered at 5.12 GHz, are presented and tap-delay line based statistical models are proposed. The taps may be on or off to emulate channel non-stationarity. Measurements between a TX van and a RX van were conducted in five cities in Ohio, including a few interstate highways. The delay spread and window, and frequency correlations over a 5 MHz bandwidth are measured for the different measured environments. In [96] the authors present narrow-band measurements of the V2V channel at 5.9 GHz. The channel measurements are made between two cars as they drive in suburban Pittsburgh. A total of two data sets are collected. Pathloss models, single and dual-slope, are applied to the measurements and pathloss exponents of 2 to 4 are measured. Log-normal standard deviations of 2.6 db-8.4 db are observed. Doppler spread and Nakagami fading parameters for the data are also presented. It is not clear from the results how specific they are to the suburban Pittsburgh, and also how aspects unique to the V2V channel, specifically the effect of other vehicles in vicinity, impact the measurements. In our work we use ray tracing simulations and mock on-road scenarios with multiple cars to reproduce measured distributions.

124 107 In [97, 98] a ray-tracing based approach is used to model the complete V2V scene. Prior work in the 900 MHz spectrum [83], shows that antenna placement affects antenna pattern distortion, that the top-center position on the roof provides near-omnidirectional coverage, and that signal attenuation up to 10 db can occur inside vehicles [99]. For 2 GHz, nonuniform beam patterns for roof-mounted omnidirectional antennas are reported in [82] due to the potential creation of a local multi-path environment on the vehicle s roof. The construction of an antenna with specialized ground plane for omni-direction coverage is described in [84]. Note that these studies consider lower frequency bands, it remains unclear how significant the effects are in the 5 GHz (V2V) band. This motivates our effort of conducting measurements for an system at 5.18 GHz. Whereas, the previous studies used channel sounding equipment, in our experiments, we concentrate on characterizing received power and packet error rates of an actual, low-cost implementation. 7.3 Experimental Methodology This work seeks to characterize how performance is affected by different antenna placements on vehicles. We concentrate on measuring performance characteristics of a complete system implementation, rather than detailed channel sounding. Our measurements are based on a, since these radios are more readily available, as compared to pre-standard p radios. In addition, a MAC and PHY protocols are similar to those under consideration in the emerging p standard. Both p and a support the same modulation and coding schemes as well as training sequences. However, a few differences remain. The radios use 5.18 GHz, compared to 5.9 GHz DSRC band p does use a larger guard interval, which makes it less susceptible to inter-symbolinterference in outdoor environments. Moreover, it uses 10 MHz channels, which respond differently to frequency selectivity of the wireless channel in such environments. Overall, due to the smaller guard intervals, our a measurements likely serve as a lower bound for future p performance. More importantly, however, our goal is to provide relative performance comparisons of different antenna placements, rather than absolute performance bounds. Insights obtained from these comparisons will likely also be valuable for p designs.

125 108 We choose the received signal strength indicator (RSSI) and packet error rate (PER) as performance metrics. RSSI is an estimate of the signal energy at the receiver, according to the standard it is calculated over the PLCP preamble (12 OFDM symbols in a) of a packet. It is reported by all commodity wireless NICs on proprietary scales. The Atheros 5212 chipset used in our experiments reports RSSI approximately on a db scale, relative to the noise floor). These RSSI measurements can serve only as approximation of true SNR values, which would require calibration with an accurate RF measurement device. However, since they represent SNR as measured by actual radio implementations, we believe that these measurements are of value for practical mechanisms which must depend on RSSI readings in real deployments. Note that neither RSSI nor PER can individually provide complete information on the radio channel. Since a majority of NICs report RSSI only if a frame is correctly detected, mean RSSI measurements are biased toward higher values at the fringes of the communication range. On the other hand, PER is meaningful only at the fringes of the communication range, it provides little differentiation on a good channel where all packets are received. We discuss key aspects of our experimental platform, setup and methodology in the following sections Hardware and Software Configuration Each vehicle contains a small form factor PC with a 1-GHz VIA C3 CPU, 512 MB of RAM, and a 20 GB local hard disk running Debian GNU/Linux with the 2.6 kernel. These nodes are equipped with two IEEE a/b/g interfaces based on the Atheros 5212 chipset (this is the same hardware platform as used in the ORBIT indoor testbed, described in more detail in [100]). In addition, we use Magnetic mount external antennas for2.4/5 GHz. 12-to-120 V power inverter that serves as the power supply (via the car battery). Garmin etrex GPS devices for speed and location.

126 109 Table 7.1: Default Experimental Parameters used Parameter Wireless Card Driver Value Atheros 5212 chipset MadWifi MAC and PHY protocol a Frequency Transmit Power Antenna Type Antenna Gain PHY Data Rate ICMP Payload size Transmission Frequency 5.18 GHz 40 mw folded dipole 3 dbi 6 Mbps 56 bytes 1000 packets per second The main components of the hardware setup are shown in Figure 7.1a. Our software transmits 1000 frames per second at 6 Mbps (the lowest rate), since RSSI is only calculated when a frame preamble is received, and the fade duration in Rayleigh environments can be on the order of milliseconds or less. The use of broadcast mode suppresses MAC-level features such as retransmissions, acknowledgments and RTS/CTS and enables us to measure the packet error encountered due to impairments suffered at the PHY layer. We modified the UNIX ping program to control the duration of time between two outgoing frames, each a 56 byte payload ICMP packet, to be on the order of hundreds of microseconds and assign it the highest run-time priority. Using this approach we were able to consistently generate packets at millisecond granularity, without noticeable packet loss in indoor tests. We chose a low transmit power of 40 mw, to reduce the amount of space needed for our experiments. The results could be scaled to higher transmit powers considered in DSRC. The default parameters used in our experiments are summarized in Table 7.1. Since the association protocol has been changed in p, we disable the a association protocol by operating all receivers in monitor mode. In this mode a node can passively listen to all data on a particular channel without being associated, meaning that packet errors

127 110 can be caused if frames are not detected or corrupted, not by a loss of association. The receiver sniffs the packets from the wireless interface using the tcpdump [101] utility, which gives it relevant information on a per packet basis from both the physical layer (PHY) as well as the MAC layer. Currently, the information captured includes the PHY layer bit-rate, RSSI as measured by the Atheros wireless card, per-frame Atheros receiver timestamp with a microsecond granularity and complete header information (including MAC sequence numbers). The packet error rate (PER) is computed by making use of 32-bit sequence numbers which are incremented by the transmitter for every successive packet. The sequence number is transmitted as a part of the ICMP payload. In addition, all the nodes continuously log their location and speed information using a GPS device once per second. The system time on each node is set to the GPS time so that the system clocks of all nodes are synchronized. The transmitter includes its timestamp in the ICMP packet s payload so that the receiver can correlate its GPS record with the corresponding GPS record of the transmitter. Two cars are used in all experiments, one configured as a transmitter (TX Car) and the other as a receiver (RX Car). Figure 7.1a shows the hardware setup used in the TX Car, which is fitted with a single folded dipole antenna in the center of the roof. The RX Car is fitted with a total of six antennas, and carries 3 PCs, with each antenna connected to one of the six radios. Five antennas are placed on the car roof and one inside the car as shown in Figure 7.1b. As indicated in the figure, the antenna positions are referred to as Front Driver (FD), Behind Driver (BD), Front Passenger (FP), Behind Passenger (BP), Car roof Center (CC), and Rear View mirror (RV). Note that the RV antenna is attached to the mirror inside the car. We conducted experiments to evaluate and understand the effect of different antenna positions on performance of vehicular networks. Below, we list the different experiment scenarios and their objectives Open Space Baseline This experiment evaluates the effect of RX Car geometry on the signal transmitted by the TX Car. The effect of car geometry is the effect on packet reception of the absolute antenna position at the RX Car and the relative orientation of the transmit antenna (at the TX Car) with respect

128 111 to the antenna at the RX Car. The effect can cause asymmetric antenna patterns at the RX Car. We quantify the effect using the metric of per packet RSSI observed at the RX Car. In general the signal received is affected by the signal propagation environment that is a result of various factors like the propagation path, surrounding structures, and mobility of communicating nodes and the surroundings. To reduce effects not due to car geometry, we conduct the experiment in an open space environment with no identifiable nearby scatterers and diffractors. We also begin by characterizing remaining environmental effects using an RX antenna on a tripod stand instead of on the car. The height of the tripod is adjusted to the car height. During the experiment the TX Car transmits packets, see Table 7.1, driving around the tripod in 7 equally spaced circles of radii between 12 feet and 72 feet. Next, the experiment is repeated with the tripod replaced by the RX Car, with its six receiving antennas Parking Lot and Freeway Experiments The parking lot experiments further characterize the magnitude of antenna performance differences in environments with significant scatterers and diffractors and under NLOS conditions. The RX Car drives along three rectangular paths of increasing perimeter around the TX Car, up to a maximum distance of 60 m. Each path is repeated thrice. This experiments aims to collect samples for the same inter-vehicle distance at different locations and with different car orientations, thus it allows averaging out some effects of surrounding structures and other temporal characteristics. Changing orientation of the RX Car with respect to the TX Car will lead to different parts of the RX Car geometry affecting an antenna placed in or on the RX Car. We conducted experiments in two additional parking lots, one office parking lot (WIN- LAB) and one shopping mall lot (WALMART). The WINLAB parking lot is surrounded by office buildings and a number of vehicles were parked on the lot during the experiment. Movement in the environment (other than the experiment cars) was very limited. The WALMART parking lot contains many rows of densely packed vehicles and a shows a continuous influx and outflow of shoppers. Line of sight between the RX Car and TX Car was frequently obstructed at WALMART, but more rarely at WINLAB. We also conducted a similar experiment, although with extended maximum inter-vehicle distance of 250 m, at the Livingston parking lot to provide a baseline for a largely open-space environment, save for sparsely distributed trees

129 112 and street lights on the parking lot. No other fixed structures exist in the vicinity of this parking lot. The freeway experiment is considerably different from a parking lot because both experiment cars are moving, and the presence of other vehicles moving at high speed. We conduct this experiment on a 2.7 mile stretch of US Highway 1, in New Jersey. This is a busy 3 lane freeway and a snapshot of it is shown in Figure 7.1d. The TX Car and the RX Car, drive along this stretch making two loops during moderately high traffic conditions. They maintain an average speed of 50 mph, intermittently switching lanes and overtaking each other, while maintaining a maximum distance of 60 m. 7.4 Experimental Results In this section we present the results of the experiments defined in Section 7.3. We first show that the gain patterns of omnidirectional antennas can be distorted by the effect of car geometry, depending on its position on the car roof and its orientation to the transmitter. We then analyze propagation in the open space and the freeway environment. Next, we compare antenna differences in the busy parking lot environments with the open space scenario. Finally, we discuss an antenna diversity technique than can alleviate pattern distortion and provide additional diversity gains Effect of Car Geometry on Antenna Patterns We perform Experiment Baseline, section 7.3.2, to measure the receive patterns of the six antenna placed at the RX Car. To accomplish this we measure the change in the RSSI received at an antenna placed on the RX Car as the position of the TX Car changes. Note that for a circular path the distance of the transmit and receive antennas remains approximately the same. Given that the experiment is performed under strong LOS conditions, one might expect RSSI to remain constant while the TX Car circles the receiver. Figure 7.2 shows the effect of changing TX Car position on different RX antennas. The RX Car is facing north and is placed at the center of the polar plot. The plots only show the results for 72 ft radius, since other radii lead to similar results.

130 113 From these graphs, we observe that (i) most antennas show strong asymmetric patterns, with up to15 db variance (on Atheros cards one RSSI equals ca. 1 db); (ii) the CC mounted antenna shows the most omnidirectional pattern, apparently the top-center position is also preferable in the 5 GHz band; (iii) the baseline experiment with the tripod mounted RX antenna, in contrast to most other antennas, shows a typical omni-directional pattern. The tripod baseline indicates that the presence of the car geometry affects these measurements. This motivates us to quantify the effect of asymmetric patterns on the communication link between the RX Car and the TX Car Effect of Car Geometry on Communication Link In this experiment the TX Car is parked in one corner of an empty and isolated parking lot. The RX Car drives away and then returns, at a speed of approximately 5 miles per hour. The RX Car s trajectory is a straight line joining placeholders RX Start and RX End (approx. 180 m apart) shown in Figure 7.1c. Figures 7.3a and 7.3b show the RSSI and PER over distance for the FD antenna when the car approaches to and departs from the transmitter, respectively. The dotted lines show empirical measurements, the continuous line indicates results from an analytical two-ray model described below. Consider first the PER plots. The distance at which significant packet errors occur varies in forward and reverse direction by about 100 m (note logarithmic scale), which can be attributed to the asymmetry in antenna patterns observed in the previous experiment. To eliminate possible other factors we repeated similar PER experiments with two other omnidirectional antenna makes, an antenna raised 30 cm over the car roof (by placing it on a cardboard box), and an antenna on an additional steel ground plane (motivated by promising results with such a ground plane in [102]). All antenna types showed significant differences in forward and reverse direction when installed on the car roof. The reported results here are for the least affected antenna. Adding the steel plate provided at best a marginal improvement. As expected, raising the antenna height yielded a significant reduction in packet errors when moving away from the TX, since a higher antenna should be less affected by reflections and diffractions of the car geometry. Further, the graphs indicate that even in this open-space line-of-sight environment a clear

131 114 communication threshold, as modeled in many wireless network simulators (e.g., ns-2), does not exist. Packet error bursts may occur early (compare distance 15) and significant numbers of packets may be received after the PER rate first reached 100%. Comparing the PER and the RSSI plot, consider for example the two marked rectangles in Fig 7.3b, the packet error bursts correlate with drops in RSSI. To explain these drops, consider the two-ray propagation model [2], which describes propagation in a LOS environment with the earth s surface as the only significant reflector. Intuitively, this model appears appropriate for our experimental environment. The spacing of the SNR dips in the model indeed matches well with the RSSI dips in the region where packet errors occur. Interestingly, the two-ray graph shown, however, includes an attenuation factor on the reflected ground component, which we empirically determined to provide a good fit with the measurement results. Without this attenuation factor the two-ray model predicts much more severe signal fading [2] than observed in the measurement results. For clarification, Figure 7.4 shows two-ray propagation without this adjustment, and its piecewise linear approximation that ns-2 uses. The analytical results were obtained with a transmit power of 40 mw, a wavelength of 5.79 cm, and assuming unity antenna gains. 2 A similar observation about the reduction in the magnitude of two-ray fades is reported in [103]. This work attributes the reduction in fading to the presence of multipath components in addition to the direct and ground reflection component. The received power is then statistically defined as a Rician random variable. Although such a model leads to a reduction in the depth of fades, in our environment we were unable to obtain a good fit with the experimental results using even large Rice factors as one would expect for our open-space environment. We believe that the observed attenuation of the reflected component is an artifact of diffraction along the vehicle roof edges and reflections from the roof combined with absence of reflectors/scatterers in the environment that could redirect the scatter to the receiver. 2 The fall of received power in the model can be divided into three segments as shown in the figure. The first segment is for distances less than the transmitter height. Given the small transmitter height in our experiments, 1.3 m, the first segment is of no interest to us. The second segment between the two vertical dotted lines shows considerable fading. The third segment is for distances greater than the Fresnel s breakpoint distance or the critical distance, d c, where the received power falls with a pathloss exponent of4. The received powerp r in the two ray model is given as [ λ ] 2 Gl P r = P t 4π l + R G re j φ x + x 2, where P t is the transmit power (40 mw),λis the wavelength (5.79 cm),g l andg r are antenna gains for the LOS and reflected component respectively (assumed to be unity), φ is the phase difference between the two components, l is the LOS distance between the transmitter and receiver and x + x is the total distance traveled by the ground reflection component. R is the ground reflection component and is 1 for assumptions made under the two ray model [2].

132 Effect on Communication Link in Freeway Scenario In the Freeway scenario, two vehicles follow each other, under moderate traffic conditions, at constant distance, thus free-space loss remains constant. To determine the channel environment, we plot the cumulative distribution function for the empirical RSSI data, and try to fit chi-square, gamma, and exponential distributions to it. The best fit was obtained with the exponential distribution. Figure 7.5a and Figure 7.5b plot the empirical Cumulative Distribution Function (CDF) of the received packet RSSI values (in mw) for packets received at inter-vehicle distances of 50 m and 48 m, respectively (we selected these distances because a sufficient sample size was available for them in the freeway scenario). The empirical CDF is plotted against the exponential distribution that best fit (likelihood-wise) the empirical data. An exponential power distribution is associated with a Rayleigh fading environment which occurs in NLOS conditions (K-factor of 0). Received power in typical Rician fading environment, in contrast, is known to be distributed as a non-central chi-square distribution, with parameters degrees of freedom (number of Gaussian RVs, 2 in our case) and the sum of the squared mean of the Gaussian RVs (related to K-factor of the Rician channel). We conjecture based on the prior results that the placement of antenna on/inside the car leads to scatter that together with reflections from other vehicles and road side structures results in an exponentially distributed received power Effects of Antenna Placement in LOS and Dynamic Multi-path Environment Here, we compare the effect of vehicle geometry in the near-los environment of the isolated Livingston parking lot with the near-nlos multipath environments at the WINLAB and WAL- MART parking lots. These experiments address the question whether the many reflected signal components in a NLOS multipath environment alleviate the observed antenna differences. We choose the cumulative percentage packet error (CPPE) to characterize the relative performance differences due to antenna placement in the following experiment. This metric is

133 116 especially useful when the same distances and locations are repeatedly visited during the experiment. We define the cumulative packet error for distancedas the total count of lost packets at all distances less or equal to d. We can then derive the CPPE through dividing CPE by the total number of packets sent during the experiment. The slope of a CPPE curve corresponding to an antenna position is determined by the number of packet errors at a distance as well as the distribution of distances covered in the experiment, as seen in the results for the parking lot experiments. Since we transmit packets at a constant rate and the RX Car s speed is nearly constant the distribution of distances also determines the percentage of total packets transmitted at a distance. The distribution of the distances affects different antenna CPPE curves in the same way. Figure 7.6 shows the CPPE comparison between all six antennas obtained for the Livingston parking lot experiment. Recall from section 7.3.3, that in this experiment the RX Car with the six antennas drives around the TX Car in rectangles of different size. All antennas (except the inside antenna RV) are in LOS of the TX during the entire experiment. As expected based on the previous results, Figure 7.6 shows that a significant 25% CPPE difference exists between antenna positions. In this particular instance, FD performs best and FP shows the highest error rate, although this can be expected to vary with different environments. Note that RV shows good performance for distances of m after which its performance deteriorates markedly compared to the other antennas. Inspecting the RSSI values of received packets, we find that their mode is about 7 RSSI points higher than other antennas. Its good performance at short distances may be due to less car diffractions and reflections. At longer distances it may be more likely to move into NLOS conditions compared to the other antennas, which would explain its deteriorating performance. Figure 7.7, finally shows the CPPE comparison for the similar experiments in NLOSdominated WINLAB and WALMART parking lots. Here, CC is the best performing single antenna and FD only shows average performance. Note that the difference in PER across antennas is about 25-30% for all parking lots. This shows that the effect of car geometry on antenna performance remained surprisingly stable across these changing propagation environments (NLOS and LOS).

134 Diversity Gains The performance differences across antenna positions at the RX Car motivated us to investigate the gains obtainable by exploiting multiple antennae. Note, that we can only consider Multi-Radio Packet Selection (MRPS), since our antennas are connected to different radios. We consider a packet correctly received if it passes the CRC check on at least one of the radios. This notion differs from traditional diversity techniques at the physical layer, which counter fading [2]. It is more similar in nature to multi-radio diversity which aims to exploits differences in shadowing across widely distributed receivers [104]. Overall prospects for gain appear low, since the antennas are positioned too close for significant differences in shadowing. Still, our results show 10-15% reductions in PER for two antennas at WALMART and even under LOS conditions in the LIVINGSTON experiment, as depicted in Figure 7.8a. A further 5-10% may be acheived by using the best combination of three antennas. Choosing the best combination of four gives a marginal improvement over the combination of three. In terms of PER, the gains for the WINLAB and US1 look smaller, because in these trials the overall number of packet errors was too small. Figure 7.8b shows the gains in term of RSSI, essentially the RSSI difference between the strongest and weakest antenna for packets that were correctly received on all antennas. The plot shows a gain of 2-5 db (on the Atheros hardware one RSSI point is approximately equal to one db). Here, WINLAB and US1 show similar gains. Overall, this indicates that diversity gains can be achieved in the LOS, multipath, and highly dynamic freeway LOS environment. We attribute these gains to the difference in antenna pattern due to the vehicle geometry effect. Figure 7.8c also shows that this diversity technique leads to more omni-directional gain patterns. The graph shows combinations of the FD&BP and FP&BD antennas and both cases show more isotropic patterns than the center antenna. This technique may be useful if center rooftop installation of antennas is not possible (e.g., because of light bars in emergency vehicles, or because devices should be mounted inside cars for ease of installation).

135 Effects of Antenna Placement on Vehicular Protocol Design Our experimental results show that antenna placement significantly affects receiver performance. Even though the antennas specifications claim isotropic gain patterns, figure 7.2 shows that the RSSI patterns of different antenna positions deviates up to 15 db from the ideal isotropic gain patterns. These differences can cause packet errors at surprisingly short distances of 50 m LOS for40 mw transmit power. The following simulations evaluate the effect of these asymmetric patterns in network sizes beyond experimental capabilities. We conduct the simulations using ns-2 with CMU extensions [105] with the following simulation parameters: Number of nodes: 100, Area - 2 Km X 2 Km, Speed: 40 m/s, Mobility model: random waypoint Transmission range: 250 m, Carrier sense range: 550 m. Packet size: 100 bytes, sent periodically (period selected randomly from (0.75, 1.25) seconds), Simulation time: 500 seconds. We further modified the propagation model to account for antenna asymmetry. For each antenna in Figure 7.2, to approximate antenna patterns observed in experiments. The received signal strength is first calculated through ns-2 s 2-slope two-ray propagation model. We then subtract the gain loss based on angle of arrival, which is obtained from a lookup table initialized with the empirical data. As in the default ns-2 model, a packet will be received if the resulting signal strength is greater than a reception threshold. Note that channel utilization is very low and we expect packets to be in error due to limited transmission range or hidden-node collisions, rather than MAC collisions due to congestion. Table 7.2 shows the number of correctly received packets at different antenna positions assuming the asymmetric antenna patterns plotted in Figure 7.2. For each antenna position, we sum packets received at all the 100 nodes. The last row, corresponding to the Ideal Antenna, represents an antenna with unity omni-directional gain. In other words, RSSI for each received

136 119 Table 7.2: Simulation results. Antenna Position #(packets received) %(packets received) FP RV BP BD FD Tripod CC Ideal Antenna packet is obtained using the two-slope propagation model alone, without considering any antenna effects. Our observations are as follows. Since we are only considering the propagation environment, the Ideal Antenna receives the maximum number of packets and outperforms other antenna positions. CC performs second best. which may be attributed to the antenna pattern of CC, which is very close to omni-directional. Similarly, the poor performance of FP can be explained by its antenna pattern, which has a lot of significant dips in RSSI with changing angle. In summary, we observe significant imbalances between the different antenna positions, in terms of number of successfully received packets. This will have implications for reliability protocols at the MAC layer Discussion We expect that our results could have serious implications on the behavior of higher layer protocols and vehicular networking applications. At the MAC layer, these RSSI patterns could imply hidden terminal problems [106] (due to asymmetric directional gain and the ineffectiveness of RTS/CTS frames), specifically associated with the use of directional antennas. Node deafness [107] is another problem that could arise, where two nodes are unable to communicate because their antenna beams are formed in different directions. At the network layer, neighbor discovery (a node needs to be aware on which antenna beam its one hop neighbors lie

137 120 on) [108] could be affected by the non-uniform RSSI gains reported here. Further, our results (in section 7.5), which show the advantages of using multiple antennas on a car s roof, motivate further investigation of diversity techniques in higher layer protocols (e.g., [104]). From an applications perspective, safety messages need to be delivered with low latency and high reliability. Differences in the assumptions made about the effect of antenna position can lead to significant differences in the results of different broadcast protocols. We also hope that our results motivate, and contribute toward the continuous improvements to simulation models for VANETs. 7.7 Conclusions This chapter presented a study of the effect of antenna position and other vehicles on vehicle to vehicle communication links that use frequencies in the5ghz band. We have measured the relative performance of several vehicle mounted antennas connected to a radios in terms of packet error rate and received signal strength indicator, in an open space isolated parking lot, populated parking lots, and a freeway environment. Specifically, we observed that Antenna gain patterns of omnidirectional antennas become asymmetric in many mounting positions, showing distortions with a spread of up to 15 db over different angles of arrival for an a radio at 5.18 GHz. This effect is caused by scattering and diffractions from the vehicle geometry. Antenna positions lead to25-30% difference in cumulative link PER performance in our experiments using the5ghz band, the band of interest for V2V communications. Propagation between a stationary and a moving vehicle in an open-space environment can be modeled with an attenuated ground reflection component in the two-ray ground reflection model. No clear communication range exists, rather several packet error bursts occur before loss of the communication link. The vehicle-to-vehicle channel between the transmitter and receiver in a freeway environment and moderate traffic conditions is better modeled as Rayleigh than Rician or the often assumed two-ray model.

138 121 Via ray-tracing simulations we show that a cluster of very few vehicles in close vicinity of the transmitter and/or receiver can lead to a Rayleigh faded communication link. A packet level diversity technique that collects packets received from all antennas at the receiver and discards duplicates can provide 10-25% gains in packet reception rate and 2-5 db gains in received packet RSSI in vehicular networks, even in strong LOS environments, as it alleviates the effect of vehicle geometry. This provides an alternative if center mounting of the antenna is not feasible. We have also discussed the effect of these observations on vehicular network applications. As future work, we plan to build channel models for different antenna configurations in different propagation environments with emphasis on geometries that are typical to on-road traffic. Such models will be integrated with current network simulators (e.g., NS-2) for more realistic simulations. We are also investigating the tuning of parameters in previously proposed protocols and applications for vehicular networks given the observations mentioned in this work.

139 122 (a) The hardware setup is replicated in(b) Antennas positions used in experi-(cments. The experimental scenario every vehicle. with stationary sender and mov- ing receiver in an empty parking lot and line of sight communication. (d) A satellite view of the path traversed by the Freeway experiment. The TX and RX cars made two complete loops of this trajectory. Figure 7.1: Experiment scenario, hardware setup and placement of antennas

140 FP RV CC Tri (a) BD FD BP Tri (b) Figure 7.2: RSSI received at antenna (a) BD, FD, BP and (b) FP, RV, CC, compared to the antenna on a tripod.

141 124 RSSI RSSI, RX Car moving towards RX Car Two ray Model PER *log10(d) (a) RX Car moving towards the TX Car. RSSI (dbm) RX Car moving away from TX Car Two ray X: Y: Packet Error Rate * log 10 (d c ) * log10(d), d is the distance between TX Car and RX Car (b) RX Car moving away from TX Car. Figure 7.3: Empirical PER, RSSI and the Two Ray model.

142 Figure 7.4: The Two-ray ground reflection model. The illustration is from [2]. The piecewise approximation is drawn at an offset for clarity [2]. 125

143 126 1 F(x) exponential(mean = 1.273e 007mW) empirical data RSSI (mw) x 10 6 (a) Cars at a distance of 50 m RSSI samples 1 F(x) exponential(mean = 3.05e 007mW) empirical cdf RSSI (mw) x 10 6 (b) Cars at a distance of 48 m RSSI samples Figure 7.5: Empirical CDF plotted against exponential and gamma distributions.

144 127 CPPE BD FD FP RV BP CC distance(m) Figure 7.6: CPPE comparison of antenna positions, Livingston parking lot experiment (section 7.3.3).

145 128 CPPE BD CC RV FD FP BP distance(m) (a) CPPE BD FD FP RV BP CC distance(m) (b) Figure 7.7: Performance comparison of antennas at (a) WALMART and (b) WINLAB.

146 129 PER (Packet Error / Sec) Single Two Three Four WINLAB WALMART Livingston US1, NJ (a) Diversity gains, in terms of PER. Combined RSSI values Single Two Three Four 5 0 WINLAB WALMART Livingston US 1, NJ (b) Diversity gains in terms of RSSI BP+FD BD+FP CC (c) Smoothing of antenna patterns using diversity Figure 7.8: Diversity gains using MPRS. Comparison of the best single antenna with the combination of best 2, 3 and 4 antennas.

147 130 Chapter 8 Vehicle-to-Vehicle Short Range Channel Modeling 8.1 Introduction Understanding of wireless propagation between any two on-road vehicles is an important step towards deploying a variety of applications over networks of vehicles. Unlike cellular, in many vehicle-to-vehicle communication scenarios both transmitting and receiving antennas are at similar heights and close to the ground. Also, both the transmitter and receiver may experience continuously changing scatterers in their vicinities. The scatterers are either large and static, for example buildings and the ground (road), and/or small and mobile, for example other onroad vehicles. The mobile scatterers while much smaller than buildings have dimensions much larger than wavelengths in the band of interest (5 GHz), are not point scatterers, often have the transmitter and receiver in their near field, and can lead to scattering patterns that may not be modeled as simple reflection or obstruction. In this work we perform an empirical study of a small set of on-road scenarios in which the wireless channel is affected only by the mobile scatterers in vicinity of the transmitting and the receiving vehicle, and by the ground. Most of the related work in the 5 GHz band make measurements in less controlled environments making it difficult to distinguish the effect of small mobile scatterers from the large static ones, the effect of which has been modeled earlier in cellular environments [2]. Our scenarios involve scatterer vehicles passing by the transmitter vehicle (TX) and the receiving vehicle (RX) while the RX approaches the TX. The RX and the TX are always within 50 m of each other. There a maximum of 4 other vehicles in their vicinity. The scenarios are chosen to represent a 1-4 lane road network. The study is carried out in a vacant parking lot, which allows us to perform the experiments in a controlled setting. The obtained measurements are also modeled using sum-of-sinusoid models, which can be used in simulation environments

148 131 of vehicular networks. Specifically, our contributions include: Measurements of path loss vs. distance for a wide array of short-range V2V scenarios. Use of the measurements to assess the benefits of simple dual diversity in these scenarios. Derivation, from the pathloss (PL) measurements, of a model for PL(d) as a sum of 4 sinewaves, and tabulation of the model parameters for all scenarios. Use of the model to predict link performance, and comparison of the predictions with those based on the measurements. Our contributions are organized as follows. In Section 8.2 we describe the measurement setup and all the scenarios that were measured. Section 8.3 proposes a multi-sinusoid model and evaluates it using the metric of error in channel gain prediction. We also show a comparison of the BER performance achieved by a system that uses the actual measurements and one that uses the model, under the assumption of quantized transmit power levels. Model parameters for all scenarios are tabulated too. The section ends with a tabulation of possible diversity gains if two antennas separated by0.5 1 m are placed on the RX car roof. In Section 8.4 we describe the related works. We summarize our contributions in Section Measurement Methodology and Scenarios We attempt to capture a representative set of physically possible scenarios over a 1 4 lane road network when the communicating cars TX and RX are within a distance of about 50 m, with up to four other cars in their vicinity. We next describe the scenarios and their orchestration. At the beginning of all scenarios, see Figure 8.2, the transmitter TX is stationary and the RX is about 50 m from the TX. We are only interested in the relative motion between the TX and the receiver car RX. In all scenarios the car RX approaches the TX. The RX maintains a speed of about 1 mph till it reaches the TX or passes it (if not in the same lane), at which time the measurement of the scenario comes to a halt. The goal is to capture the variation in received power as a function of distance between the TX and RX as other cars, scatterers and obstructors, move in the vicinity of, go past and/or come in between, the TX and RX. In every scenario, the other cars move at speeds of about3mph.

149 132 Figure 8.2 exemplifies how power measurements are made during a typical scenario. In the scenario the TX and RX are in the same lane. There are two other cars in the lane to their right. Snapshot I shows the placement of cars at the start of the scenario. The selected scenarios differ from each other in their initial placement of the cars. The example scenario has two cars move in the lane adjacent to that of the TX and RX. Since the other cars move faster, they reach/pass the TX before the RX. This enables us to measure the affect of the two cars passing, for various distances between the RX and the TX. Measurement of the scenario is made in multiple snapshots. A snapshot ends when either the RX or all the other cars have passed/reached the TX. We stop the RX and pause measurements at the end of a snapshot, reset the positions of the other cars with respect to the RX as in the beginning of the measurement and then restart the measurements, that is start measuring a new snapshot. Snapshots are created till the RX reaches the TX, which marks the end of measurement of the scenario. The measurement of the scenario in Figure 8.2 spans three snapshots, as do most other scenarios, because the other cars move thrice as fast as the RX. Scatterer cars in the same lane always maintained a safe following distance during a measurement while maintaining a speed of about 3 mph. Figure 8.3 shows all the scenarios measured. Scenarios A, B, C and D, shown in figures 8.3a, 8.3b, 8.3c and 8.3d, respectively, are sets of measurement scenarios. For example, Scenario A consists of a total of 11 scenarios, including the one depicted in Figure 8.2, which contains two scatterers and 0 lanes in between the lane containing the scatterers and that containing the TX and RX. The output of a scenario measurement is a vector of power (squaredamplitude) measured at the receiver and a corresponding vector of the distance between the TX and RX, which we obtain using the GPS co-ordinates that are logged at5 Hz at both the TX and the RX. The power and GPS measurements come with timestamps that are used to synchronize the measurements at the RX and the TX. Note that when discussing measurement results we show gain at a distance, which we derive from the power measurement obtained from the spectrum analyzer by assuming that free-space propagation models the channel between the TX and the RX at the end of a measurement scenario. At the end of all scenarios the receiver is very close to the TX, with the line-of-sight component the most dominant, and power measurements are seen to fit a path loss exponent of 2 well. Later, we will model the relationship between

150 133 (a) Transmitter Setup (b) Receiver Setup Figure 8.1: Measurement setup installed at the transmitter and receiver on the car. the measured gain and the TX-RX distance using parametric sinusoid models. Next, we briefly describe the hardware setup at the TX and the RX Experiment Setup The TX and RX cars use roof mounted omni-directional antennas, as shown in Figure 8.1. The transmitter at the TX is a MITEQ 1 frequency synthesizer capable of generating a sinusoidal signal in the 5 GHz band. We set its output frequency to 5.5 GHz in all our experiments. The synthesizer is powered by a battery, also shown in the figure 2. A Garmin 3 GPS device is placed adjacent to the antenna and logs the position of the TX at the rate of5locations every second. The RX car receives the transmitted signal using a Tektronix SA2600 portable spectrum analyzer. The analyzer has an inbuilt GPS device that logged location at a rate of 5 Hz. Its antenna was placed adjacent to the RF receive antenna mounted on the RX car s roof. The center frequency at the analyzer is set to 5.5 GHz and its receive bandwidth to 5 KHz. We configure the analyzer to make amplitude vs. time measurements Previous attempts to power the transmitter through an inverter connected to the car batteries introduced a low frequency noise in the transmission when the TX car s ignition was turned on. 3