ROBUST-INTELLIGENT TRAFFIC SIGNAL CONTROL WITHIN A VEHICLE-TO-INFRASTRUCTURE AND VEHICLE-TO-VEHICLE COMMUNICATION ENVIRONMENT.

Transcription

1 ROBUST-INTELLIGENT TRAFFIC SIGNAL CONTROL WITHIN A VEHICLE-TO-INFRASTRUCTURE AND VEHICLE-TO-VEHICLE COMMUNICATION ENVIRONMENT By Qing He Coyright Qing He 2010 A Dissertation Submitted to the Faculty of the DEPARTMENT OF SYSTEMS AND INDUSTRIAL ENGINEERING In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2010

2 UMI Number: All rights reserved INFORMATION TO ALL USERS The quality of this reroduction is deendent uon the quality of the coy submitted. In the unlikely event that the author did not send a comlete manuscrit and there are missing ages these will be noted. Also if material had to be removed a note will indicate the deletion. UMI Coyright 2010 by ProQuest LLC. All rights reserved. This edition of the work is rotected against unauthorized coying under Title 17 United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor MI

3 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee we certify that we have read the dissertation reared by Qing He entitled Robust-Intelligent Traffic Signal Control within a Vehicle-to-Infrastructure and Vehicle-to-Vehicle Communication Environment and recommend that it be acceted as fulfilling the dissertation requirement for the Degree of Doctor of Philosohy Date: 07/23/2010 K. Larry Head Date: 07/23/2010 Wei-Hua Lin Date: 07/23/2010 Mark Hickman Date: 07/23/2010 Yi-Chang Chiu Final aroval and accetance of this dissertation is contingent uon the candidate's submission of the final coies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation reared under my direction and recommend that it be acceted as fulfilling the dissertation requirement. Date: 07/23/2010 Dissertation Director: K. Larry Head Date: 07/23/2010 Dissertation Director: Wei-Hua Lin

4 3 STATEMENT BY AUTHOR This dissertation has been submitted in artial fulfillment of requirements for an advanced degree at the University of Arizona and is deosited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without secial ermission rovided that accurate acknowledgment of source is made. Requests for ermission for extended quotation from or reroduction of this manuscrit in whole or in art may be granted by the coyright holder. SIGNED: Qing He

5 4 ACKNOWLEDGEMENTS I would like to exress my dee gratitude to my advisor Dr. K. Larry Head for his guidance and suort on this research in ast several years. He rovides me not only research insights and suggestions but also the way to work with other eole and the way to deal with different kinds of issues. He is a great advisor as well as a great mentor. Also I areciate numerous hel and suort from my co-advisor Dr. Wei-Hua Lin. I learned so much from him on traffic flow theory traffic models and logistics. I want to thank Dr. Mark Hickman for teaching me urban lanning transit and traffic assignment. Also I want to thank Dr. Yi-Chang Chiu for teaching me traffic engineering traffic assignment and roviding lots of research sources. I am grateful to Professor Pitu Mirchandani for his long term suort on my research and study in ATLAS center. The research was suorted by Arizona Deartment of Transortation ADOT). I want to exress my thanks to Faisal Saleem from Maricoa County of Transortation MCDOT) Ravi Puvvala Ramesh Siriurau and Sreenivasulu Guduguntla from Savari Networks Michael Hicks and Simon Ramos from City of Tucson Deartment of Transortation. Secial thanks to my fellow graduate student Jun Ding in the lab. Jun hels me solve the roblems on the roject share the research exerience and build the simulation models in my dissertation. Last but least I wish to exress my deeest gratitude to my wife Cheng Zhu and my arents who have been constant source of motivation encouragement and insiration.

6 5 DEDICATION To my wife Cheng Zhu Thanks for your love strength and atience in my life.

7 6 TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES ABSTRACT CHAPTER 1: INTRODUCTION Current traffic control systems IntelliDrive SM - advanced vehicle communications and caabilities Research objectives Pseudo-lane-level GPS ositioning Robust multile riority control within a v2x environment Multi-modal traffic control within a v2x environment Summary of the dissertation CHAPTER 2: LITERATURE REVIEW U.S. IntelliDrive SM VII) California Michigan New York Virginia Arizona... 43

8 7 TABLE OF CONTENTS Continued 2.2 Traffic Signal Control Fixed-time traffic signal control Actuated traffic signal control Adative traffic signal control Probe vehicle technology Traffic state and travel time estimation with robe data Traffic control with robe data Summary CHAPTER 3: PSEUDO-LANE-LEVEL LOW-COST GPS POSITIONING WITH VEHICLE-TO-INFRASTRUCTURE COMMUNICATION AND DRIVING EVENT DETECTION Introduction The V2I ositioning environment Extended Kalman filter Lane status monitor EWMA SPC control chart Turn event-driven lane alignment otimization Field data results Summary... 99

9 8 TABLE OF CONTENTS Continued CHAPTER 4: ROBUST ACTUATED PRIORITY TRAFFIC SIGNAL CONTROL WITH VEHICLE-TO-INFRASTRUCTURE COMMUNICATIONS Introduction Phase-time diagram: a new tool to model traffic signal controller logic Deterministic mixed integer linear rogram MILP) formulation Robust mixed integer linear rogram MILP) formulation Integration of robust MILP formulation and actuated control Green extension reresentation in MILP Green extension grou GEG) and a k reassignment Robust signal coordination with riority Numerical exeriments Summary CHAPTER 5: A HEURISTIC ALGORTIHM TO IMPLEMENT MULTIPLE PRIORITY CONTROL FOR EMBEDDED CONTROL AT A SINGLE INTERSECTION Introduction Simlification of multile riority control roblems Simlification to a olynomial solvable roblem Revised exhaustive search algorithm and delay evaluation

10 9 TABLE OF CONTENTS Continued Simulation results Field imlementation System structure RSE and OBE introductions NTCIP imlementation DSRC field exeriences Field tests Summary CHAPTER 6: PAMSCOD: PLATOON-BASED ARTERIAL MULTI-MODAL SIGNAL CONTROL WITH ONLINE DATA Introduction Platoon-based signal otimization Hierarchical latoon recognition Mixed integer linear rogram MILP) in PAMSCOD Unified recedence constraints Platoon delay categorization and evaluation Multi-modal dynamical rogression Formulation enhancement

11 10 TABLE OF CONTENTS Continued Objective and summary of PAMSCOD Design of exeriment Illustration of solutions from PAMSCOD Exeriment results Summary CHAPTER 7: CONCLUSIONS AND FUTURE RESEARCH Summary of the Research Pseudo lane-level GPS ositioning in a v2x environment Multile riority control and field imlementation in a v2x environment Multi-modal traffic control in a v2x environment Future Research Toics REFERENCES

12 11 LIST OF FIGURES Figure 1.1. Tyical intersection with detectors Figure 1.2 IntelliDrive SM VII) architecture data flow Faradyne 2005) Figure 1.3 Intersection layout with multile riority requests Figure 2.1 Actuated hase timing diagram Federal Highway Administration 2008) Figure 2.2 Coordination on a time-sace diagram Sunkari et al. 2004) Figure 2.3 a) Pre-defined slits; b) Fixed force-offs imlementation; c) Floating forceoffs imlementation Figure 3.1 Intersection layout defined in a MAP Figure 3.2 The GPS error in the test site in Tucson AZ Figure 3.3 A driving event of making a turning maneuver and the actual and the uncorrected measured osition before and after the event Figure 3.4 GPS ositioning System Structure Figure 3.5 A lane changing model Figure 3.6 The relationshi between and T given 0. 4 l n 3. 2m and lane v k 13.33m / s Figure 3.7 a) An examle of vehicle events detection; b) Events detection with EWMA control chart Figure 3.8 a) GID ma with inbound-outbound trajectory of two tye turns; b) Line aroximations for inbound-outbound trajectories of right turn Figure 3.9 The test intersection in Tucson AZ... 96

13 12 LIST OF FIGURES Continued Figure 3.10 GPS noncommon-mode error fixed by lane alignment otimization for the left turn event Figure 3.11 Lane change detection by SPC control chart Figure 4.1 Dual-ring eight-hase controller Figure 4.2 Precedence grah reresentation of a dual-ring controller Figure 4.3 Phase-time diagram reresentation of a dual-ring controller Figure 4.4 a) A cyclic serving rectangle CSR) for an interval riority request; b) Four ossible service cases for a CSR Figure 4.5 Reresentation of flexible signal lan for actuated control Figure 4.6 The rocedure for generating GEG in a ring Figure 4.7 a) An examle of green extension grou and reassignment; b) Green extension reassignment in GEG Figure 4.8 Priority requests with coordination Figure 4.9 Evaluation latform Figure 4.10 Layouts of a two-intersection arterial Figure 4.11 Overall vehicle delay and bus delay under ASC-TSP coord. and Robust riority coord Figure 4.12 Side bus delay and left-turn delay under ASC-TSP coord. and Robust riority coord Figure 4.13 overall vehicle delay and bus delay with or without riority control Figure 5.1 Illustration of searation of J requests into K cycles

14 13 LIST OF FIGURES Continued Figure 5.2 Priority request assignment table for hase in two cycles Figure 5.3 Revised exhaustive algorithm to find the near-otimal solutions Figure 5.4 a) CSRs on the hase-time diagram b) Phase-time diagram evaluation of an assignment of serving R 22 in the second cycle Figure 5.5 Performance comarisons of five different methods a) Average total vehicle delay; b) Average bus delay; Figure 5.6 Test intersection layouts at Southern Ave. & 67 Ave. Phoenix AZ Google Earth) Figure 5.7 System structure of field imlementation Figure 5.8 RSE installnations a) Inside cabinet for demonstration uroses); b) On a ole Figure 5.9 OBE installation Figure 5.10 Web age dislays a) OBE aroaches a intersection; b) OBE receives MAP and request table; c) OBE sends a riority request; d) OBE travels through the intersection. GID is a former name of MAP in SAE J2735) Figure 5.11 NTCIP tree structure of reds grou 1 in ASC controller Figure 5.12 DSRC communication ranges: a) A urban intersection; b) A suburban intersection Figure 5.13 Field tests a) REACT vehicles ready to test; b) A riority request is being served

15 14 LIST OF FIGURES Continued Figure 5.14 a) CSRs of two requests on the hase-time diagram b) Phase-time diagram evaluation of an cut of serving both requests in the first cycle Figure 6.1 a) Original oint vehicles on a link; b) Platoon one-dimensional maing and 2-level clustering with 2s and 1s headways resectively Figure 6.2 a) Intersection layout; b) A dual-ring eight-hase controller Figure 6.3 Precedence grah reresentation of a dual-ring controller at intersection i Figure 6.4 An examle illustrate currently active hases at intersection i Figure 6.5 Platoon serving cycle selection Figure 6.6 a) Queue delay when two latoons are served in the same cycle; b) Queue delay and signal delay when two latoons are served in different cycles Figure 6.7 Signal delay evaluation for the leading latoon Figure 6.8 Queue delay and signal delay at downstream intersection Figure 6.9 Evaluation latform Figure 6.10 Seedway arterial in Tucson AZ Figure 6.11 Comarisons between otimized cycle length from SYNCHRO and average cycle length in PAMSCOD at two critical intersections. a) Intersection at Euclid & Seedway; b) Intersection at Cambell & Seedway Figure 6.12 Online otimized signal lan from PAMSCOD when SR=0.9 in set 3 intersection 1 is in the bottom) Figure 6.13 a) Network throughut; b) Average all vehicle delay on each hase at each intersection. c) Average bus delay on each hase at each intersection

16 15 LIST OF TABLES Table 3.1 Probability of no lane drift for turns in NGSIM data Table 3.2 Exerimental Results Table 4.1 Symbol definition of decision variables and data Table 4.2 Traffic volume for seedway Table 4.3 Descrition of comared different methods Table 4.4 Basic otimal coordination timing lan from SYNCHRO Table 4.5 Measured average delay under each scenario with eight different methods Table 4.6 Delay changes from ASC-TSP to robust riority %) Table 5.1 Delay increment %) from Robust free to Heuristic Table 5.2 Field test scenarios and results Table 5.3 Field test data with two conflicting riority requests on March Table 6.1 Notation definition of decision variables lower case) and data uer case) 190 Table 6.2 Four sets of stochastic traffic volume under seven different saturation rates. 225 Table 6.3 Performance comarisons with four methods Table 6.4 Performance imrovements of PAMSCOD comared with other methods

17 16 ABSTRACT Modern traffic signal control systems have not changed significantly in the ast years. The most widely alied traffic signal control systems are still time-of-day coordinated-actuated system since many existing advanced adative signal control systems are too comlicated and fathomless for most of eole. Recent advances in communications standards and technologies rovide the basis for significant imrovements in traffic signal control caabilities. In the United States the IntelliDrive SM rogram originally called Vehicle Infrastructure Integration - VII) has identified 5.9GHz Digital Short Range Communications DSRC) as the rimary communications mode for vehicle-to-vehicle v2v) and vehicle-to-infrastructure v2i) safety based alications denoted as v2x. The ability for vehicles and the infrastructure to communication information is a significant advance over the current system caability of oint resence and assage detection that is used in traffic control systems. Given enriched data from IntelliDrive SM the roblem of traffic control can be solved in an innovative data-driven and mathematical way to roduce robust and otimal oututs. In this doctoral research three different roblems within a v2x environment enhanced seudo-lane-level vehicle ositioning robust coordinated-actuated multile riority control and multimodal latoon-based arterial traffic signal control are addressed with statistical techniques and mathematical rogramming. First a seudo-lane-level GPS ositioning system is roosed based on an IntelliDrive SM v2x environment. GPS errors can be categorized into common-mode errors and noncommon-mode errors where common-mode errors can be mitigated by

18 17 differential GPS DGPS) but noncommon-mode cannot. Common-mode GPS errors are cancelled using differential corrections broadcast from the road-side equiment RSE). With v2i communication a high fidelity roadway layout ma called MAP in the SAE J2735 standard) and satellite seudo-range corrections are broadcast by the RSE. To enhance and correct lane level ositioning of a vehicle a statistical rocess control aroach is used to detect significant vehicle driving events such as turning at an intersection or lane-changing. Whenever a turn event is detected a mathematical rogram is solved to estimate and udate the GPS noncommon-mode errors. Overall the GPS errors are reduced by corrections to both common-mode and noncommon-mode errors. Second an analytical mathematical model a mixed-integer linear rogram MILP) is develoed to rovide robust real-time multile riority control assuming enetration of IntelliDrive SM is limited to emergency vehicles and transit vehicles. This is believed to be the first mathematical formulation which accommodates advanced features of modern traffic controllers such as green extension and vehicle actuations to rovide flexibility in imlementation of otimal signal lans. Signal coordination between adjacent signals is addressed by virtual coordination requests which behave significantly different than the current coordination control in a coordinated-actuated controller. The roosed new coordination method can handle both riority and coordination together to reduce and balance delays for buses and automobiles with real-time otimized solutions. The robust multile riority control roblem was simlified as a olynomial cut roblem with some reasonable assumtions and alied on a real-world intersection at Southern Ave. & 67 Ave. in Phoenix AZ on February and March The

19 18 roadside equiment RSE) was installed in the traffic signal control cabinet and connected with a live traffic signal controller via Ethernet. With the suort of Maricoa County s Regional Emergency Action Coordinating REACT) team three REACT vehicles were equied with onboard equiments OBE). Different riority scenarios were tested including concurrent requests conflicting requests and mixed requests. The exeriments showed that the traffic controller was able to erform desirably under each scenario. Finally a unified latoon-based mathematical formulation called PAMSCOD is resented to erform online arterial network) traffic signal control while considering multile travel modes in the IntelliDrive SM environment with high market enetration including assenger vehicles. First a hierarchical latoon recognition algorithm is roosed to identify latoons in real-time. This algorithm can outut the number of latoons aroaching each intersection. Second a mixed-integer linear rogram MILP) is solved to determine the future otimal signal lans based on the real-time latoon data and the latoon request for service) and current traffic controller status. Deviating from the traditional common network cycle length PAMSCOD aims to rovide multi-modal dynamical rogression MDP) on the arterial based on the real-time latoon information. The integer feasible solution region is enhanced in order to reduce the solution times by assuming a first-come first-serve disciline for the latoon requests on the same aroach. Microscoic online simulation in VISSIM shows that PAMSCOD can easily handle two traffic modes including buses and automobiles jointly and significantly reduce delays for both modes comared with SYNCHRO otimized lans.

20 19 CHAPTER 1 INTRODUCTION Traffic signals lay an imortant role in the transortation network of urban areas. With correct installation and control strategy they can imrove both traffic throughut and the safety of all road users. As indicated in the 2007 National Traffic Signal Reort Card an otimally oerated traffic signal can reduce traffic delay by 15~40 ercent fuel consumtion u to 10 ercent and harmful emission u to 22 ercent National Transortation Oerations Coalition 2007). Today there are more than traffic signals in the United States National Transortation Oerations Coalition 2007). The use of traffic signals at a busy intersection in a tyical urban area might direct the movement of as many as vehicles er day. It is estimated that many of these signals could be imroved by udating equiment or by simly adjusting and udating the timing lans. Outdated or oor traffic signal timing accounts for a significant ortion of traffic delay on urban arterials and traffic signal retiming is one of the most cost effective ways to imrove traffic flow and is one of the most basic strategies to hel mitigate congestion. The U.S. Deartment of Transortation s U.S. DOT) Intelligent Transortation Systems Joint Program Office maintains a benefit-cost database that documents many traffic signal studies from across the United States. These studies show that there is as much as a 1:40 cost-benefit from

21 20 signal retiming. That is the benefits of investing in signal timing outweighs the costs by as much as 40:1 Sunkari 2004). Desite their imortant role in traffic management traffic signals once installed are often not roactively managed. Maintenance activities are frequently delayed or canceled in reaction to shrinking budgets and staffs. More than half of the signals in North America are in need of reair relacement or ugrading Federal Highway Administration 2008). In 2007 the National Traffic Signal Reort Card concluded that the nation scored a D in terms of the overall quality of traffic signal oeration if the nation suorted its signals at an A level. Therefore traffic signal timing lays a critical role within the overall transortation network. Signal timing offers the oortunity to imrove the mobility and safety of the signalized street transortation system as well as to imrove environmental conditions that result from vehicle emissions due to inefficient signal oerations. According to the many imroer imlementations in United States Federal Highway Administration 2008) there is a growing oortunity to imrove the strategy of traffic signal control. This dissertation is intended to address oortunities to imrove traffic signal control under new and emerging oortunities in advanced communications and an enriched data environment in a multi-modal transortation environment. 1.1 Current traffic control systems The state-of-the-art in traffic control today is actuated traffic signal control where different conflicting movements of vehicles are controlled by hases that are called by

22 21 detectors when vehicles are resent. Figure 1.1 deicts a tyical intersection where resence detectors exist at each of the minor traffic movements - which include the main street left turns and side street movements. These resence detectors will call e.g. request service) from the associated movement hase when a vehicle arrives at the detector. In addition sometimes assage detectors are used to call a hase as well as to extend the green time as a vehicle aroaches the intersection. Extension intervals are tyically timed to rovide sufficient time for a vehicle to clear the intersection sto bar after they cross the fixed detector osition. The details of current traffic control systems will be introduced in Chater 2. Adjacent intersections or collections of intersections on an arterial or a grid can be coordinated to allow vehicles to rogress along the arterial or desired direction of vehicle travel. Each intersection oerates using the same actuated control rinciles as single isolated intersection but constrained by a timing lan that can rovide coordination through a fixed cycle length offset and hase slits.

23 22 Figure 1.1. Tyical intersection with detectors The cycle length is tyically chosen to rovide sufficient time to serve all vehicles and edestrians on all movements. Phases that are not called may be skied and if so return their allocated green slit time to the following hase or to the main-street coordinated hase. The offset is defined to be the amount of time between start of green at one intersection and the associated green at a downstream intersection and is selected to rovide rogression in at least one direction generally the direction with the largest volume of traffic) and ossibly both directions. Generally the offset is set to be the travel time between intersections lus some time for a standing queue to clear before a vehicle from the ustream signal would arrive. The slits are selected to rovide sufficient time for each hase to serve the traffic movement demand. Minor hases are allowed to ga

24 23 out before the entire slit is timed if no vehicles generate/request an extension from the detectors. A signal timing lan that contains a cycle length offset and hase slits may be defined for each characteristic traffic attern that might result from time-of-day demand - such as morning and evening commutes or secial events such as sorting events school shoing center activities etc. Signal timing lans are sometimes defined for secial weather conditions such as snow ice and rain. Generally signal timing lans are selected on a time-of-day basis but lans can be selected manually from a traffic control center or a closed-loo master or using a traffic resonsive method that looks at data from system detectors and selects a lan that has been defined as a good match based on volume occuancy and/or seed data. Modern traffic control systems have not changed significantly in the ast years. Most major cities today have traffic control systems that include coordinated-actuated controllers that can adat to minor changes in traffic demand on a er-movement basis as determined by simle oint detection systems. Most of these systems have a higher level control system either a central traffic management system or a closed-loo master where different signal timing lans can be activated based on either a re-determined time-of-day schedule or sometimes based on system detectors that measure volume and occuancy at single oints on network links. While these systems have erformed adequately for long eriods of time there has continually been a desire to develo traffic adative traffic signal control systems that can make changes in how the traffic signals rovide service so that they can imrove

25 24 efficiency. Early traffic adative systems made minor adjustments to signal timing arameters based on observed atterns of traffic flow but these systems were resonding after the traffic flow had changed and were essentially reactive. In the ast decade several attemts to develo roactive or rediction based) adative control systems have occurred. There has been some moderate rogress but tyically these systems have deended on elaborate communications comutation and detection system that are difficult to maintain and require highly secialized knowledge and understanding to oerate. 1.2 IntelliDrive SM - advanced vehicle communications and caabilities With the advent of IntelliDrive SM for Mobility RITA 2010) soon it will be ossible to obtain additional network and vehicle oeration information. IntelliDrive SM formerly known as vehicle infrastructure integration VII) AASHTO 2009) is a suite of technologies and alications that use wireless communications to rovide connectivity that can deliver transformational safety mobility and environmental imrovements in surface transortation. IntelliDrive SM alications rovide connectivity: with and among vehicles V2V) between vehicles and the roadway infrastructure V2I) among vehicles infrastructure and wireless devices consumer electronics such as cell hones and PDAs) that are carried by drivers edestrians and bicyclists v2x)

26 25 Like the Internet which rovides information connectivity IntelliDrive SM rovides a starting oint for transortation connectivity that ultimately will enable countless alications and sawn new industries. Today only the ti of the iceberg has been seen. The two dominant communication channels will be 5.9 GHz Dedicated Short Range Communications DSRC) with communication distance 500~1000 meters Y. Liu et al. 2005) and cell hone based data connectivity with bandwidths of several 100 Kbit/sec. This will enable the vehicle to send and receive messages to and from other vehicles and the infrastructure to enhance safety and to rovide robe vehicle data. Equiing vehicles with DSRC will also necessitate the installation of Global Positioning System GPS) so that ositioning caability will be available on all vehicles that communicate. The vehicles will send out dynamic data e.g. vehicle osition seed heading acceleration yaw rate steering wheel angle etc.) vehicle status data e.g. electronic stability system data wheel sli anti-lock brake status turn signals windshield wier status rain sensor data etc.) and ossibly data from other autonomous safety systems on the vehicle e.g. vision systems forward collision radars and lidars). The entire IntelliDrive SM system structure is shown as Figure 1.2.

27 26 Figure 1.2 IntelliDrive SM VII) architecture data flow Faradyne 2005) The On-Board Equiment OBE) is the vehicle side of the IntelliDrive SM system as deicted in Figure 1.2. OBE s are used to describe the functions erformed within the vehicle in addition to the radio transmission element. An OBE is logically comosed of a 5.9 GHz DSRC transceiver OBE) a GPS system an alications rocessor and interfaces to vehicle systems and the vehicle s human machine interface HMI) Faradyne 2005). OBEs rovide the communications both between the vehicles and the road-side units RSU) and between the vehicle and other nearby vehicles. The OBEs may regularly transmit status messages to other OBEs to suort safety alications. The OBEs may also gather data to suort ublic alications. The OBEs will accommodate storage of many snashots of data deending uon its memory and communications caacity. After some eriod of time the oldest data may be overwritten. The OBEs also

28 27 assembles vehicle data together with GPS data as a series of snashots for transmission to the Roadside Equiments RSEs). RSEs may be mounted at interchanges intersections and other locations roviding the interface to vehicles within their range. An RSE is comosed of a DSRC transceiver an alication rocessor and interface to the IntelliDrive SM back-haul communications network. A RSE may have a GPS unit attached. The RSE is connected to the IntelliDrive SM back-haul communications network that rovides communications services between alication servers and vehicles. Using its interface to the IntelliDrive SM backhaul communications network it forwards robe data to the IntelliDrive SM message switches and can send rivate data to and from the OEMs Original Equiment Manufacturer). The RSE may also manage the rioritization of messages to and from the vehicle. Although the OBE has riorities set within its alications rioritization must also be set within the RSE to ensure that available bandwidth is not exceeded. Local and vehicle-tovehicle safety alications have the highest riority; messages associated with various ublic and rivate network alications have lower riority. Entertainment messages will likely have the lowest riority. Although it is anticiated that infrastructure instrumentation of IntelliDrive SM may take many years including time for instrumented vehicle enetration into the market it is desirable to develo new traffic signal control algorithms and traffic management strategies that resond to changing traffic and environmental conditions to mitigate congestion.

29 Research objectives In this doctoral research three objectives are aimed under a v2x environment: Lane-level GPS ositioning with sole GPS and v2x communications for enhanced safety control. Real-time robust multile riority control with current coordinated-actuated traffic signal control system assuming the enetration of IntelliDrive SM is u to rivileged vehicles. Online multi-modal traffic control with high enetration of IntelliDrive SM in all vehicles Pseudo-lane-level GPS ositioning A key caability necessary for successful and wide-scale deloyment of v2x alications is the ability to rovide lane-level estimation of vehicle osition. First lane level osition data enhances roadway safety by suorting collision avoidance system such as Cooerative Intersection Collision Avoidance Systems CICAS) in United States Amanna 2009). Second lane control with different advisory seed and lane restriction are feasible when lane level ositioning is available. Third driving behavior such as lane changing can be studied intensively based on lane level ositioning data. Forth lane level ositioning can also benefit traffic oerations and control; for examle lane level queue length could be obtained. This is a significantly challenging technical roblem that

30 29 must engage ublic sector infrastructure as well as advanced vehicle technologies for ositioning including the global ositioning system GPS) inertial navigation INS) and other technologies such as vision based radar and lidar sensors and magnetic roadway markers. No single technology is currently caable of roviding the required fidelity and reliability of osition estimates. A solution that best leverages both the infrastructure caabilities and advanced ositioning technologies is needed. To be successful for wide scale deloyment this solution must also be cost effective. A solution that is too exensive is unlikely to be widely deloyed and suorted. Modern vehicle ositioning technology is caable of roviding high fidelity ositioning using a combination between Differential GPS DGPS) and inertial navigation systems. These systems are generally very exensive - in the order of $20K-$80K - and are hence too exensive for wide scale deloyment. Technological solutions using a combination of lidar video GPS and inertial navigation have the otential to achieve the high level of accuracy but are likely to be exensive and suscetible to environmental conditions as well as GPS interrutions. The standard deviation of a non-differential low cost GPS osition estimates is on the order of meters J. Farrell & Barth 1999) and J. Farrell et al. 2003). This level of accuracy is not sufficient to estimate the vehicle lane status which could be used to track the turning roortion and analyze driving behavior. Traffic density and queue length measurement and/or estimation could also be affected by the GPS ositioning inaccuracy. Therefore the first goal of this research is to rovide a method that will correct low cost GPS error and achieve seudo-lane level GPS ositioning where lane change behavior

31 30 could be tracked by the OBEs. In this context seudo means that lane level accuracy is achieved only under the assumtion that v2x is available and there is no GPS outage Robust multile riority control within a v2x environment A variety of challenges as well as oortunities arise when considering traffic control within a v2x environment. One of the oortunities is that different classes of vehicles such as assenger cars transit vehicles buses light rail street cars) trucks and emergency vehicles can be identified and can request riority signal timing treatment to allow multi-modal timing considerations. This oortunity resents some significant challenges including how to imlement riority oerations that resolve multile conflicting requests from different classes of vehicles - such as emergency vehicles and buses as shown as Figure 1.3. With V2I communication in an IntelliDrive SM world vehicle information will be able to be obtained u to 1000 meters away from the roadside equiment RSE) near the intersection.

32 31 Figure 1.3 Intersection layout with multile riority requests Traditional riority control system in United States can be categorized into emergency vehicle reemtion and transit signal riority TSP). Emergency vehicle can request signal reemtion treatment by using either otical acoustic secial inductive loo or Global Positioning System GPS) technology Nelson & D. Bullock 2000). Preemtion generally involves a control strategy that immediately switches from current hase to a re-selected hase for the first received request. Transit vehicles can be served by either assive riority or active riority systems. Passive riority timing is achieved when signal lan arameters offsets green slits hase insertion or rotation) are tuned in favor of the movements of transit vehicles Evans & Skiles 1970)Yagar & Han 1994)Balke et al.

33 )Furth & Muller 2000)Skabardonis 2000)Baker et al. 2002)Head 2002)H. Liu et al. 2003)H. Smith et al. 2005). Active riority systems involve adating the signal timing by extending the green or roviding early green. In current emergency vehicle reemtion systems only one request can be served at a time. Therefore multile requests with conflicting hases could create unsafe conditions resulting in situations where emergency vehicle accidents may occur The Transortation Safety Advancement Grou 2010). With V2I communication systems the road-side equiment RSE) can receive requests from multile vehicles rioritize the requests based on class and time then work with the traffic signal controller to generate an otimal signal timing lan that simultaneously accommodates multile requests in a safe and efficient manner. The RSE can also send request list information back to each of the requesting OBEs to enhanced intersection safety by roviding feedback so that each vehicle is aware of the other vehicles on conflicting aroaches. Requests from multile transit vehicles are retty common in high oulation density urban areas. In other words it is likely that more than one transit vehicle would aroach an intersection at any time. The transit network is comosed of different level class) of bus lines e.g. exress and local) and bus frequency is generally high in large metroolitan areas of cities like New York City Los Angeles and other major cities. One or more buses may arrive on one or more aroaches of an intersection during any cycle. Every bus request has its own characteristics e.g. class lateness occuancy) and the efficiency of signal riority for them would be different deending on the situation. Bus occuancy and adherence to the schedule could be considered for real-time active riority

34 33 control. Providing riority for a bus with high occuancy or late of schedule is much more efficient for an emty bus or a bus that is ahead of schedule. The research issues to be addressed in riority control are as follows: 1. Show that first-come first-serve is not efficient Head et al. 2006a) and formulate a mathematical rogram that simultaneously considers multile riority requests in otimizing signal timing. 2. Develo a robust and reliable signal timing solution that accounts for the uncertainty of the traffic state e.g. queue length) that may effect the actual arrival times of riority requesting vehicles 3. Integrate riority control with the state-of-ractice in traffic signal control that is coordinated-actuated control. First coordination is considered within the multile riority control cormulation by adding virtual coordination requests. Second vehicle actuations are considered when the otimal solutions are imlemented by introducing the concet of green extension grou GEG). Therefore the method develoed in this dissertation addresses multile riority requests coordination as well as assenger vehicle real-time actuations. 4. Imlement a real-time algorithm that does not utilize a commercial solver e.g. CPLEX) on an embedded latform and demonstrate riority control at a real field intersection Multi-modal traffic control within a v2x environment

35 34 The changes within a v2x environment include more than just changing how vehicles are detected and making small adjustments in signal timing arameters but include actual consideration for multi-modal vehicle oeration that includes assenger vehicles transit commercial vehicles emergency vehicles cycles and edestrians. It can include riority for transit and emergency vehicles. It will be ossible to rovide lane-by-lane and vehicle-by-vehicle controls to suort highly cooerative and integrated behavior to utilize the network caacity in the most efficient and safe manner ossible. The advanced vehicle information and communications oens the oortunity for significant imrovement in traffic signal control. The most obvious imrovement is that vehicles can call request) a hase as they aroach a signalized intersection from any location on the roadway as oosed to only where the detectors have been installed. More correctly they can continuously notify the traffic signal controller that they are on the aroach and request service. In addition the vehicle can communicate information about seed that can be used to determine when they would arrive at and cross the sto bar. In the middle or final stage of deloyment of v2x alications the fraction of OBEequied vehicles will be relatively significant. New kinds of enriched traffic data from OBEs will easily overwhelm traditional traffic control logic. Not only will real-time ositions and seeds be available but also multi-modal traffic comosition data with requested traffic control hases and arrival times throughout the network. Given information about the current mix of traffic modes and the requested hases and arrival times the traffic signal control roblem can be transformed to be a multi-modal

36 35 multi-riority request roblem. New traffic control objectives with this multi-modal concet of traffic control include: 1. A clustering algorithm to quickly locate latoons by grouing nearby requests thus lowering the comutation comlexity of the area-wide otimization algorithm. The vehicles in a latoon can be treated as one single low riority request with a defined time interval for service. 2. A latoon-based multi-modal arterial traffic control formulation is addressed as a new concet of area-wide traffic control. Dynamical coordination which is different than traditionally fixed-cycle fixed-offset coordination is achieved by servicing the real-time latoon data. Platoons can be served in one cycle or slit into two cycles deending on the total delay assessed in current intersection and downstream intersections. 1.4 Summary of the dissertation Chater 2 resents current literature review of revious work on IntelliDrive SM traffic signal control algorithms traffic control systems and robe vehicle technology. Relevant ioneering work on traffic control with advanced communications is also summarized. Chater 3 resents a framework for obtaining seudo lane-level ositioning using lowcost GPS vehicle-to-infrastructure v2i) communication and driving event detection. In this context seudo means that lane level accuracy is achieved only under the assumtion that v2i is available and there is no GPS outage. GPS errors can be categorized into common-mode errors and noncommon-mode errors where common-mode errors can be

37 36 mitigated by differential GPS DGPS) but noncommon-mode cannot. First commonmode GPS error is cancelled from differential corrections broadcast from the road-side equiment RSE). With v2i communication a high fidelity roadway layout ma and satellite seudo-range corrections are broadcast by the RSE. The on-board equiment OBE) corrects for the GPS common-mode errors based on the received seudo-range corrections from the RSE the current lane estimate and the segment status determined by a general ma matching algorithms. To enhance and correct the lane level ositioning a statistical rocess control aroach is used to detect significant vehicle driving events such as turning at an intersection or lane-changing. Whenever a turn event is detected a mathematical rogram is solved to estimate and udate the GPS noncommon-mode errors. This chater does not consider vehicle sensor data which could be used to imrove osition estimates but requires an interface to the vehicle electronic system) and it is assumed that there is no GPS outage. Next Generation Simulation NGSIM) data is used to validate driving behavior for turn movements and to calibrate the lane-changing detection model. A field exeriment is conducted to validate the ositioning models. Chater 4 examines the multile riority roblems in traffic signal control under the condition that OBEs are only installed on high riority class vehicles such as emergency vehicle or transit vehicle. A riority request is sent to RSE if the emergency vehicle is aroaching the intersection or the bus falls behind schedule. Given the current multile riority request information a mixed integer linear rogram MILP) is solved in the RSE to obtain the otimal signal lan. First a deterministic MILP is roosed only for multile riority control of emergency vehicles. Second a robust MILP is develoed for

38 37 transit vehicles e.g. buses) to accommodate the uncertainty in the traffic state e.g. queues). Third actuated control is integrated into the robust MILP formulation to mitigate the delay for assenger cars caused by riority control. Last but not least the signal coordination constraints are added in the MILP formulation to achieve better erformance on an arterial. Both exeriments on isolated intersections and coordinated intersections are conducted to rove the efficiency of roosed strategy to achieve realtime control. Chater 5 resents an aroximation algorithm to the mathematical rogram from chater 4 for field imlementation. Currently our OBEs and RSEs are running on embedded Linux systems which is not a comatible oerating system for sohisticated solvers such as CPLEX. Therefore it is necessary to develo a solution algorithm for the multile riority control roblem that can erform in a reasonable fashion on an embedded comuter. First the roblem is transformed to a olynomial solvable cut roblem according to some reasonable assumtions. Second a hase-time diagram is develoed to evaluate the feasible solutions and search for the sub otimal solutions. Finally a real-world exeriment is conducted in a live intersection of Southern Ave. and 67 th Ave in Maricoa County AZ. OBEs are installed on three REACT Regional Emergency Action Coordinating Team) vehicles from Maricoa County Deartment of Transortation MCDOT). One RSE is connected with and Econolite ASC/3 traffic controller in the cabinet. Different scenarios of multile riority requests are tested and the results showed that the algorithm roosed could serve the multile riority requests in real-time.

39 38 Chater 6 outlines a methodology called PAMSCOD Platoon-based Arterial Multimodal Signal Control with Online Data) for multi-modal traffic control when market enetration of IntelliDrive SM is relatively high in assenger cars. Here multi-modes include emergency vehicles buses and assengers cars. Due to the large number of assenger cars in the network clustering methods are develoed to grou the nearby service requests into traffic latoons. Then a uniform request-based formulation is develoed to otimize traffic signal control for concurrent different motorized travel modes e.g. buses and emergency vehicles given the assumtion of v2x environment.

40 39 CHAPTER 2 LITERATURE REVIEW Recent advances in communications standards and technologies rovide the basis for significant imrovements in traffic signal control caabilities. In the United States the IntelliDrive SM rogram originally called Vehicle Infrastructure Integration - VII) has identified 5.9GHz Digital Short Range Communications DSRC) as the rimary communications mode for vehicle-to-vehicle v2v) and vehicle-to-infrastructure v2i) safety based alications. The IntelliDrive SM architecture Faradyne 2005) also includes the use of other communications channels such as IEEE wi-fi) digital cellular Bluetooth etc. for non-safety critical alications. Regardless of the communications channel used the ability for vehicles and the infrastructure to communication information is a significant advance over the current system caability of oint resence and assage detection that is used in traffic control systems. This chater reviews the literature related to IntelliDrive SM as well as traffic signal control strategies and robe vehicle techniques. 2.1 U.S. IntelliDrive SM VII) IntelliDrive SM VII) has been demonstrated and evaluated in several states over the ast several years. Michigan and California are both leading field oerational tests FOT). Large test beds were established in these two states. New York is in the early stages of

41 40 develoing an IntelliDrive SM rogram focused on commercial vehicles. Virginia conducts some early research on ram metering control and signal dynamical ga with IntelliDrive SM. Arizona focuses on researching and develoing technology to assist emergency-resonder vehicles California In the VII California Program Caltrans and Metroolitan Transortation Commission MTC) have created a VII test bed in the Bay Area Misener 2008a). The large-scale test bed extends over aroximately 60 miles of roadway freeways and arterials). The VII California test bed is continuing to exand. Currently there are 12 DSRC radios deloyed with lans to grow this number u to 40. Several alications are being testing including Misener 2008b): 1). Traveler information; 2. Ram control; 3). Electronic ayment tolling); 4). Intersection safety including a roject called Cooerative Intersection Collision Avoidance Systems Violation CICAS-V) J. Chang et al. 2007); 5). Curve overseed warning; 6). OEM secific alications K. Li et al. 2007) Michigan Michigan has embarked on an early IntelliDrive SM VII) deloyment. Formally Michigan has been designated the national IntelliDrive SM VII) roof of concet POC). Preliminary testing has focused on roving that data can be shared between the infrastructure and vehicles in a timely and accurate manner to suort IntelliDrive SM

42 41 alications Piotrowicz 2008). Michigan Deartment of Transortation MDOT) has installed 60 RSEs and is cooerating with Chrysler to equi 15 vehicles. The MDOT Data Use Analysis and Processing DUAP) roject and Cooerative Intersection Collision Avoidance System CICAS) are two significant rojects conducted using the POC testbed. The DUAP roject Mixon/Hil of Michign Inc. 2007) is a research rogram to determine how new VII data imacts safety traffic oerations and management asset management winter oerations and transortation lanning. The rogram is focused on demonstration and assessment of data transformation and management and DUAP system develoment is a means to that end. From a systems engineering functional viewoint the DUAP system has four high-level caabilities: Collecting data Consolidating the collected information Converting data into information needed by transortation agencies Communicating the unified information to various agencies and the ublic The CICAS rojects McHale 2008) can be categorized by CICAS Ga rojects and CICAS Violations rojects. In CICAS Ga rojects there two sub rojects CICAS-Sto Sign Assist roject and CICAS- Signalized Left Turn Assist. CICAS-Sto Sign Assist roject enhances driver s decision at sto sign through information and warnings by dynamic sign gas assessed with infrastructure sensors and v2i warnings. In CICAS- Signalized Left Turn Assist roject drivers will be warned when it is unsafe to make a left turn because of oncoming vehicles resence of edestrians and other road

43 42 users. CICAS- Violations CICAS-V) is a 4 year roject to develo and evaluate a rototye system intended to assist drivers in reducing the frequency of crashes between vehicles due to violations of traffic signals and crashes between vehicles due to violations of sto signs New York The New York IntelliDrive SM rogram is designed esecially for commercial vehicles. The commercial vehicle infrastructure integration CVII) rogram NYSDOT 2008) includes 13-mile test site on the New York State NYS) Thruway Authority s Sring Valley Corridor. The goal of the CVII Program is to develo test and demonstrate commercial vehicle based data communication with the roadside equiment RSE). The Deartment and its artners desire to leverage the existing light vehicle based VII technology to enhance commercial vehicle safety security and mobility by artnering to develo test and demonstrate a rototye system that utilizes the VII architecture and system requirements as well as the SAE J1708 vehicle data bus and the standard message sets defined in the SAE standards SAE J1587 SAE J1939 and SAE 2735). Commercial vehicle in-vehicle hardware and software have been develoed tested and demonstrated to allow data message sets DMS) to be wirelessly transmitted via DSRC Virginia

44 43 The Virginia Deartment of Transortation VDOT) has been an active articiant in the national IntelliDrive SM develoment effort. They assessed national develoment activities and quantitatively evaluated two otential system oeration alications: traffic monitoring and signal control B. L. Smith et al. 2007). The IntelliDrive SM benefits to traffic signal control was analyzed to determine how traffic signal control could be imroved. A dynamic ga-out feature was develoed that takes advantage of higher resolution vehicle location data available in IntelliDrive SM. In the dynamic ga-out system vehicle headways were analyzed at a distance of 300 ft ustream of the sto bar. Based on this headway the controller redicts a vehicle arriving at the sto bar before or after the ga timer exiring. If the headway ga at 300 feet ustream is larger than the ga time the signal is allowed to ga out immediately hence effectively transferring the additional ga time to the other hases movements) Arizona The Arizona Deartment of Transortation ADOT) develoed a system called the Emergency IntelliDrive SM E IntelliDrive SM ) system that is focused on researching and develoing technology to assist emergency-resonder vehicles ADOT 2008). This dissertation is artially funded by Arizona E- IntelliDrive SM roject which has been conducted by the ATLAS Advanced Traffic and Logistics Algorithms and Systems) research center in the College of Engineering at the University of Arizona.

45 44 The Arizona E- IntelliDrive SM initiative has a very unique focus on incident management and emergency resonse which is not currently being addressed by other state or national IntelliDrive SM efforts. The Arizona E- IntelliDrive SM effort focused on four alications including: 1. Preemtion and Priority Oerations at Traffic Signals. 2. Preemtion Oerations at Ram Meters. 3. Ad hoc Incident Warning Broadcast. 4. Lane Road Closure and Incident Information Communication to Traffic oeration center TOC). These alications were develoed and demonstrated in the Maricoa County DOT arking lot in 2008 at the AASHTO Annual Meeting 2009 in Palm Desert CA and the traffic signal riority alication was tested and demonstrated at a live intersection in Maricoa County in Traffic Signal Control Traffic signal lights were invented nearly 150 years ago when the first traffic lights were installed outside the British Houses of Parliament in London by the railway engineer J. P. Knight. Traffic signal control can be categorized into three different control schemes: fixed-time traffic signal control actuated traffic signal control and adative traffic signal control.

46 Fixed-time traffic signal control Many of state-of-the-ractice re-timed systems are oerated in a time-of-day mode in which a day is segmented into a number of time intervals and a signal timing lan is redetermined for each time interval. Tyically 3 5 lans are run in a given day. The basic remise is that the traffic attern within each interval is relatively consistent and the redetermined. Fixed time control has low cost installation and timing lan is best suited for the condition of this articular time of day. But it is not robust or adative to current traffic conditions since real-world travel demands are intrinsically fluctuating and traffic flows at intersections may vary significantly even for the same time of day and day of week Yin 2008). Usually fixed time control lan is roduced from off-line signal otimization considering time-of-day constant flows. Some well-known traffic signal off-line otimization algorithms are listed as below MAXBAND Little 1966) Little et al. 1981) and Chaudhary et al. 1991). MAXBAND is develoed based on the fact that vehicles leaving from an ustream intersection are groued into a latoon by the green light. It is desirable to set the signals at the downstream intersections in such way that the latoon of traffic is able to go without sto when traveling through the network. In other words the control objective is to maximize the bandwidth. It rovides rogression along arterial but the algorithm doesn t work well for oversaturated intersections since residual queue can easily disrut the rogression.

47 46 MULTIBAND Gartner Assman et al. 1991) and Stamatiadis & Gartner 1996) MULTIBAND is another well-known off-line rogression based otimization model develoed by Gartner. MULTIBAND incororates a systematic trafficdeendent criterion which guarantees the suitable rogression scheme for different traffic flow atterns. The method generates a variable bandwidth rogression in which each directional road section can obtain an individually weighted bandwidth hence the term multi-band). Mixed-integer linear rogramming is used for the otimization. TRANSYT Robertson 1969) TRANSYT was first develoed by Robertson but was substantially extended and enhanced later. TRANSYT has been widely recognized as one of the most useful tools in studying the otimization of area traffic control. It is the most known and most frequently alied signal control strategy and it is often used as a reference method to test imrovements enabled by real-time strategies. TRANSYT-7F Wallace et al. 1998) and M. Li & Gan 1999) TRANSYT-7F TRAffic Network StudY Tool version 7F) is a version of TRANSYT for United States. TRANSYT-7F has been used by ractitioners for traffic network signal timing design and analysis. The latest version of TRANSYT-7F release 11 features genetic algorithm otimization of cycle length hasing sequence slits and offsets McTrans 2010). It combines an otimization rocess including genetic algorithm multi-eriod and direct CORSIM

48 47 otimization) with a state-of-the-art macroscoic simulation model including latoon disersion queue sillback and actuated control simulation) PASSER II Chaudhary & Chu 2003) PASSER II was originally develoed with Texas Deartment of Transortation TxDOT) more than 30 years ago. The otimization technology used in PASSER II is simle but efficient. In addition it has roven to roduce high-quality timings for signalized arterials. Furthermore bandwidth-based timings are easily recognized and areciated by motorists in Texas and many other arts of the United States. Synchro Trafficware 2009) Synchro is a macroscoic traffic signal otimization model and software ackage roduced by Trafficware. They have aroximately 1600 users throughout North America and are used by most state DOT s. Sychro uses SimTraffic as its microscoic simulation model to fully simulate signalized or unsignalized intersections. One disadvantage of above fixed time control algorithms is that the traffic control roblem is not addressed very well under oversaturated traffic condition since traffic flow model is oversimlified in their algorithms. Recently a number of aers have develoed dynamic traffic signal control formulations based on the cell transmission model CTM) in Daganzo 1994) and Daganzo 1995). The significant benefit of embedding CTM in signal control is to cature traffic dynamics. CTM-based signal

49 48 control formulation is to address both unsaturated and oversaturated conditions considering shockwaves and hysical queues. Lo formulated the network signal otimization roblem as a mixed-integer linear rogramming roblem using CTM in Lo 1999) and Lo 2001) assuming that the cycle lengths are fixed. Lin and Wang formulated a more comutationally efficient version of the mixed integer linear rogram for the signal otimization roblem with CTM in Lin & C. Wang 2004). But only two-hase signal was considered in their work. Beard & Ziliaskooulos 2006) roosed a CTMbased system otimal signal otimization formulation combined with system otimal traffic assignment which rovides several imrovements over existing mixed-integer linear rogram formulations including turning movements for exclusive turn lanes. Most recently L. Zhang et al. 2010) examined the design of robust traffic signal control with the CTM. A scenario-based stochastic rogramming model was roosed to otimize the timing of re-timed signals along arterials under day-to-day demand variations. The disadvantage of CTM-based formulations is the comlexity of the mixed-integer linear rogram MILP). The roblem size grows very quickly with the size of the network the number of hases and the time horizon. The curse of dimensionality makes it imossible to solve these formulations directly using commercially available ackages such as CPLEX LINDO etc. Therefore Genetic Algorithm GA) is widely acceted to solve the comlicated analytical traffic signal control models Abu-Lebdeh & Benekohal 2000)B. Park et al. 1999)Girianna & Benekohal 2002)Lo 2001) and L. Zhang et al. 2010) though it is likely to converge to local otimum.

50 Actuated traffic signal control Nowadays traffic actuated control is already imlemented within controllers. It make use of real-time measurements rovided by inductive loo detectors that are usually located some 40 m ustream of the sto line to execute some more or less sohisticated vehicle-actuation logic Paageorgiou et al. 2003). The basic rinciles of timing the green interval in a traffic actuated controller is as follows: There is a minimal green time for each timing hase so that vehicles have enough time to start and ass through the intersection and edestrians can walk through the intersection before yellow signal. Minimal green that is too long may result in wasted time at the intersection; one that is too short may violate driver exectation or in some cases) edestrian safety. Each following vehicle generates a call or actuation) to the traffic controller to ask for additional green time. This is called green extension or ga. There is also a maximal green time or slit in coordinated-actuated mode) for each timing hase which is the limit of total green time when there is a conflicting hase vehicle call. Figure 2.1 illustrates the timing diagram of actuated traffic controller. The actuated controller can be configured to oerate in one of two modes: fully actuated and semi-actuated Federal Highway Administration 2007). In fully-actuated

51 50 mode detection is rovided on all aroaches to the intersection and the controller oerates without a common background cycle i.e. oerating free ). Figure 2.1 Actuated hase timing diagram Federal Highway Administration 2008) In semi-actuated or called coordinated-actuated) mode detection is rovided only on the side-street aroaches and erhas main-street left-turn movements). The main street signals remain green until a call for service is laced by the side-street detectors. Semi-actuated oeration is used to rovide rogressive vehicle flow through a series of controlled intersections. In this mode each controller in the coordinated system oerates within a common background cycle length. The coordinator in the controller guarantees

52 51 that the coordinated hases generally hase 2 in ring 1 and hase 6 in ring 2) will dislay green at a secific time within the cycle relative to a system reference oint established by the secified cycle length and system synch reference time. An offset time relative to the system reference oint is secified for each controller in the series to maintain the smooth rogression of vehicles through the intersections. The coordinator also controls when and for how long non-coordinated hases can indicate green so that the controller will return to the coordinated hases at the roer time Advanced features in coordinated-actuated traffic signal control Each coordinated system has the set of arameters to be determined to achieve signal coordination. These settings are necessary inuts for coordination which are listed as follows: Cycle length: Cycle length defines the time required for a comlete sequence of indications. Usually the traffic engineer utilizes the greatest cycle length among all the intersections along arterial to accommodate the traffic and then design the rest of the rogression scheme around that intersection. Slits: slits are the ortion of time allocated to each hase at an intersection including yellow and all red clearance time). For imlementation in a signal controller the sum of the hase slits must be equal to or less than) the cycle length

53 52 Offsets: The offset is usually defined as the time differential between the initiation of green indications of the coordinated movements relative to the master intersection i.e. the intersection dictates the signal timing requirements of the other intersections). The offset value is derived based uon the distance between the master intersection and the desired travel seed of traffic on the arterial. Figure 2.2 shows a time-sace diagram illustrating offsets and bandwidth of a coordinated traffic signal system Sunkari et al. 2004). Figure 2.2 Coordination on a time-sace diagram Sunkari et al. 2004) Yield oint: Yield oint is only for coordinated hases. It is a oint where the controller starts to make decisions to terminate the coordinated hase as shown in Figure 2.3 a).

54 53 Force-off oint = 100s 2 slit = 25s 1 slit YR 2 slit 3 slit = 25s 4 slit = 25s slit = 25s Force-off oint = 75s YR YR Yield oint =25s slit YR 3 slit Force-off oint = 50s a) 100s YR demand = 25s 75s YR 3 YR 25s 3 demand = 15s 4 demand = 40s 4 YR 1 demand = 25s 40s b)

55 54 90s YR 2 2 demand = 25s 1 3 YR 25s 3 demand = 15s 4 demand = 40s 65s YR 4 YR 1 demand = 25s 40s Figure 2.3 a) Pre-defined slits; b) Fixed force-offs imlementation; c) Floating forceoffs imlementation. c) Force-offs: The force-offs are oints where non-coordinated hases must end even if there is continued demand. The use of force-offs overlays a constraint on all non-coordinated hases to ensure that the coordinated hase will receive a minimum amount of time for each cycle deicted in Figure 2.3 a). There are two tyes of force-offs: fixed and floating Federal Highway Administration 2008). o Fixed force-offs: The fixed force-off maintains the hase s force-off oint within the cycle. If a revious non-coordinated cycle ends its hase early any following hase may use the extra time u to that hase s force-off.

56 55 o Floating force-offs: Floating force-offs are limited to the duration of the slits that were rogrammed into the controller. The force-off maintains the non-coordinated maximum times for each noncoordinated hase in isolation of one another. Floating force-offs are more restrictive for the non-coordinated hases. If a hase does not use all of the allocated time then all extra time is always given to the coordinated hase. An examle is resented in Figure 2.3 a) b) and c) to distinguish fixed and floating force-offs. Suose hase 2 is coordinated hase cycle length is 100seconds and each hase slit is equal to 25 seconds shown as Figure 2.3 a). If the demand of hase 2 and hase 1 equal to the slits 25 seconds) hase 3 has lower demand 15 seconds) and hase 4 has larger demand 40 seconds) than slits fixed force-offs and floating forceoffs have totally different slit imlementation. In fixed force-offs the force-off oint of hase 4 is fixed at 50 s. The unused green time in hase 3 can be re-allocated to hase 4. In addition to the redefined slit 25 seconds hase 4 has total 35 seconds actual time. In floating force-offs the maximal slit of hase 4 is 25 seconds. So hase 4 needs to be forced off no matter that there are unused green times in revious hase 3. So extra green time are all assigned to coordinated hase hase 2) in floating force-off. Therefore fixed force-offs give beneficial to side streets if there are fluctuations in traffic demand and a hase needs more green time. And floating force-offs give more green on coordinated hase which may result in early return to disrut coordination but may also clear the

57 56 queue on arterial in congested traffic condition. There are both trade-offs for fixed and floating force-offs Adative traffic signal control Since 1970 s first generation of adative traffic signal control systems was develoed in UK and Australia such as SCOOT and SCAT. SCOOT was first develoed by Robertson s team Hunt et al. 1982) and has been extended later in several resects. It is considered to be the traffic-resonsive version of TRANSYT and has been alied to over 150 cities in the United Kingdom and elsewhere. SCOOT utilizes traffic volume and occuancy similar to traffic density) measurements from the ustream end of the network links. It runs in a central control comuter and emloys a hilosohy similar to TRANSYT. More recisely SCOOT includes a network model that is fed with real measurements instead of historical values) and is run reeatedly in real time to investigate the effect of incremental changes of slits offsets and cycle time at individual intersections functionally decentralized oeration). SCOOT also has some vices P. Martin 2001). Only u to 15% detector failure is accommodated. The erformance of SCOOT degrades back to a fixed time lan if faults not rectified. And it is unable to accommodate oversaturation. SCAT was installed in Sydney in 1970s offers a substantial imrovement to movement on arterial roads at low cost thereby enabling usage of the arterial road network to be otimized Sim & Dobinson 1980). Now it is imlemented in 50 cities worldwide including Oakland County Minneaolis and Atlanta in the USA. The main

58 57 objective of the system is to minimize overall stos and delay when traffic demand is less than system caacity. When demand aroaches system caacity SCATS maximizes throughut and controls queue formation Lowrie 1982) and Luk 1984). UTOPIA Urban Traffic Otimization by Integrated Automation)/SPOT System for Priority and Otimisation of Traffic) was develoed by FIAT Research Centre Italy Mauro & Taranto 1989). This system is a hierarchical control model in which UTOPIA is alied in area level control and SPOT is for local intersection control. It also contains three layer controls like other systems. PRODYN is another real-time traffic control system develoed by CERT/ONERA in France and imlemented in three French cities Henry et al. 1983). It includes the rediction model of arrival vehicles and estimates queues at each intersection for 16 time intervals of 5 seconds. Local otimization is made for the time horizon by a controller imlementing the estimated control strategy for each successive eriod. The system transmits the redicted states to controllers downstream to imrove their redictions. In United States during the ast decades the Federal Highway Administration FHWA) has focused on the develoment and deloyment of Real Time Traffic Adative Control System RT-TRACS) in the USA. Several traffic adative signal control systems were develoed since 1980 s. The Otimized Policies for Adative Control OPAC) was develoed by Gartner Gartner 1983)Gartner Tarnoff et al. 1991) and became a art of RT-TRACS of FHWA. It was develoed earlier for isolated intersection control which could be exanded to control a subnetwork with a grou of intersections. It is based on the Dynamic

59 58 Programming to minimize the total intersection delay and stos over a user-secified rolling horizon interval. During otimization it rogressively selects from among a number of ossible signal atterns at each intersection. The atterns are recalculated based on udated traffic data over a shorter time interval and used for comuting the globally otimized solution. Sensors are laced ustream of sto line to redict arrival flow attern. RHODES is another art of RT-TRACS of FHWA develoed by ATLAS center University of Arizona Head & P. Mirchandani 1992) Sen & Head 1997)P. Mirchandani & Head 2001). University of Arizona s rototye is comosed of a main controller called RHODES) APRES-NET which simulates latoons REALBAND a section otimizer) PREDICT which simulates individual vehicles and COP a local otimizer). This rototye which is a hierarchical control system has three levels of otimization namely intersection control network control and network loading. For local intersection control the signal hase durations are otimized by a Dynamic Programming aroach. The decision is re-evaluated every 7 to 15 seconds using a decision horizon of 90 seconds. At the second level the otimization of network flow control is erformed based REALBAND. This model attemts to form rogression bands based on actual observed latoons in the network. All the ossible resolution of a conflict among the redicted latoon movements are listed as the decision tree. Then the best one based on the erformance index is chosen as the otimal setting. At the highest level network loading redicts the general demand over longer eriods of time tyically one hour.

60 59 Both OPAC and RHODES were develoed in the U.S. and were imlemented in the 1990s and early 2000s. These systems were both offsring from FHWA s RT-TRACS develoment effort Selinger & Schmidt 2009). Most recently In 2001 FHWA initiated the ACS-Lite adative control systems) rogram to assess and then ursue the best most cost-effective solution for alying ACS technology to current state-of-the-ractice closed loo traffic signal control systems. This effort is intended to make ACS technology accessible to many jurisdictions without the ugrade and maintenance costs required to imlement ACS systems that rovide otimized signal timings on a second-by-second basis Luyanda et al. 2003). Due to ast wireless communication limitation none of the current adative signal control makes use of robe vehicle data to gain better erformance. 2.3 Probe vehicle technology The state of the art in traffic monitoring is to utilize wireless location technology as a means to track robe vehicles as they traverse the transortation network. The robe vehicle track rovides information on vehicle locations over time which can be used to derive travel times and seeds on articular roadway links. The wireless location technology most commonly used is cellular hone GPS locations and/or cell handoff information Traffic state and travel time estimation with robe data

61 Transit as robes Some researchers roosed the use of mass transit buses as robes since they can be equied with AVL automated vehicle location) technologies. Buses can be easily tracked since they have fixed routes and schedule. It will rovide relative stable data set than assenger cars. However the ercentage of bus in entire traffic is relative low to estimate traffic state in real time. Hall & Vyas 2000) found that when automobiles have long delays buses traveling nearby on the same route are also likely to be delayed. The reverse situation however is not always true because buses frequently wait for extended eriods when they run ahead of schedule. Any useful bus robe algorithm needs to distinguish between actual congestion and a stoing delay. Cathey & Dailey 2002) develoed a mass transit tracking system based on AVL data and a Kalman filter to estimate vehicle osition and seed were described as were a system of virtual robe sensors that measure transit vehicle seeds by using the track data. Bertini & Tantiyanugulchai 2004) showed that actual arterial traffic conditions may be exlained by using transit vehicle AVL information. The set of transit data bus movements generated from the maximum instantaneous seed achieved between each sto air was found to most reliably deict the traffic movement of non-transit vehicles. Cathey & Dailey 2003) resented a corridor aroach to travel-time estimates by using transit vehicles as robes. This work rovided seed estimates that track the

62 61 significant changes identified in inductance-loo data but aears to rovide a conservative estimate of the seed GPS ositioning as robes With the develoment of GPS ositioning technology in last decades GPS error 10~20 meters) J. Farrell & Barth 1999) can be much lower comared with cellular ositioning ~100 meters) Ygnace et al. 2000). Many researchers started to utilize GPS to estimate traffic state and travel time. However the market enetration of GPS equiment is not as high as cell hone. So some researchers use smart cell hone with GPS device to collection robe data which seems much more realistic for widely imlementation of estimation algorithm. It is showed that the number of robe vehicles required increases nonlinearly as the reliability criterion is made more stringent. Probe vehicles aear to be an attractive source of real-time traffic information in heavily traveled high-seed corridors such as freeways and major arterials during eak eriods but they are not recommended for coverage of minor arterials or local and collector streets or during off-eak hours. Quiroga & D. Bullock 1998) collected tremendous GPS historical data for considering three analysis: segment lengths samling rates and central tendency. The samling rate analysis addresses the effect of collecting GPS data at different samling eriods and shows that for a segment to have GPS data associated with it the GPS samling eriod should be smaller than half the shortest travel time associated with the segment. The analysis also shows a tradeoff between samling rates and segment seed

63 62 reliability and emhasizes the need for even shorter GPS samling eriods 1 2 s) in order to minimize errors in the comutation of segment seeds. The central tendency analysis comares harmonic mean seeds and median seeds and shows that median seeds are more robust estimators of central tendency than harmonic mean seeds. Y.B. Yim & Cayford 2001) used a vehicle equied with differential GPS DGPS) and managed to match its route for 93% of the distance it traveled. Recently some researches combine GPS device and cellular hone for travel time and traffic state estimation. Young 2007) encomassed two rimary methods: GPS data obtained from fleet management services and geo-location schemes that leverage cellular hone infrastructure. Yoon et al. 2007) identified traffic conditions on surface streets given location traces collected from on-road vehicles this requires only GPS location data lus infrequent low-bandwidth cellular udates. Herrera & Bayen 2009) develoed a real exeriment using GPS with cell hones to estimate traffic state called Mobile Millennium see htt://traffic.berkeley.edu/). In this exeriment cell hones equied with a Global Positioning System GPS) rovide new oortunities for location based services and traffic estimation. When traveling on board vehicles these hones are able to accurately rovide osition and velocity of the vehicle and can be used as robe traffic sensors. This article resents a new technique to incororate mobile robe measurements into highway traffic flow models and comares it to a Kalman filtering aroach Cellular hone as robes

64 63 Although Cellular hone ositioning technique has less accuracy cellular hone also has much high market enetration in real world. Due to its ositioning error cellular hone ositioning is not good for intra-city arterial) traffic estimation. However it could be efficiently imlemented for sarse network like highway networks. Some researchers in California PATH Partners for Advanced Transit and Highways) are the ioneers in this area. Sanwal & Walrand 1995) utilized vehicles as sensors instead of the conventional stationary sensors such as the inductive loos used in many laces) for highway travel time estimation. Westerman et al. 1996) roosed four ossible methods for estimating real time travel times and erforming automatic incident detection for ATMIS based on induction loo or robe vehicle data alone. It concludes that the fourth aroach statistical techniques is the best which focuses on the macroscoic level of traffic and to analyze how information about these macroscoic traffic characteristics can be extracted from received robe vehicle data. Ygnace et al. 2000) revealed that at least 5% of freeways travelers are equied with a cell hone; one can redict a 95% accuracy in freeway link travel time estimates. Y.B. Yim 2003) did some surveys for cell hone enetration and claimed that Cellular robe technology one of the otentially romising technologies for data collection of accurate travel time. Recently Bar-Gera 2007) found that there is a good match between the two measurement methods indicating that the cellular hone-based system can be useful for various ractical alications such as advanced traveler information systems and evaluating system erformance for modeling and lanning. Equiing floating vehicles with GPS can imrove the accuracy of the measurements. Valerio et al. 2009) outlined a

65 64 unified framework that encomasses UMTS and GPRS data collection in addition to GSM and rosectively combines assive and active monitoring techniques Traffic control with robe data Currently there are very few literatures about traffic control with robe data. Comert 2008) roosed a robabilistic method to estimate queue length given the last robe vehicle osition in the queue. Based on the queue information max green arameter was adjusted to achieve better erformance. However no detailed signal control scheme or analytical model was roosed in this work. H. Park 2008) utilized VII enhanced data and develoed three VH-enabled ram metering algorithms the variable seed limit the lane changing advisory and the GAP). The results showed that VII-enabled ram metering algorithms imroved the network erformance by roviding 4.3% more vehicle miles traveled while reducing vehicle hours traveled by 4.6% which resulted in 9.3% higher average seeds. J. Y. Park 2009) develoed a network wide signal control system based on Persistent Traffic Cookies PTC) which is similar as IntelliDrive SM. A decentralized control embedded with indirect signal coordination scheme was resented. Signal otimization is accomlished at each local intersection by a dynamic rogramming aroach with the redicted arrival atterns resulting from PTC data. However robe data uncertainty was not considered in this work.

66 Summary Advanced traffic management is a cost-effective otion to reduce total delay fuel consumtion and air ollution in urban networks. Nevertheless Adative signal control the most advanced scheme for real-time traffic resonsive oerations is still not widely used due to inadequate sensor systems and the deficiencies in the control algorithms. With the advent of advanced communication systems nowadays the traffic data are dramatically enriched. In order to imlement advanced traffic control systems in the field the adative signal control systems need to be re-develoed in more simle and direct way given that full size of real-time traffic data is available. This dissertation resents a innovative seudo-lane-level GPS ositioning system a robust mixed integer linear rogram MILP) for multile riority signal control and a latoon-based multi-modal arterial traffic control aroach all within a v2x environment.

67 66 CHAPTER 3 PSEUDO-LANE-LEVEL LOW-COST GPS POSITIONING WITH VEHICLE-TO- INFRASTRUCTURE COMMUNICATION AND DRIVING EVENT DETECTION 3.1 Introduction Recently the concet of cooerative systems have gained increased attention by both infrastructure owner-oerators and vehicle manufacturers because of the otential of wireless communications between vehicles and the roadside to rovide a safer and more efficient oerating environment. Vehicle-to-vehicle v2v) or vehicle-to-infrastructure v2i) - generally referred to as v2x - has the otential to transform travel as we know it today. v2x alications combine leading edge technologies such as advanced wireless communications on-board comuter rocessing advanced vehicle-sensors GPS navigation smart infrastructure and others to rovide the caability for vehicles to identify otential collision and hazards on the roadway and communicate relevant information to give driver alerts warnings and critical traffic control information RITA 2010). A key caability necessary for successful and wide-scale deloyment of v2x alications is the ability to rovide accurate lane level estimation of vehicle osition. First lane level osition data enhances roadway safety by suorting collision avoid system such as Cooerative Intersection Collision Avoidance Systems CICAS) in United States Amanna 2009). Second lane control with different advisory seed and lane restriction are available with lane level ositioning. Third driving behavior -such as

68 67 lane changing - can be studied intensively based on lane level ositioning data. Forth lane level ositioning can also benefit traffic oerations and control; for examle lane level queue length could be obtained. This is a challenging technical roblem that must engage the infrastructure as well as advanced vehicle technologies. To be successful for wide scale deloyment any solution must also be cost effective. A solution that is too exensive is unlikely to be widely deloyed and suorted. Although the use of low cost GPS receivers for navigation has recently become very oular as a variety of units from Garmin TomTom and others have flooded the market the accuracy requirements of navigation and v2x are significantly different. The standard deviation of a non-differential GPS osition estimates is on the order of meters J. Farrell & Barth 1999)J. Farrell et al. 2003). Increased accuracy in few meters or even centimeters can be achieved through different kinds of Differential GPS J. Farrell & Barth 1999) H. Blomenhofer et al. n.d.) and Tan et al. 2003). DGPS is an excellent ositioning tool but GPS receivers on most of vehicles are not caable of receiving differential corrections and differential receivers are more exensive and many times require subscritions to correction services OminiSTAR 2010) that are costly. In order to make GPS ositioning systems oular many researchers focus on how to correct the error from low-cost nondifferential GPS Clanton et al. 2009) and Toledo-Moreo & Zamora-Izquierdo 2009). This chater resents a otential solution to the low-cost ositioning roblem and includes four low-cost elements. The first low-cost element is the use of GPS not necessarily differential GPS) that is available on many vehicles hand held devices and on v2x radio units e.g. Dedicated Short Range Communication DSRC) radio units

69 68 Savari 2010). The second element is the high fidelity mas of key infrastructure elements that rovide information about intersection and roadway geometry called MAPs defined in SAE DSRC-J2735) which contain very accurate GPS wayoints in the center of each roadway lane. These mas are to be rovided as art of the infrastructureto-vehicle communications Le et al. 2009). The third element is low cost vehicle sensors that can be used to enhance osition information when GPS signals are erroneous or undetectable in laces such as urban canyons. The fourth element is the cooeration between equied vehicles by sharing information about current GPS osition error. These four key elements can be combined to rovide highly accurate and reliable vehicle osition estimates that will enable new safety and efficiency alications. This chater exlores a low cost ositioning framework based on solely GPS and detailed mas called the MAP) of the roadway system. GPS ositioning with other vehicle sensors will be considered in future work. This chater is organized as follows. The system structure is roosed in section 2. Section 3 resents a statistical rocess aroach to detect lane-changing and turn movements. Section 4 develos a lane alignment otimization model to estimate GPS noncommon-mode errors. Section 5 reorts the findings of a field test of the roosed ositioning system. Conclusions and remarks are in Section 6.

70 The V2I ositioning environment In the environment of v2x each equied vehicle has on-board equiment OBE) which communicates with road-side equiment RSE) or other vehicles equied with OBEs by some reliable wireless communication technology such as DSRC. The RSE broadcasts a high fidelity ma MAP). The vehicle will receive the MAP and using the received GPS osition will estimate its current osition shown as Figure 3.1. MAPs are an integral art of the infrastructure of a v2x system. MAPs are small ASCII text file that describes the roadway geometry in terms of segments lanes Figure 3.1 Intersection layout defined in a MAP intersections and key traffic control measures. Figure 3.1 shows a simle intersection with a set of GPS wayoints that rovide the highly accurate osition information that

71 70 forms the MAP. It is assumed that the MAP should be based on accurate GPS measurements which can be obtained using survey grade RTK-GPS equiment and on a frequency of wayoints that catures the roadway geometrics including curvature intersection geometry and lane dro geometry. The requirement for highly accurate wayoints in the MAP is imortant due to the additive nature of the error that includes both the MAP accuracy and the real-time measurements. In addition to the MAP GPS corrections can also be broadcast from RSE since the osition of RSE is fixed and surveyed. Given that the range of DSRC radio is less than 1km Y. Liu et al. 2005) a small range local-area DGPS system can be established in this v2i environment either by osition domain corrections and seudorange domain corrections Kalan & Hegarty 2006). In osition domain corrections the coordinate differences between the surveyed RSE osition and the osition estimated from GPS measurements are communicated from the RSE to the OBEs. The latitude longitude and height differences are directly broadcasts from RSE to nearby OBEs. Although the osition domain corrections are the simle to imlement it requires that both receivers use the same set of satellites and the same osition solution techniques on all receivers which is very hard to be ensured because of the variety of GPS receiver roviders in the low cost market. In seudorange domain corrections the reference station determines and disseminates seudorange corrections for each visible satellite. Since it is a local-area DGPS system the common-mode noises sources are cancelled to achieve 1m accuracy. Detailed discussion of DGPS algorithms can be found in J. Farrell & Barth 1999) and Kalan & Hegarty 2006).

72 71 In this chater the authors suggest using seudorange domain corrections. However the details of how to imlement seudorange domain DGPS is not the scoe of this chater. It is assumed that the RSE-based local-area DGPS accuracy is achieved by low cost GPS under good visibility conditions. In order to test if this assumtion is valid a simle test was conducted in the intersection of Mountain and Seedway Tucson AZ when it was sunny and clear. A stationary RSE with low cost GPS was installed on the to of a traffic controller cabinet for 11 hours. The GPS osition errors are shown in Figure 3.2 The GPS error in the test site in Tucson AZ Figure 3.2. The average GPS error is 1.29m with standard deviation 0.748m which nearly matches the accuracy of code-based DGPS.

73 72 Although the GPS noncommon-mode error is unknown and difficult to track it can be estimated when some secific driving events occur e.g. vehicle right hand turn or left hand turn. Given a current MAP and measured vehicle trajectory it is very simle to identify a vehicle turn movement occurs at an intersection. First the actual inbound and outbound lanes could be estimated by the MAP network and ma matching algorithms surveyed in Quddus et al. 2007) given the 1m DGPS accuracy. The measured vehicle trajectory can also be divided into inbound and outbound trajectories after the vehicle turn movement is comleted and detected. The offset between the actual and measured vehicle inbound and outbound trajectory can be regarded as the current GPS noncommon-mode error. A turn event-driven lane alignment otimization model is solved to cature the GPS noncommon-mode error to rovide an offset that can be used for correction. The occurrence of a turn event or lane change event is monitored by using an exonentially weighted moving average EWMA) statistical rocess control SPC) chart based on the vehicle heading in relation to the roadway heading. The vehicle lateral deviation is tracked in order to detect the number of lanes changed. Lane changing events can also be used to determine the vehicle lane status as well as to correct revious lane status estimated by the ma matching algorithm. Figure 3.3 shows an illustration of the actual and measured osition of a vehicle after it makes a right hand turn at an intersection. In this situation it is not known if the vehicle is in the right most lane or the left lane but a combination of this driving event and the revious error estimate can be used to rovide a accurate and reliable estimate of the osition error.

74 73 Figure 3.3 A driving event of making a turning maneuver and the actual and the uncorrected measured osition before and after the event The entire system structure is shown as Figure 3.4. First an event-searated Extended Kalman Filter EKF) is chosen to estimate the vehicle state from the raw GPS data and the estimated GPS errors including common-mode errors from RSE and noncommonmode errors from an otimization model). Due to age limitation the EKF discussion is omitted in this chater. Interested readers can find a detailed introduction to EKF in Zhao et al. 2003)Welch & Bisho 1995). The ma matching algorithm is used to estimate the vehicle s initial lane and segment status as well as to udate the status based on the EKF estimate. Second given the vehicle heading from the EKF states and the lane heading from MAP the heading error is monitored by an exonentially weighted moving average EWMA) SPC control chart. The EWMA control charts track both lane change and turn events. Once the EWMA data exceeds the defined control limits of lane change

75 74 events a lane change is detected. The number of lanes changed can be estimated by the vehicle lateral deviation. Similarly turning events are detected based on defined control limits. Finally the vehicle lane status is udated or corrected by the vehicle status management module. When a turn event is detected the lane alignment otimization module is triggered to udate the estimated GPS noncommon-mode error. This information is rovided to the v2x alications. Figure 3.4 GPS ositioning System Structure Two major contributions in this system are the EWMA control chart to monitor events and the event-driven lane alignment otimization to estimate the GPS noncommon-mode error.

76 Extended Kalman filter The Kalman filter rovides an efficient comutational recursive) means to estimate the state of a rocess. Kalman filters are very owerful in several asects including that they suort the estimation of ast resent and even future system states and they can do so even when the recise nature of the modeled system is unknown Zhao et al. 2003). The two main features of the Kalman filter formulation and roblem solution are vector modeling of the dynamic rocess under consideration and recursive rocessing of the noisy measurement data Misener & Shladover 2006). In the vehicle states tracking alication of a Kalman filter the nonlinear dynamical system model must be linearized. A Kalman filter that linearizes about the current mean and covariance is referred to as Extended Kalman Filter EKF). Although the linearization and Gaussian distributed noise assumtion in the EKF may seriously affect the accuracy of the obtained solution or can sometimes lead to divergence of the system Welch & Bisho 1995). the EKF can handle aroximate nonlinear filtering in real time without the curse of dimensionality which greatly reduces the comutational comlexity of the system. Since the low cost GPS receiver is the only sensor/information source used in this chater the longitude latitude heading and velocity are the only measurements available assuming that altitude remains constant within the localized lane centered by the MAP). We assume that the seed of the vehicle is constant during each GPS measurement interval 1 second). Since the GPS data is in the WGS-84 coordinate

77 76 system we convert each GPS measurement from onto a local lanar coordinate system El-Rabbany 2006). The following states are selected X ) [ x ) y ) sin ) cos ) v )] v v v T Where x ) = vehicle location in the east direction at time ste measured in meters. y ) = vehicle location in the north direction at time ste measured in meters. sin v ) = sine of the vehicle heading at time ste in radians with north being zero heading and clockwise being ositive. cos v ) = cosine of the vehicle heading at time ste in radians with north being zero heading and clockwise being ositive. v v ) = velocity of the vehicle at time ste in m/s. The rocess to be estimated is now governed by the non-linear stochastic difference equations x ) x 1) v 1)sin v 1) w1 1) 3.1) y ) y 1) v 1)cos v 1) w2 1) 3.2) sinv ) sinv 1) w3 1) 3.3) cos v ) cos v 1) w4 1) 3.4) vv ) vv 1) w5 1) 3.5)

78 77 The choice of sin v ) and cos v ) as state variables instead of v ) simlifies the state equations since v ) is in radians and is cyclic meaning that -π and π are the same state and this discontinuity or state jum is not easily accounted for in the EKF. For the measurement equations the observation variables are chosen to be the same as the state variables. Z ) [ x ) y ) sin ) cos ) v )] m m vm vm vm T Where x ) m = the corrected measurement of the vehicle easting osition at time ste in meters. y ) m = the corrected measurement of the vehicle northing osition at time ste in meters. sin vm ) = the sine of the vehicle heading measurement at time ste in radians with north being zero heading and clockwise being ositive. cos vm ) = the cosine of the vehicle heading measurement at time ste in radians with north being zero heading and clockwise being ositive. v vm ) = the measurement of velocity of the vehicle at time ste in m/s. Note that x m ) and y m ) are not equal to the raw osition x' ) and y ' ) from the GPS receiver but are the corrected measurements that include the last event driven estimate of the GPS error x ' M) and y ' M ) which occurred before time ste. x m ) x' ) ' M ) 3.6) x

79 78 y ) y' ) ' M ) m y 3.7) Where x' M ) and y ' M ) are the GPS error estimates offsets) for the east and north direction resectively from the th M event. And the measurement equations are defined as x m y m ) x ) v1 ) ) y ) v2 ) sin vm ) sin v ) v3 ) cosvm ) cosv ) v4 ) v vm ) v ) v5 ) v 3.8) 3.9) 3.10) 3.11) 3.12) The nonlinear state equations and measurement equations above can be written in matrix form X f X w 1 1) 3.13) Z h X ) v 3.14) Where T w [ w1 ) w2 ) w3 ) w4 ) w5 )] and T v [ v1 ) v2 ) v3 ) v4 ) v5 )] reresents the vector of rocess noise and the measurement noise resectively. The function f can be used to comute the redicted state from the revious estimate and similarly the function h can be used to comute the redicted measurement from the redicted state.

80 79 f and h are nonlinear and cannot be alied directly. Hence they are linearized about the revious and current states resectively and are written as follows Welch & Bisho 1995) ) ˆ ~ w X X A X X 3.15) v X X H Z Z ) ~ ~ 3.16) Where X and Z are the actual state and measurement vectors X ~ and Z ~ are the aroximate state and measurement vectors defined as follows ) ˆ ~ 1 X f X ) ~ ~ X h Z Xˆ is the a osteriori estimate of the state at ste and A is the Jacobian matrix of artial derivatives of f with resect to x that is ) cos 1) ) sin 0 1) 0 1 ) ˆ 1 ] [ ] [ ] [ v v v v j i j i v v X X f A 3.17) H is the Jacobian matrix of artial derivatives of h with resect to X that is an identity matrix.

81 ) ~ ] [ ] [ ] [ X X h H j i j i 3.18) At each time ste the Jacobian is evaluated using the current redicted states. This rocess essentially linearizes the non-linear function around the current estimate. The comlete set of EKF equations is shown below ) ˆ ˆ 1 X f X 3.19) Q A P A P T ) R) H P H H P K T T 3.21) )) ˆ ˆ ˆ X h Z K X X 3.22) P K H I P ) 3.23) The filter is started with I P 0 and the covariance matrix Q and R are both defined as fixed diagonal matrices Q

82 R Lane status monitor EWMA SPC control chart Statistical rocess control SPC) consists of a diverse set of tools for quality monitoring and rocess imrovement. The most common method in the SPC tool-set is the control chart. A control chart is used to track changes in the mean and variance of a deendent-variable time-series Shewhart 1931). The chart contains a center line that reresents the average value of the quality characteristic deendent variable or control data) being monitored and corresonds to the in-control state. Two additional horizontal lines called the uer control limit UCL) and the lower control limit LCL) are also shown on the chart. These control limits reresent the statistical decision value that is used to determine the in-control and out-of-control state of the rocess. As long as the oints control data) remain within the control limits the rocess is assumed to be incontrol and no action is necessary. However a oint that exceeds the control limits is interreted as evidence that the rocess is out-of-control. The traditional Shewhart control chart Shewhart 1931) uses only the information about the rocess contained in the most recent samle observation and ignores any information given by the entire time series of oints. The exonentially weighted moving average EWMA) control chart utilizes a

83 82 weighted average of all ast and current data to detect small rocess shifts Montgomery 2008). The control data used in EWMA is defined as W t) Y t) 1 ) W t 1) W 0) Y 3.24) 3.25) The UCL and LCL of the EWMA control charts are UCL Y L [1 1 ) 2 2t ] 3.26) 2t LCL Y L [1 1 ) ] 3.27) 2 Where Y t) is the observation at time t and W t) is the EWMA data at time t. is the standard deviation of control variable Y.The starting value W 0) is equal to the average of reliminary data Y. 01 ] is a constant which assigns weight between new data and ast data. L is a factor which defines sensitivity of detection and false alarms and can be interreted as a multilier of the standard deviation for control limits. To imlement EWMA SPC control on lane changing detection the observation data is defined as v ) l ) Y ) h ) 180 * 3.28) Where h ) is the heading error degrees) between the vehicle heading ) radians) and the lane heading l ) radians) at time. v

84 83 In this chater both the detection of lane change events and turn right or left) events are imortant. Lane change events are used to udate the vehicle lane status. For the detection of lane change events one assumtion is made: Assumtion: If the curvature of roadway is not sufficiently catured by discrete wayoints then slines would be required from the RSE MAP this is not addressed in this imlementation). Figure 3.5 shows the comonents of the lane change model. Assumtion 1 ensures that the curvature of the roadway can be catured at any time. To simlify calibration average heading error h is calculated from h ). The UCL and LCL of lane change events are defined as 2 UCL lane Y L lane lane [1 1 ) ] 3.29) 2 2 LCL lane Y L lane lane [1 1 ) ] 3.30) 2 and the UCL and LCL of turn events could be defined as 2 UCL turn Y L turn turn [1 1 ) ] 3.31) 2

85 84 2 LCL turn Y L turn turn [1 1 ) ] 3.32) 2 A v k l n v c T h B Figure 3.5 A lane changing model Since the common-mode GPS errors are corrected by differential corrections the average heading error Y should be zero. L lane and L turn are usually equal to 3 as tyical 3-sigma control limits. The most imortant arameter is the standard deviation of heading error lane which affects the UCL and LCL of lane change events. In order to calibrate lane the lane changing rocess is modeled as a deterministic rocess given assumtion 2 as shown in Figure 3.5. T l n v k v c and h denote the duration of lane changing the lane width lane longitudinal seed lateral seed and the absolute value of average heading error in the lane change resectively. The rocess of lane changing could be described as follows: Suose lane changing starts from time 1 EWMA SPC control data W ) will increase until T when the lane changing

86 85 rocess comletes shown as equation 3.33)-3.36). W T) W1) h h h W2) 1 T 1 T h W T) 1 1 T h 3.33) 3.34) 3.35) 3.36) A lane changing event is claimed to be detected if W T ) is greater than UCL or less than LCL deicted in equation 3.37). W T) ) 2 lane If a driver changes behavior and does not commit to the lane change the data may indicate the start of the change but will include the return to the original lane. The latest time to regret is T. Therefore W T ) should stay in the control limits in order to 2 2 avoid false alarm shown as equation 3.38). W T ) ) 2 2 lane A bound on lane can be defined as 3.39) by combining 3.36)-3.38) as T h lane h 3.39) h in equation 3.39) can be substituted by a inverse trigonometric function T

87 86 arctan ) derived from Figure 3.5. Suose the outut of arctan ) is in degrees) ln h arctan 3.40) vkt Therefore the bound of lane is determined by lane width l n vehicle seed v k and lane changing duration T given a fixed as shown in 3.41). l n arctan vkt T l n lane arctan v k T 3 2 T 3.41) The false alarm false ositive) and miss detection false negative) errors are both undesirable for lane changing detection. The smaller the value of lane the higher the robability of a false alarms. The larger the value of lane the higher the robability of miss detection. Therefore the median value is selected to be the value of lane shown in equation 3.42). lane l n arctan vkt T T ) 6 2 In 3.42) ln and v k are assumed known. The only random variable is the duration of the lane changing event T. The duration of the lane change event is modeled by Toledo and Zohar in Toledo & Zohar 2007). They found that the range of lane change duration varies from 1 second to 13 seconds with mean 4.6 seconds and standard deviation 2.3 seconds.. Thiemann et al. Thiemann et al. 2008) examined the Next Generation Simulation data NGSIM) Federal Highway Administration 2009) from

88 87 Federal Highway Administration FHWA) and showed that the mean duration of lane changing is 4.01 seconds with standard deviation 2.31 seconds which comly with the findings of Toledo and Zohar. Figure 3.6 The relationshi between and T given 0. 4 l n 3. 2m lane and v k 13.33m / s To imlement the EWMA SPC control chart the initial value of T for real-time alication can be determined as the mean of lane changing duration in revious studies aroximately 4~5 seconds. Since different eole have different driving behaviors it is likely to have a different T for each driver. Given the assumtion that drivers behave somewhat consistently when changing lanes T could be estimated from driver s historical lane changing data and the osition of surrounding vehicles by vehicle-tovehicle communication which could be considered as future research. The relationshi

89 88 between lane and T can be described as shown in Figure 3.6 as a monotonically decreasing curve given fixed ln and v k.

90 89 a) b) Figure 3.7 a) An examle of vehicle events detection; b) Events detection with EWMA control chart

91 90 When a turn even occurs the EWMA control data W ) exceeds the control limits established for a turn event. Both the lane and vehicle headings will change when the segment status is udated to match the MAP ma hence the EWMA control data W ) will dro back into the turn detection control limits. However the EWMA control data will not converge back into the control limits of lane change event immediately even if the new heading observation is within the lane control limits due to the inertial effect of EWMA control chart Montgomery 2008). It usually takes several seconds for the EWMA data to dro into the control limits of lane change event after a turn event is detected. As a result any new lane change event occurring within the duration of inertial effect would not be detected. This inertial lag can be addressed by restarting a new control chart when a new turn event occurs. An examle of the EWMA control chart alied to driving event detection is shown in Figure 3.7a). A vehicle heads eastbound then merges into the right lane and executes a right turn. The on-board GPS receiver oututs data every 1 second. The rocess of vehicle movement is monitored by the EWMA control chart as shown in Figure 3.7b). The heading error t h ) is treated as raw data. Every second the EWMA data W t) is calculated by using 3.24). The arameter values are set to: Y =0 =0.4 L lane =3 Lturn =3 and turn =18. According to field data l n 3. 3m v k 11.5m / s and T 5s lane is equal to by equation 3.42). The UCL and LCL for lane change event detection and turn event detection are: UCL 2.7 LCL -2.7 UCL 27 LCL -27. To lane address the latency of lane changing detection the model roosed in equation 3.38 lane turn turn

92 91 shows that the lane changing can be detected after half time of lane time which can be validated in the examle in Figure 3.7b). The lane changing time takes about 5~6 seconds by counting from third heading error oints stars in Figure 3.7 b)) deviated from zero line. The EWMA data exceeds UCL at third seconds when the lane changing event is detected. So our roosed algorithm can detect lane change once the vehicle asses the lane marker which is assumed to be the middle of lane changing time. 3.5 Turn event-driven lane alignment otimization The EKF and SPC control chart rovides state udates and detects turning events. However the vehicle osition is still uncertain due to the otentially noncommon-mode GPS errors 0.1-4m). In order to estimate the noncommon-mode error the vehicle turning inbound and outbound trajectories are combined with the MAP to measure the vehicle offset from the estimated actual lane inbound and outbound trajectories shown in Figure 3.8 a) & b). A turn event-driven lane alignment otimization roblem is solved to estimate the average noncommon-mode error in the rocess of turn movements. To better understand driver s behavior for turn movement more than 2000 turns are observed in NGSIM raw video data in Lankershim Boulevard in Los Angeles CA and Peachtree Street in Atlanta GA. Table 3.1 shows that the robability of not drifting lanes is retty low about 0.6 for left turns and 0.4 for right turns. Therefore it is hard to recisely redict which lane the driver selects after the turn. However the lane number could be set to an initial estimate using the ma-matching algorithm. If the initial lane number is correct the subsequent lane changing events will be reasonable. Otherwise if

93 92 the initial lane estimate is incorrect the subsequent lane changing may violate the geometry of roadway for examle a detected right lane change violates the revious status that the vehicle was in the most right lane. The otimization roblem can be resolved to re-estimate noncommon-mode error after the vehicle s revious lane number is determined.

94 93 a) b) Figure 3.8 a) GID ma with inbound-outbound trajectory of two tye turns; b) Line aroximations for inbound-outbound trajectories of right turn

95 94 There are two characteristics of this roblem that rovide an oortunity to estimate the error: First the GPS inbound-outbound trajectory across the intersection contains information about the direction of the turn that the driver makes. Second given a MAP and a turn tye the true inbound-outbound trajectories can be comared to the measured trajectory and the GPS error alignments. ' x ' y ) can be estimated from the lane and turn Table 3.1 Probability of no lane drift for turns in NGSIM data Number of outbound Lanes Turn tye Number of observed turns Number of turns with no drift 1 lane drift 2 lanes drift Probability of no drift 2 Left N/A 0.62 Right N/A Left Right Two scenario sets S x and S y are created by samling some of the recorded GPS oints. S x contains some x s s which are used to test the vertical distance between S x two horizontal lines while S y contains some y s which are used to estimate the s S y horizontal distance between two vertical lines as shown as Figure 3.8b). The lane alignment otimization roblem can be stated as: Objective function: min Z x y

96 95 Subject to the constraints: S y s s s m y x y x y x S 2 )) ) 1 S x s s s m x y x y x y S 2 )) ) 1 x y s s m d c cy y x ' ' ) y S s ' ' ) d y c y x s s y S s y x s s m b a ax x y ' ' ) x S s ' ' ) b x a x y s s x S s This otimization roblem can be solved as a weighted least square roblem. Z is minimized when its gradient with resect to each variable is equal to zero 0 ' 0 ' y x Z Z 3.43) The otimal solution is derived from 3.43) as follows ) 2 ) 1) ' 1) 2 ) 1) ' ac K c a K a ac K c a K c y x 3.44) Where x S y s s y S s s x Y S X S a K and y S x s s x S s s y X S Y S c K Therefore the GPS noncommon-mode error can be roughly catured from turn events.

97 Field data results To evaluate the effectiveness of the seudo-lane level osition estimation system an exeriment was conducted around the Mountain and Seedway intersection in Tucson AZ as shown in Figure 3.9. The OBE installed on the test vehicle features a 500Mhz rocessor 256MB of memory 4GB of comact flash disk sace multile radios WiFi DSRC) and an integrated USB GlobalSat BU-353 GPS receiver and antenna. The DSRC communication range of v2i has been measured to be about 600~700meters in this test site. Figure 3.9 The test intersection in Tucson AZ Once a turn is detected and finished two linear equations are estimated by the trajectory lines. The otimal solution is calculated by 3.44) which is considered as the

98 97 GPS noncommon-mode error. Then the states of the EKF are alied with this GPS drift error. The GPS error is corrected just after the turn event as shown in Figure A lane change detection examle with 1-lane left turn 1-lane right turn and 2-lane left turn is deicted in Figure Figure 3.10 GPS noncommon-mode error fixed by lane alignment otimization for the left turn event

99 98 Figure 3.11 Lane change detection by SPC control chart Three routes were driven with each having different lane change durations. The results are summarized in Table 3.2. The Number of false ositives a detected event which is false) and the number of false negatives a true event without detection) are both equal to 2 out of 61 total lane-change events. The total lane changing detection rate is about 93%. All of the turns were detected because heading errors are significant and easy to detect. There was no observed error for turn detection. Even though a few lane change detection failures occurred due to the inaccuracy of the low cost GPS the vehicle lane status was reset each time that a turn event was detected.

100 99 Table 3.2 Exerimental Results 1st exeriment 2nd exeriment 3rd exeriment lane change duration sec) # of lane changing # of false ositives # of false negatives 2~3 4~ Summary A seudo lane-level ositioning system was develoed using only low cost GPS in a v2i environment. The system consists of three major comonents: v2i communication of GPS common-mode corrections; an Exonentially Weighted Moving Average EWMA) control chart monitor for lane changing and turn detection; and a lane alignment otimization model to estimate the noncommon-mode GPS errors. Pseudo lane-level ositioning is achieved under the assumtions that no GPS outage occurs drivers change lanes at a constant seed and the roadway geometry is well catured in the MAP. Future research will focus on solving some otential roblems existing in this initial aroach. First the roblem of GPS blockage can be addressed by other vehicle sensors

101 100 such as gyro odometer and vehicle wheel encoders that can also address the GPS drift issue at low seeds and rovide imortant information about lane. Second GPS noncommon-mode error estimation on a straight road is another challenge. It is likely that some vehicles will not execute turning maneuvers and the time between GPS offset udates may be long enough that the GPS drift will significantly affect ositioning. This might be addressable by cooerative sharing of information using vehicle-to-vehicle v2v) communications where all of the equied vehicles on a street share GPS offset estimates and udates based on the oulation information.

102 101 CHAPTER 4 ROBUST ACTUATED PRIORITY TRAFFIC SIGNAL CONTROL WITH VEHICLE- TO-INFRASTRUCTURE COMMUNICATIONS This chater examines riority based traffic signal control using vehicle-toinfrastructure communication to send riority requests from a vehicle to an intersection. Priority control allows certain classes of vehicles such as emergency vehicles or buses to receive referential treatment at a traffic signal. At any time it is ossible that more than one qualified vehicle is aroaching an intersection and each vehicle may send a riority request. The traffic control algorithm must consider multile requests as well as be robust to uncertainty in the desired service time. Given the current information from multile riority requests a mixed integer linear mathematical rogram MILP) is solved for each intersection to obtain an otimal signal timing lan. This chater first resents a deterministic MILP that is alicable for control of multile emergency vehicles. Then a robust MILP is develoed for transit vehicles e.g. buses) where the desired service time might be uncertain due to oerational factors such queuing and assenger boarding/alighting. The solution to the robust control roblem is integrated with actuated traffic signal control to be resonsive to real-time non-riority vehicle demand. Finally coordination between adjacent signals is achieved by adding coordination requests along with other riority requests. Due to the limited number of binary variables in the formulation the robust MILP can be imlemented in real-time signal control. The

103 102 roosed aroach is comared with state-of-ractice coordinated- actuated traffic signal control with transit signal riority TSP) under several oerating scenarios using microscoic traffic simulation. The simulation exeriments show that the riority based traffic signal control is able to reduce transit delay by 18% and all vehicle delay by 3%. 4.1 Introduction With the advent of IntelliDrive SM for Mobility in United States RITA 2010)AASHTO 2009) it may soon be ossible to obtain additional information about the network state and vehicle oerations. IntelliDrive SM formerly known as Vehicle Infrastructure Integration VII) Faradyne 2005) is a suite of technologies and alications that use wireless communications to rovide connectivity which includes vehicle-to-vehicle v2v) communication and vehicle-to-infrastructure v2i) communication called v2x in general. A variety of challenges as well as roblems arise when considering traffic control within a v2x environment. One of the challenges is how to imlement riority oerations that resolve multile conflicting requests from a variety of different classes of vehicles including emergency vehicles and buses. With v2i communication in an IntelliDrive SM world vehicle information will be able to be obtained u to 1000 meters away from the road-side equiment RSE) at an intersection. Traditional riority control system in United States can be categorized into Emergency vehicle reemtion and transit signal riority TSP). An emergency vehicle can request signal reemtion treatment by using either otical acoustic secial inductive loo

104 103 technology or based on Global Positioning System GPS) ositions Nelson & D. Bullock 2000). Preemtion generally involves a control strategy that immediately switches from current hase to a re-selected hase for the first received request. Transit riority can use the same technology but can be served by minor modifications to traffic signal lan arameters offset adjustment green slit reallocation hase insertion or hase rotation) to favor the movements of transit vehicles Evans & Skiles 1970) Yagar & Han 1994) Balke et al. 2000) Furth & Muller 2000) Skabardonis 2000)Baker et al. 2002) Head 2002) H. Liu et al. 2003) and H. Smith et al. 2005). In current emergency vehicle reemtion systems only one request is served at a time. Therefore if multile vehicles are aroaching an intersection at one time and they request conflicting hases the first request received would be served even if a safer and more efficient solution could be achieved by considering all active request simultaneously. While emergency vehicle oerators are trained to be observant and vigilant there have been cases where two emergency vehicles have collided in an intersection ABC ). Roadway safety has been noted as a significant emergency resonder issue The Transortation Safety Advancement Grou 2010). With vehicle-toinfrastructure communication systems the signal controller can generate an otimal signal lan for multile requests and send feedback back to the vehicles so that they are aware of otential conflicting requests and lanned signal controls. Transit signal riority is a oular tool for imroving transit erformance and reliability H. Smith et al. 2005). Tyically the riority strategy include extending a hase to allow a transit vehicle to ass or terminating conflicting hases allowing early service

105 104 to reduce delay. However it is ossible and maybe likely that more than one bus may arrive on conflicting aroaches at an intersection during a cycle. In this case there is a need to simultaneously consider the multile requests for riority is a way that is not disrutive or inefficient to other traffic. Other factors such as occuancy and schedule adherence are imortant considerations that can be used to manage riority requests but it is still likely that multile transit vehicles will desire riority. Advanced communication technologies have been alied on transit signal riority TSP) control rojects in the ast G. Chang et al. 1996)Liao & Davis 2007) and Ekeila et al. 2009). However very few references can be found that address the multi-riority request issue. Head et al. Head et al. 2006a) roosed a mixed integer nonlinear rogramming MINP) formulation which could accommodate multile riority requests and minimize the total riority delay. However there are several shortcomings in this formulation. First the MINP formulation takes relatively long time to generate otimal solutions due to its nonlinearity. Second bus arrival times are assumed to be deterministic which is reasonable for emergency vehicles but not realistic for buses. Third vehicle actuation is not incororated into the formulation which limits the control to behave as fixed-time and does not allow for vehicle detection to be used to take advantage of gas in traffic flow. The goal of this chater is to address the multile riority request issue within coordinated traffic signal oerations through a robust mathematical otimization aroach and an imlementation that allows vehicle actuation. Robustness of roosed aroach is reresented in two-folds. The first robustness is from the definition of robust

106 105 otimization. Robust otimization is defined as a modeling methodology combined with comutational tools to rocess otimization roblems in which the data are uncertain and is only known to belong to some uncertainty set Ben-Tal and Nemirovski 2002). Estimated time arrivals of riority request are considered as an uncertainty interval with unknown distribution rather than a oint of time arrival. The other robustness is including actuated control when it comes to imlementation of our roosed methods since future vehicle actuations are unknown. Therefore riority control and vehicle actuations are both considered to imrove riority delay as well as traffic delay. In this aer three traffic modes are considered: emergency vehicles buses and assenger vehicles within a decision framework that can accommodate edestrians and bicycles. One assumtion is made: The sequence of hases in a ring is fixed and hase skiing is not allowed. This is a reasonable assumtion since hase rotation and skiing can cause confusion to the motorist loss of coordination and long delay to the traffic stream Skabardonis 2000). It is understood that hase rotation such as lead-lag and lag-lead can roduce useful behavior is some circumstances. This chater is organized as follows. Table 4.1 contains a summary of the model notation. Section 4.2 introduces a new signal lan modeling tool called hase-time diagram which enhances the recedence grah reresentation of a dual-ring controller develoed in Head et al. 2006a) and rovides a useful visualization of the riority timing roblem. Section 4.3 resents a deterministic mixed integer linear rogram MILP) formulation to linearize the MINP formulation in Head et al. 2006a). This deterministic

107 106 MILP formulation is designed for emergency vehicles which are assumed to travel at a constant seed. Section 4.4 addresses the uncertainty of bus arrival and rooses a robust MILP formulation. In Section 4.5 actuated control is integrated into the robust formulation to imrove the efficiency of the control strategy by reducing the delay for assenger cars. In Section 4.6 additional constraints for signal coordination are added into the robust MILP formulation to simultaneously consider both a rogression or green wave for assenger vehicles and riority for requesting vehicles. Section 4.7 resents two numerical examles for isolated intersections and coordinated intersections resectively comaring the different strategies. Concluding remarks along with future extensions are reorted in the Section 4.8. Table 4.1 Symbol definition of decision variables and data Tye Symbol Definition P The set of hases c P c The set of coordinated hases P c P Sets k K The set of cycles j ) J P The set of riority requests jth request that is active for hase ) J is a subset of the integers) k) P K The set of coordination requests for hase c in cycle k) c c Decision variables a k Maximal available green extension time for actuated control at hase during cycle k d jk Priority delay in cycle k for riority request j)

108 107 d jk Maximal riority delay in cycle k for riority request j) c d ck Coordination delay in cycle k for coordinated hase g k Green time for hase during cycle k Necessary green time the maximal one of minimial green and g k re-allocated green time) for hase during cycle k starting from t k Starting time of hase during cycle k t k Latest starting time of hase during cycle k v k v k Phase duration time of hase during cycle k including clearance time Maximal hase duration time of hase during cycle k including clearance time 0-1 binary variables for assigning a riority request to a cycle if jk jk 1 the riority request j) is served in cycle k; else not served in cycle k) C Common cycle length for coordination min g k Minimal green time for hase during cycle k Data max g k Maximal green time for hase during cycle k M A large number O Offset for the current intersection r Red clearance time for hase

109 108 Q j Necessary green time to clear the queue for riority request j) c Q c k Necessary green slit for coordinated request c k) R j Estimated time of arrival for riority request j) c R c k Estimated time arrival for coordination request c k) R j Lower bound of estimation of time arrival for riority request j) R j Uer bound of estimation of time arrival for riority request j) c R c k Lower bound of time interval for coordination request c k) c R c k Uer bound of time interval of time arrival for coordination request c k) w j Weight for riority request j) w c k Weight for coordination request c k) y Yellow clearance time for hase 4.2 Phase-time diagram: a new tool to model traffic signal controller logic The signal controller model considered in this research is based on the standard North American NEMA dual-ring eight-hase controller. A four-legged intersection with eight movements is shown in Figure 4.1a). Tyically each ring in the controller contains 4 hases deicted in Figure 4.1b). A barrier exists that crosses both rings between grous

110 109 of conflicting movements so that all hases in one grou have to terminate before any hase in the other grou starts. 4 7 Grou Barrier Grou 2 5 Ring Ring Barrier a) b) Figure 4.1 Dual-ring eight-hase controller The dual-ring controller can be modeled by a traditional recedence grah as deicted in Figure 4.2 Head et al. 2006b). Arcs in the recedence grah reresents the duration of hases while nodes reresents the hase transitions. Phase intervals can be easily visualized in the recedence grah by decomosing each arc into its resective interval recedence grah. However the recedence grah is only a one dimensional grah which has some drawbacks: 1) the sloe of arcs and vertical osition of nodes are not quantified; 2) the feasible timing region defined by minimal and maximal green is not visualized; 3) The riority requests are shown only as events in time with an association to an arc not as ossibly being served in multile cycles.

111 110 t 21 t 41 t 22 t 42 t 11 t t 31 t t 12 t t 32 t t 61 t 81 Cycle 1 Cycle 2 t 62 t 82 Figure 4.2 Precedence grah reresentation of a dual-ring controller R 21 t 42 R 63 t Figure 4.3 Phase-time diagram reresentation of a dual-ring controller To better model the signal controller logic with riority requests a new tool called a hase-time diagram is roosed. Given the revious assumtion of a fixed hase sequence a hase-time coordinate system is constructed with one horizontal time axis and two vertical hase axes as shown in Figure 4.3. The origin denotes the current time and current hase. Phases in ring 1 are evenly distributed on the left vertical axis in a

112 111 sequence starting from the current hase while the hases in ring 2 are shown on the right vertical axis. Based on the initial settings the roerties of hase-time diagram are listed as below: 1. Physical meaning of arc sloe) Nodes reresent hase transition events and arcs reresent hase duration time. The sloe of the arcs deends on the hase duration. If a hase times the minimum time the arc will be short with a high sloe hase times for the maximal time the arc will be long with a low valued sloe ). If a max 1/ k g ). 2. Feasible region) Any iecewise line starting from the origin stands for a signal lan in the hase-time diagram. However the feasible region of the signal lan is bounded in a fan-shaed area by the shortest ath fastest timing as determined by each hase s minimal green times) and the longest ath slowest time as determined by each hase s maximal green times). Any iecewise linear ath through each hase between the shortest and longest ath is feasible. 3. Request reresentation) A riority or service ) request is associated with a desired service time and service hase P) is denoted as min 1/ g k R j which reresents the arrival time of jth request for hase ). Any request R j will be served in one of the future cycles during hase deending on the realization of the signal lan. as cyclic serving bars CSB) on the hase-time diagram. R j can be deicted 4. Delay visualization) There are two cases that occur when a request R j is served by a signal lan: without delay or with delay. If the iecewise line of a signal lan intersects a CSB at any oint R j is served at that oint in time without delay. If the

113 112 iecewise line of a signal lan does not intersect any of the CSBs R j gets served at the moment when the iecewise line cross right hand side of a CSB for the first time. The corresonding delay for CSB deicted as dashed lines in Figure 4.3. R j is horizontal distance from the iecewise line to the served Two riority requests R 18 and R 13 are shown as CSBs in Figure 4.3. R 18 is served in cycle 1 by hase 8 in ring 2 as shown by the iecewise line. R 13 is served in cycle 2 by hase 3 in ring 1. However both of requests are delayed in this illustration for the samle signal lan. Thus the delay for R 18 occurs during the first cycle and the delay for R 13 during the second cycle. The delay is calculated as d t R 21 seconds; d t R 9 seconds The diagram resented here is comletely extensible to controllers with more or fewer rings and hases and can accommodate any ring barrier and hase configuration. In fact the hase-time diagram can be considered as a rojection from recedence grah with determined vertical ositions for each node. The hase-time diagram also rovides an intuitive visualization for the roblem of determining the best signal timing lan given a set of riority requests. Any iecewise linear ath in the feasible region can be selected as the timing lan. The ath that minimizes the total delay would be the otimal lan. Similarly the hase-time diagram will allow consideration of other controller behaviors such as coordination and hase actuation in subsequent research.

114 Deterministic mixed integer linear rogram MILP) formulation Head et al. Head et al. 2006a) roosed a mixed integer nonlinear rogramming MINP) formulation which could accommodate multile riority requests and minimize the total riority delay. However the solution times increase dramatically due to nonlinearity of the formulation. For ractical uroses a MILP formulation is roosed in this section to linearize the MINP formulation in Head et al. 2006a). Also the total number of integer variables is reduced by 50% in MILP formulation. The MILP model is: Minimize j k w j d jk 4.1) Subject to t t 0 4.2) t2 k t1 k v1 k k 4.3) t6 k t5 k v5 k k 4.4) t3 k t2 k v2 k t3 k t6 k v6 k k 4.5) t7 k t2 k v2 k t7 k t6 k v6 k k 4.6) t4 k t3 k v3 k k 4.7) t8 k t7 k v7 k k 4.8) t1 k 1 t4 k v4 k t1 k 1 t8 k v8 k k 4.9) t5 k 1 t4 k v4 k t5 k 1 t8 k v8 k k 4.10) v g y r k 4.11) k k

115 114 R g max g g k 4.12) min k k k t g 1 ) M j k 4.13) j k k jk Rj t k 1 g k 1 1 jk) M j k 4.14) d 1 j 4.15) k jk 0 1 j k 4.16) jk t R 1 ) M j k 4.17) jk k j jk d g v 0 j k 4.18) jk k k The objective of the mathematical model is to minimize the total weighted delay for all active riority requests. The weights w j can be considered as function of real-time bus occuancy and adherence of schedule or as mission riority for emergency vehicles. Constraints 4.2)-4.10) reresent the same recedence constraints deicted in Figure 4.2 to model a set of recedence relationshis starting at t = 0 and considering K total cycles. Different initial hases will result in different structure of constraints from 4.2)- 4.10). There are 8 different starting hase combinations given the standard NEMA 2- ring 8-hase configuration. The recedence constraints can be modified according to alternative ring configurations. Constraints 4.11)-4.12) are hase interval constraints which define the feasible hase duration based on minimal and maximal green times as well as yellow and all red clearance intervals. Constraints 4.13)-4.16) are enhanced hase service selection constraints. As deicted in Figure 4.3 request j) at time R j )

116 115 could be served in several cycles by hase on CSBs. Binary variables jk are introduced to address the combinatorial otimization roblem to select the cycle to serve request j). When 1 R j is bounded by constraints 4.13) and 4.14) which are modified to be jk t 1 g k 1 Rj t k g k j k 4.19) k which means request j) is served in cycle k. When 0 constraints 4.13) and 4.14) are relaxed meaning request j) is not served in cycle k. Constraint 4.17) is used to evaluate the delay when the request j) is served in cycle k. Combining the nonnegativity constraint 4.18) and minimal objective function 4.1) riority delay can be assessed by the equivalent equation 4.20) as below when 1: d jk k j jk max 0 t R 4.20) Although MILP address the same roblems as MINP the solution times in the new MILP formulation are decreased by a factor of 5 to 10 times even for small roblems. jk 4.4 Robust mixed integer linear rogram MILP) formulation Traffic dynamics include significant randomness due to the driver behavior based flow rocesses. Due to the uncertainty of the traffic state e.g. queue length) the actual arrival times of riority requesting vehicles may drift away from the redicted or most desired time. The otimal solution from deterministic MILP could actually be sub-otimal or even result in worse erformance due to this uncertainty. Therefore it is necessary to

117 116 develo a formulation which can accommodate the stochastic factors and roduce a signal lan that is robust in roviding good erformance when uncertainty is a factor. When considering that riority request times R j are random variables it is very difficult for a decision maker to to exlicitly model the underlying robability distribution that would be required for a traditional stochastic otimization aroach. In the case of riority control with deterministic requests the request is usually lanned to be served at the end of the requested hase to minimize the delay of other conflicting requests. The worst case occurs when the vehicles cannot be served in the lanned hase and the hase is unnecessarily extended. A robust otimization aroach which erforms well across all scenarios and hedges against the worst of ossible scenarios is another way to deal with randomness Kouvelis & Yu 1997). Insired by the merits of robust otimization randomness with robustness can be addressed in three ways: 1. Relace oint arrival time redictions with request arrival time intervals to increase the chance that the vehicle can be served when the signal lan rovides the service oortunity. 2. The objective function is modified to minimize the total ossible maximal delay for each request interval. This objective is considered to be robust in the determination of the traffic signal controls. 3. Queued vehicles are treated as aggregated requests and are addressed in the green time constraints to ensure that a queue can be cleared during the service hase to allow the requesting vehicle to successful be served.

118 117 In the robust MILP formulation it is assumed that R R j varies in an interval j R j R j with unknown robability distribution defined by a uer bound value R j and a lower bound value j R. With interval arrivals cyclic serving bars CSB) on hase-time diagram become cyclic serving rectangles CSR) shown in Figure 4.4a). There are four ossible cases of signal lan to cross CST in the first cycle shown in Figure 4.4b): Case 1: t g R j. The request cannot be served. k k Case 2: R t g R j. There is some likelihood that the request will not be served. j k k Case 3: R j t k g k and t R j. The request can be served without k any delay. Case 4: R j t k g k and R j t k.the request can be served but it is likely there will be some delay. The maximal ossible delay equals k R j max 0t.

119 118 CSR t k g k Possible missing R a) j R j Time t k Max Possible Delay R R j j b) Figure 4.4 a) Cyclic serving rectangles CSR) for an interval riority request; b) Four ossible service cases for a CSR According to the analysis of the different cases Case 1 and Case 2 have the worst outcome - there is a good chance that the request may not be served. Case 3 and Case 4 are accetable since the request will certainly be served. The sufficient but not necessary condition to ensure the request can be served in hase and cycle k is: R j t g k k k 4.21) Therefore Constraints 4.13) and 4.14) are rewritten in the robust MILP as: R j t g 1 ) M j k k k jk 4.22) R j t k g k 1 jk) M j 1 1 k 4.23) The objective function of robust MILP formulation is modified to minimize the maximum ossible delay as equation 4.24). d according to the interval request R R j R j jk j shown

120 119 Minimize j k w j d jk 4.24) By analysis in Case 4 the maximum ossible delay is always achieved by the difference between starting time of hase t k and the earliest arrival time R j. The constraint 4.17) could be rewritten as d t R 1 ) M j k 4.25) jk k j jk Congested traffic conditions or an unexected arrival of many buses requesting the same hase could result in some of the buses not being served as desired.. Exlicit consideration of the queue length in front of the buses can be utilized to calculate the green time required to clear the queue. Therefore the necessary green time Q j to clear the queue for request j R can beadded into the robust formulation to accommodate congestion. If max Qj g k define max Qj g k as the best ossible solution given the maximum green time available A new constraint is added to the formulation as g Q 1 ) M j k 4.26) k j jk 4.5 Integration of robust MILP formulation and actuated control Green extension reresentation in MILP The state-of-the-ractice in traffic control today for a single intersection is actuated traffic signal. Actuated control can be rogrammed to adat to vehicle demand by serving hases when there are vehicles resent changing hases lengths as vehicles arrive forcing-off a hase and many other oerations with the urose of shifting caacity

121 120 where and when it is needed. For examle the green time of a hase is extended by detector calls as vehicle aroach an intersection. g 1 k a y 1 k 1 r 1 g k a k y r t 1 k v 1 k t k v k t 1 k Figure 4.5 Reresentation of flexible signal lan for actuated control Actuated signal control is comlicated due to the fact that cycle times and slits are determined based on actual real-time vehicle demand which is random by nature. Therefore it is imossible to derive an exact signal lan for actuated control in advance. However a flexible signal lan including flexible hase duration times could be generated combining consideration for actuation events with riority constraints. A flexible hase duration time v k is defined in three comonents: necessary green time g k which denotes the larger one of minimal green time and re-allocated green time additional maximal ossible green extension time a k and clearance time y + r illustrated in Figure 4.5. The necessary green duration is enforced while green extension is otional. For examle hase must start timing no later than time t k and sto timing no earlier than time t k + g k ). And the duration of hase could be extended as long as k g + a k ). There are two stages to imlement the flexible hase. In the first stage the controller holds hase green for g k. After g k times out the controller imlements actuated control logic with real-time demandactuating the hase for each detected vehicle

122 121 by adding the rogrammed extension time u to the maximal green time when the hase is forced-off immediately. Given this new flexible behavior constraints 4.2)-4.10) are relaced by v k and t k in recedence v k and t k which denotes the latest starting time of hase at cycle k. In other words hase in cycle k could start timing before t k but not start after t k. The hase interval constraints 4.11) and 4.12) are modified as below: v g a y r k 4.27) k k k g g k 4.28) min k k max g a g k 4.29) k k k The objective function is modified to not only to minimize the riority delay but also maximize the total maximal ossible green extension time to each hase for actuated control without adding any additional riority delay. Minimize w j k jd jk a 4.30) k k Where and are the coefficients to balance the weight of two summation items. In order to assign more weighs on total riority delay is set to a much smaller value than. As for other constraints in robust MILP with actuated control with g k is relaced g k in constraints 4.22) 4.23) and 4.26) and t k is relaced with t k in constraints 4.25) as follows.

123 122 R t g 1 ) M j k 4.31) j k k jk R j t g k k 1 jk ) M j 1 1 k 4.32) d t R 1 ) M j k 4.33) jk k j jk g Q 1 ) M j k 4.34) k j jk The otimal solutions of the revious robust MILP formulation is not unique in most cases since there are many timing otions to achieve minimal delay given limited fixed riority requests. So the overall goal of this enhanced robust MILP formulation with actuated control is to select a timing lan among those minima-riority-delay lans to maximize the flexibility to reduce the delay for assenger vehicles in real-time actuation demand. Integration of the robust MILP formulation and actuated control will result in the hase timing gaing out if no vehicles are detected extending the hase if a riority request can be served or forcing-off the hase when the maximal green extension is reached. Therefore the efficiency of green time usage is imroved for assenger cars Green extension grou GEG) and a k reassignment When the MILP formulation is solved the real-time traffic demand for each hase is unknown. Without real-time actuation detection) information the green extension a k cannot be accurately assigned in the green extension formulation resented in Section

124 In order to understand how to assign the hase green extension a k without any additional riority delay the concet of a green extension grou GEG) is develoed. Green extensions a k from the MILP otimal solutions are clustered into GEGs along the hases in a controller ring. Within each GEG a k contributes to a total amount of grou green extension time with each other. When the signal timing lan is imlemented reassigned within the GEG according to real-time actuations using the actuated signal control logic. GEG is accounted for on each controller since each ring oerates indeendently excet for the barrier crossing that must be coordinated between rings. The barrier is not considered in the algorithm resented here since the actuated controller logic enforces the barrier constraint. The generation of GEG takes two stes as defined in the algorithm in Figure 4.6. First given a defined set of fixed riority request intervals the robust MILP is solved to determine the best jk which assigns each riority request to a hase and a cycle. Once jk is determined j indicates the number of requests served by hase jk during cycle k. Second hases sequenced along a ring and across a few cycles can be searated by ositive j jk a k. Each searation is treated as one GEG. The ith GEG set is defined as s _ GEG[ i] contains all the hases k) which shares the same amount of green extension time which is denoted t _ GEG[ i]. The total green extension time t _ GEG[ i] in ith GEG is determined by: t _ GEG[ i] a ) _ [ ]) k) k k s GEG i 35) is

125 124 The green extension imlementation in the robust MILP utilizes the same control logic as actuated signal control. There are two differences: 1) the minimal green time in actuated control is substituted by necessary green time g k as determined by the solution to the MILP roblem; 2). The green extension time is not only constrained by the the maximal green or slit) but also by the remaining unassigned green extension time in the current GEG. Procedure GEG_in_Ringr) 1. Obtain jk and a k by solving the robust MILP formulation. 2. Calculate wk for hase 1.. P and cycle k 1.. K. j jk 3. Let k 1 first _ hase_ of _ ring r) i 1 s _ GEG[1] and the total green extension time t _ GEG[1] While k K do 5. While num_ hases_ in _ ring r) do 6. If w 0 then k 7. s _ GEG[ i] s _ GEG[ i] { k)} t _ GEG[ i] t _ GEG[ i] a 8. k 9. Else 10. i i s _ GEG[ i] s _ GEG[ i] { k)} 12. t _ GEG[ i] t _ GEG[ i] ak 13. End if 14. next _ hase_ in _ ring r) 15. End while 16. k k 1 //next cycle 17. End while 16. End rocedure Figure 4.6 The rocedure for generating GEG in a ring

126 125 R13 R 12 R 22 Request Times) MIP solutions j jk GEG s _GEG[1] s _ GEG[2 ] s _GEG[3 ] Flexible green extension g g t _GEG[1 ] g g g t _ GEG[2 ] g g t _GEG[3 ] 22 g Times a) t22 100s YR t 31 45s YR= Clearance interval 5s 1 3 YR YR 4 t 12 t41 65s b) Figure 4.7 a) An examle of green extension grou and reassignment; b) Green extension reassignment in GEG2

127 126 A detailed examle is illustrated in Figure 4.7a). Phases sequenced along 1st ring within 2 cycles can be reresented as a sequence of hases denoted Given three riority request intervals R 13 R 12 and R 22the otimal signal lan and cycle service selection variables j are obtained from the jk robust MILP solution. The corresonding sequence of j is reresented as jk where the first riority request is served in hase 3 of cycle 1 and the other two riority requests are served in hase 2 of cycle 2. The sequence of hases is searated into three GEGs by the ositive j jk values. The starting time of each GEG[i] is determined as well as the duration of the first hase in GEG[i] excet GEG[1]) to ensure that the riority request can be served during the allocated time interval which is exactly same as requested Q j. However the duration of each hase in the GEG is flexible and determined by the hase minimum time and the vehicle actuations. All hases in a GEG must share the total green extension time. Imlementation of GEG[2] is deicted in Figure 4.7b) using a cycle style diagram. GEG[2] contains three hases in sequence: 3 and 4 in cycle 1 and 1in cycle 2. First 3 must start timing at 45 seconds and is held for 15s. Then 3 can be extended by real-time vehicle actuations until either it gas out or it reaches the maximum time allowed by the maximum green or the total green time extension available After 3 terminates 4 starts timing. The rocess is similar excet the necessary green time is not constrained by the duration of the riority request interval. 4 times u to either its maximum green time or until the remaining green extension time is

128 127 used t_geg[2] = 0. Note that this method of green time allocation is identical to the floating force-off modes in actuated-coordinated traffic control. Similarly this could be executed using fixed force-offs as well. The details of coordination force-off modes can be found in the Traffic Signal Timing Manual Federal Highway Administration 2008). Floating force-offs flavor to assign slack or remaining green extension time to coordinated hases or riority requested hases in this research where fixed force-offs allow more unused green extension time to be used be non-coordinated or non-riority requested hases. They both have different trade-offs. Force-off modes are an imortant consideration in coordinated traffic control. Therefore the defined robust MILP formulation can also be alied for coordination with riority requests. The final goal of this Chater is to show how the MILP formulation can address the multile riority request issue on coordinated traffic control utilizing the mathematic otimization aroach as well as actuated control imlementation which systematically lans for riority requests while accommodating uncertain vehicle flow as measured through vehicle detection and hase actuation. 4.6 Robust signal coordination with riority The state-of-the-ractice in traffic control today is coordinated-actuated traffic signal control. Coordination aims to rovide smooth rogression of vehicle latoons through the determination of traffic lans that contain aroriate offsets slits and cycle times at each intersection. The benefits that can be obtained from coordination drive the need to

129 128 develo an analytical framework that simultaneously considers signal coordination and riority. Traditionally signal coordination with riority has been achieved using either assive riority or active riority. In assive riority control the signals along an arterial are coordinated in a way to create rogression for buses. Thus buses would be able to travel through intersections with minimal stos and delay Estrada et al. 2009) Furth et al. 2010). However assive riority may result in increased delay for assenger vehicles due to seed differences between buses and assenger vehicles. In active riority control the state-of-ractice is signal lan transition from coordination lan to transit signal riority TSP) lan when a delayed bus checks in. The transition methods usually include green extension red truncation and hase omits. After the bus checks out The lan is transited back from TSP lan to coordination by add subtract short way dwell max dwell and so on S.G. Shelby et al. 2006). This method of dealing active riority erforms well under low riority frequency. However it cannot handle conflicting riority requests or high frequency riority request since the logic is limited to a serving a single request at a time and tyically limited to only one request every two cycles. There is no known literature that considers the combined coordination and riority roblem in single mathematical formulation within an actuated control strategy. There are three major factors considered in a coordinated signal timing lan: offset hase sequence and slits and a common cycle length. These three factors can be easily reresented as riority request intervals. Suose the coordinated hase is c c c Requests R k R k R ck c c c in one ring. are called the coordination request to distinguish them from

130 129 riority requests. The offsets from the master clock corresonds to the lower bound c R c k. The hase slit of the coordinated hase c can be considered as c Q c k which ensures the desired green time for the coordinated hase as c g Q k 4.36) c k ck c Hence the uer bound c R c k equals c ck R Q ). The background common cycle c ck length can be ensured by scheduling the lower bound c in each cycle k such that R c c k c c c R c k for each coordinated hase c 1 R k C k 4.37) Within the MILP formulation the introduction of coordination requests does not increase the number of binary decision variables since coordination request c R c k should be always served in hase c of cycle k. Hence the hase selection constraints are not needed for coordination requests. Therefore constraints 4.31)-4.33) can be rewritten as follows. R c k c ck ck c t g k 4.38) c R k t g k k c k c ) c c d c t R k 4.40) c c k ck ck c

131 130 The objective of the robust MILP formulation with signal coordination is not only to minimize the riority delay and maximize the total green extension but also to minimize the coordination delay. A weight c d c k. The objective in equation 3.30) is modified as follows. w c k is introduced for each coordination request delay c Minimize w d w d a 4.41) j k j jk k k k c c c k Where is the coefficient for adjusting the total coordination request delay. Therefore fixed-cycle fixed-offset coordination roblems are modeled as riority control roblems that can simultaneously address coordination and riority control in the same formulation. An examle of riority control with signal coordination is illustrated in Figure 4.8. Consider ring 1 over two cycles where there is a single riority request at t R14 for hase 4 and two coordination requests c R 21 and k c R 22 for coordinated 2. Suose the coordination arameters are rovided by some signal otimization software such as TRANSYT Wallace et al. 1998) SYNCHRO Trafficware 2009) or PASSER Chaudhary & Chu 2003). In this examle the common cycle length is 80 seconds and the offset is 10 seconds. The distance between interval c R 21 and c R 22 is one cycle length. The interval length of c R 21 and c R 22 equals to the designed 2 slit minus the clearance time. The otimal solution is given by solving the robust MILP formulation with the coordination constraints. The formulation can roduce the best lan over the next few cycles in real-time without the need for traditional lan transition. To imlement the

132 131 otimal signal lan the concet of GEG is executed the exactly as described in Section Initially coordinated hase 2 2 ) in cycle 1 and cycle 2 create GEG[1] and GEG[2]. Next riority request served in hase 4 4) of cycle 2 generates GEG[3]. If there were no riority request in the formulation the GEG would equal the total available time across all the hases in each cycle. The secific imlementation of each GEG deends on different force-off modes as discussed in Section It should be noted that a different trade-off value of the signal lan can be generated by adjusting the weights in equation 4.41). The general idea is that the riority weight could be higher than the coordination weight in low volume traffic and the oosite in high volume traffic. Offset c R 21 c R 22 R Master clock GEG 1 GEG 2 GEG 3 Common cycle Coordination requests interval Priority requests interval Figure 4.8 Priority requests with coordination 4.7 Numerical exeriments

133 132 The numerical exeriments were conducted using VISSIM a microscoic simulation tool. To better simulate the real traffic signal controller logic the ASC/3 SIL software in the loo) controller was installed with VISSIM. The ASC/3 SIL feature allows a VISSIM user to utilize the same logic as a hysical ASC/3 controller during the simulation. This includes the transit signal riority TSP) rovided as an advanced feature of the controller firmware Econolite 2009). ASC/3 SIL Phase control Signal status Detector data Vehicle data MILP VISSIM COM GAMS/CPLEX Figure 4.9 Evaluation latform Otimal signal lan The entire evaluation latform contains VISSIM with COM Comonent Object Model) ASC virtual controller as the simulation environment and GAMS as otimization solver deicted in Figure 4.9. Simulation in VISSIM can be easily controlled in COM which can be created with a variety of rogramming languages including C++. First COM runs a VISSIM model and continuously reads vehicle data as VISSIM simulates the movement of vehicles. When there is no riority request the actuated control logic is erformed by the ASC/3 SIL. When a vehicle that is designated to generate a riority

134 133 request is detected a MILP rogram is formulated by the COM comonent and sent to GAMS for solution. After retrieving otimal signal lan from GAMS the COM comonent imlements the signal timing schedule by sending hase control commands hold and force-off) to the ASC/3 SIL. The number of integer variables in roosed MILP formulations is N*K where N is total number of requests and K is the number of otimized cycles. N deends on the maximal number of co-existing buses at the intersection which is generally not a very large number. Given small N and K roosed MILP formulation can be solved less than 0.1 seconds which is suitable for real-time TSP control. Cherry Ave. i Bus routes Bus stos Detectors Cambell Ave. Signal Seedway Blvd. 362 m 3 Figure 4.10 Layouts of a two-intersection arterial

135 134 Numerical exeriments on a simle two-intersection arterial model that was based on a short section of Seedway Blvd. in Tucson AZ bounded by from Cambell Ave. to Cherry Ave. Four conflicting bus routes were added in the model shown as Figure There are six bus stos on the bus routes. All of bus stos are far-side stos. It is assumed that each bus is behind schedule. So every bus sends a riority request when it aroaches intersection. In this exeriment eight methods were tested and comared with two bus frequency and three different traffic volume scenarios as shown in Table 4.2. Four of the control methods are non-coordinated control methods and the other four are coordinated control methods as summarized in Table 4.3. Table 4.2 Traffic volume for seedway Volume veh./h) Cross street Eastbound Westbound Northbound Southbound L T R L T R L T R L T R Cherry Cambell Cherry Cambell Cherry Cambell Table 4.3 Descrition of comared different methods Modes Methods Actuated Free ASC free Bus riority Signal coordination Solving MILP formulation Determ. free Robust requests

136 135 Coordinated ASC-TSP free Robust free ASC coord. Robust coord. ASC-TSP coord. Robust riority coord. In free control methods ASC free utilizes the ASC/3 SIL actuated control at each isolated intersection without riority control. Determ. free is based om te solution to the deterministic formulation roosed in Section 4.3 and imlements its otimal lan with actuated control only for case with no bus aroaching. ASC-TSP free utilizes the ASC/3 SIL actuated control with TSP logic triggered by bus check-in and check-out detectors. The basic strategy of TSP in ASC/3 SIL is early green red truncation) and green extension. Transit Priority oeration is on a first-come first-serve basis. Only one transit vehicle can modify timing during any given cycle. The detailed settings of TSP in ASC/3 SIL can be found in Zlatkovic and the Econolite Controller Programming ManualZlatkovic et al. 2010) to Econolite 2009). Robust free is based on the solution to the robust MILP formulation without coordination requestsas defined in Section 4.4. Volume 1 2 Table 4.4 Basic otimal coordination timing lan from SYNCHRO with 90s common cycle Slit s) Offset Cross street s) Cherry 12 --* Cambell Cherry Cambell

137 136 3 Cherry Cambell *: -- means data not alicable In the coordinated control methods the basic coordination signal lan is based on otimal signal timing arameters obtained from SYNCHRO 7.0 shown as Table 4.4. The only difference between the coordinated control methods is how they realize the basic coordination lan and whether riority requests are considered. ASC coord. and Robust coord. consider coordination without riority control. ASC coord. imlements the signal lan in Table 4.4 using the ASC/3 SIL coordinator. The Robust coord. method solves the MILP by adding coordination requests in rolling horizon fashion ASC-TSP coord. and Robust riority coord. address the combined coordination and riority roblems in different ways. ASC-TSP coord. erforms similarly to the ASC-TSP free excet for coordination while Robust riority coord. solves the MILP by considering the current active coordination requests and riority requests simultaneously. The exeriments involve two bus frequencies determined by headway) under three different traffic demand volumes. A total of six scenarios are comared using the eight different control methods. In each scenario the simulation is relicated using ten different random seeds in VISSIM. The measured average delay under each scenario is resented in Table 4.5. Six different measurements are rovided: 1). All is the average delay for all vehicles in the

138 137 network; 2). Main is the average delay for vehicles traveling on the arterial; 3). Mbus is the average bus delay on arterial; 4). Side is the average vehicle delay on side streets; 5). Sbus is the average bus delay on the side streets; 6). Left-turn is the average all left-turn vehicle delay. Several observations from the exerimental results in Table 4.5 can be made: 1. Coordinated methods have much lower overall vehicle delay as well as bus delay than free methods under medium and high volume. However the free methods outerform coordinated methods under low volume. This is exected since the study network has two intersections that are relatively closely saced so that coordination would be exected to imrove overall erformance. 2. The deterministic MILP erforms fairly well under low volume. but the delay increases significantly in medium and high volume. 3. The robust methods have much less bus delay as well as less overall vehicle delay comared with state-of-ractice ASC-TSP methods shown in Figure In addition the robust methods rovide relatively stable erformance for buses from side street and left-turn vehicles illustrated in Figure 4.12.

139 138 Table 4.5 Measured average delay under each scenario with eight different methods Bus frequency 5 min/bus 10 min/bus Volume 1low volume) 2 medium volume) 3 high volume) 1 low volume) 2 medium volume) Measurement ASC free Free-actuated Determ. free ASC- TSP free Robust free ASC coord. Coordinated-actuated Robust coord. ASC- TSP coord. Robust riority coord All Main Mbus Side Sbus Side Mbus Side Sbus Leftturn All Main Mbus Sbus Leftturn All Main Leftturn All Main Mbus Side Sbus Leftturn All Main Mbus Side

140 139 3 high volume) Mbus Sbus Leftturn All Main Side Sbus Leftturn

141 ASC-TSP coord.all Robust riority coord.all ASC-TSP coord.bus Robust riority coord.bus Volume 1 Volume 2 Volume 3 Figure 4.11 Overall vehicle delay and bus delay under ASC-TSP coord. and Robust riority coord ASC-TSP coord.side bus ASC-TSP coord.left-turn Robust riority coord.side bus Robust riority coord.left-turn 0.00 Volume 1 Volume 2 Volume 3 Figure 4.12 Side bus delay and left-turn delay under ASC-TSP coord. and Robust riority coord.

142 Robust coord.all Robust coord.bus Robust riority coord.all Robust riority coord.bus 0.00 Volume 1 Volume 2 Volume 3 Figure 4.13 overall vehicle delay and bus delay with or without riority control 4. Pure robust coordination results in higher bus delay comared with robust coordination with riority control. However when the traffic demand increases ure robust coordination erforms better than robust coordination with riority as shown in Figure That means riority control results in larger delay either for assenger vehicles and buses by frequently disruting the coordination when the traffic demand is high. Closer examinations of the results based on observation 3 are shown in Table 4.6. In the high volume cases Volume 3) the robust MILP outerforms ASC-TSP under all bus frequency scenarios and measurements. Considering overall vehicle delay the ASC-TSP has better results than the robust MILP under low and medium volume. However ASC- TSP has very large average bus delay under almost all cases excet for low bus frequency in medium volume. It is also observed that the ASC-TSP increases average left-turn delay dramatically under every scenario. Considering average delay reduction

143 142 robust MILP decreases overall vehicle delay bus delay and left-turn delay by 3% 18% and 37% resectively. Table 4.6 Delay changes in both ercentage %) and seconds s) from ASC-TSP to robust riority High bus freq. low bus freq. Average Volume 1 Volume 2 Volume 3 Average All 13.13% 1.59s 7.05% 0.91s 10.09% 1.25s Bus % -3.22s -3.43% -0.89s % -2.01s % s % s % s All 0.27% 0.04s 4.70% 0.72s 2.49% 0.38s Bus % s 49.90% 5.08s -2.41% -4.60s % s % s % s All -37.6% s -9.65% -2.57s % -8.78s Bus % s % -0.67s % -9.85s % s % s % s All -8.07% -4.45s 0.70% -0.31s -3.68% -2.38s Bus % s 12.03% 1.17s % -5.5s Leftturn Leftturn Leftturn Leftturn % s % s % s 4.8 Summary The multile riority control roblem is examined in this Chater under the condition that the vehicle-to-infrastructure communication is available for each emergency vehicle or transit vehicle. Given the current multile riority request information a mixed integer linear rogram MILP) is solved to obtain the otimal signal lan. First a deterministic

144 143 MILP formulation is roosed only for multile riority control of emergency vehicles due to their deterministic oint time of arrival. Next a robust MILP formulation is develoed for transit vehicles e.g. buses) to address the randomness of time arrivals by introducing the concet of a request interval and necessary green time. Third actuated control is integrated into the robust MILP formulation to mitigate the delay for assenger cars based on real-time demand using vehicle detectors. Finally signal coordination is combined with riority control in the formulation by adding coordination requests. The roosed aroach is comared with state-of-ractice coordinated- actuated traffic signal control with Transit signal riority TSP) over several scenarios. The numerical exeriments show that the robust MILP aroach is able to reduce riority delay as well as all vehicle delay and achieve real-time robust control. In this Chater it is assumed that the market enetration of IntelliDrive SM or other vehicle to infrastructure communications is significant for emergency vehicles and transit vehicles. Our ongoing research includes addressing multi-modal traffic signal control with enetration of IntelliDrive SM for different riority classes.

145 144 CHAPTER 5: A HEURISTIC ALGORTIHM TO IMPLEMENT MULTIPLE PRIORITY CONTROL FOR EMBEDDED CONTROL AT A SINGLE INTERSECTION 5.1 Introduction Multile riority control aims to solve the roblem that multile vehicles such as emergency vehicles or transit buses may aroach an intersection and request riority at the same time. This research is motivated and suorted by the Arizona E-IntelliDrive SM called E-VII before 2009) roject conducted be a artnershi among the Arizona DOT Maricoa County DOT FHWA University of Arizona Arizona State University and the rivate sector. The goal of the Arizona E-IntelliDrive SM initiative is to develo and test advanced technologies and integrate roadway systems with emergency resonder vehicles to imrove resonse efficiency as well as enhance resonder safety ADOT 2008). The details of Arizona E-IntelliDrive SM field imlementation will be resented in section 5.3. Arizona E-IntelliDrive SM rovided the hardware and technologies of v2x environment necessary to conduct a field imlementation of multile riority control. Given the v2x environment for emergency vehicles the control strategy develoed in Chater 4 are able to be imlemented at a real intersection. However CPLEX is not comatible with small kernel embedded Linux systems such as those used and installed on both RSE and OBE. It is necessary to develo a heuristics algorithm to find near-otimal signal lan for multile riority requests without the use of solvers for mathematical rogramming roblems.

146 145 In this Chater the multile riority control roblem is simlified to a olynomial solvable cut roblem by adding few assumtions. Each cut set corresonds to a unique serving sequence of multile riority requests. First the cut roblem is roved to be a olynomial solvable roblem. Second an exhaustive search algorithm is roosed to search for the good solutions within a secified tolerance range. The total riority delay of each cut set is assessed and visualized by a hase-time diagram as develoed in Chater 4. Finally the erformance of roosed heuristic algorithm is comared with the robust MILP and other methods in microscoic simulation exeriments. 5.2 Simlification of multile riority control roblems Simlification to a olynomial solvable roblem In the robust MILP develoed in Chater 4 the jk variables are the only integer decision. These integer decision variables denote the assignment of request j) to be solved in cycle k. So jk are the only hard variables in the formulation. It is necessary to find a heuristic method to seek near-otimal jk to solve the entire multile riority control roblem. The roblem of seeking near-otimal jk can be simlified as an cut roblem since the realizations of jk essential assign or cut request j) to cycle k. In order to trim undesired solutions and enhance the feasible region two reasonable assumtions are made as follows. Assumtion 1: The sequence of hases in a ring is fixed and hase skiing is not allowed.

147 146 hase. Assumtion 2: A First-come first-serve rule holds for all requests for the same Assumtion 1 is a reasonable assumtion since hase rotation and skiing can cause confusion to the motorist loss of coordination and long delay to the traffic stream Skabardonis 2000). It is understood that hase rotation such as lead-lag and lag-lead can roduce useful behavior is some circumstances. But the solution sace for signal lans is significantly reduced by the fixed hase sequence assumtion. Assumtion 2 follows a widely acceted rule - first-come first-serve in queuing theory Gross et al. 2008). Note that the assumtion 2 of first-come first-serve is only alicable for the requests for the same hase meaning that the receding riority request j-1) should always be served before the succeeding riority request j). Assumtion 2 establishes a recedence relationshi between riority vehicles that are adjacent and requesting the same hase. If the succeeding riority request j) is assigned in cycle k the receding riority request j-1) cannot be assigned to cycle k+1 k+2. Suose the number of request is J for hase and the number of considered cycles is K. Given assumtion 1 and 2 the total number of ossible cut combinations for riority request j) within cycle K can be calculated by Remark 4.1. Remark 4.1 Given assumtion 1 and 2 the size of feasible region to cut linked J P J K 1)! requests into K cycles is equal to. 1 K 1)! J!

148 147 Proof: Assumtion 1 allows considering the cut roblem searately for each hase. Therefore the total number of ossible cut combinations is equal to the roduct of the number of cut combinations for each hase. Considering the request list in each hase the roblem is to assign J requests into K cycles. According to Assumtion 2 the cut roblem is equivalent to dividing the J sequenced linked nodes into K sets. An emty set is allowable. So K -1 cuts can searate J linked nodes into K set as shown as Figure 5.1. The total number of cut combinations is equal to C J K 1 K 1) where C n r) denotes the number of r-combinations from a given set of n elements. Figure 5.2 illustrates the case when K =2. The cut can be located before the first request or after the last request. So the total number of cut combinations is J +1. Therefore combining with assumtion 1 and 2 the size of feasible region to assign J requests into K cycles is equal to J K 1)!. 1 K 1)! J! P P 1 C J K 1 K 1) The number of cycles K considered in Remark 4.1 affects the comlexity of solving the cut roblem. The roblem can be reduced to a very simle cut roblem if only two cycles are enough long to serve all the riority requests. Thus assumtion 3 is added to further reduce the feasible region.

149 148 K -1 cuts j-1 j J = 1 2 j-1 j J J linked requests K -1 combinations in total J + K -1 Figure 5.1 Illustration of cut J requests into K cycles Phase linked request list: cut c j 1 2 j-1 j J Cycle 1 Cycle 2 c 1) ) 1) 1) ) 1) J 1 2 J Request sequence J J J J J Cut combinations Figure 5.2 Priority request cut table for hase in two cycles

150 149 Assumtion 3: All the requests can be served in 2 cycles. Assumtion 3 matches the communication range limit of DSRC. DSRC has a communication range of about 500~1000 meters Y. Liu et al. 2005) which indicates that the latest arrival of riority vehicle is aroximately 37.5~75 seconds from the current time assuming the vehicle seed is 48km/h. Tyically the cycle length is greater than 50 seconds hence two cycles are long enough to serve all riority requests. Given Assumtion 1 2 and 3 the size of feasible region is equal to J 1). Therefore the NP-hard cut roblem is reduced as a olynomial solvable cut roblem P since the number of hases in a ring P is fixed. J 1) can be written as O J ) in big O notation where J denotes the maximal number of requests for one hase. Remark 4.2 concludes the simlification as follows: Remark 4.2: Given assumtion 1 2 and 3 the comlexity of assigning J P requests into 2 cycles is equal to O J ) which is olynomial. P 1 P Revised exhaustive search algorithm and delay evaluation It is desired to find near-otimal solutions via a fast algorithm rather than enumerate all ossible solutions in the feasible region; even though Section shows that the size of the feasible region of the cut roblem is olynomial. Based on Assumtion 1 2 and 3 only one cut needs to be selected in each request list J which is the set with all request for hase ordered by the lower bound of arrival

151 150 time R j. Whether to serve a request in the first cycle or the second cycle deends on the length of time interval) between two adjunct requests. Define interval j as follows: R j if j 1 j 5.1) R j R j 1 if 2 j J The larger the value of j the higher robability that the delay will be smaller if a cut is made between request j and request j-1. Denote the cuts as c j j>0) if a cut is made before request j in request list J illustrated in Figure 5.2. Note that the number of ossible cuts is equal to J +1. The best cut c equals j * when j* is largest in all j and also larger than a defined threshold which decides if cut in J 1. If every interval j is less than the threshold c equals J 1 meaning that the entire request list can be cut into cycle 1. After the cuts are made to each request list J the entire cut combination corresonds to a request serving sequence which can be evaluated easily using the hase-time diagram roosed in Chater 4. The heuristic algorithm aims to find a near-otimal assignment with accetable riority delay through enumerating different cuts from high j to low j including threshold.

152 Calculate j by equation 5.1) 2. Define vector V... ) J J * 3. Let 1 0 minimal delay d best cut grou C * {0} i c 4. While i J If J 1 0 ; c1 find_cut_orderi 1 V 1 ); Else c 1 0. While i J 1 If J 0 ; c find_cut_orderi V ); Else c 0. While i P J 1 P If J P 0 ; c P find_cut_orderi P V P ); Else c P 0. Evaluate delay d k for selected cut grou Ck { c1 c2... c... c P } in all hases dk hase_time_diagram c 1 c2... c... c P ) where k J1 J 2... J P If d d * * d k d k and * C Ck. If * d sto and return * d. i P i P 1 End while i P i i 1 End while i i 1 i1 End while i 1 Return * d 1 Figure 5.3 Revised exhaustive algorithm to find the near-otimal solutions

153 152 The detailed algorithm is resented in Figure 5.3. Sub rocedure find_cut_orderi V ) returns the ith best cut osition for hase given in an interval vector V J ) J the request So the ith best cut osition is the osition of J +1) in vector V with the ith largest value. The sub rocedure hase_time_diagram c 1 c2... c... c P ) returns the delay of inut cut grou { 1 2 P c c... c... c } by lotting the hase time diagram roosed in Chater 4. A small examle of delay evaluation is illustrated in Figure 5.4. There two riority request lists J 2 {12 } for hase 2 and J 4 {1 } in hase 4. All the cyclic serving rectangles CSR) are lotted on Figure 5.4 a). Suose a cut grou { c 0 c2 2 c3 0 c4 1 2} is evaluated using the hase-time diagram meaning that the cut before both request 2 in J 2 and J 4. Since 2= J 4 +1 this cut assigns all the requests in J 4 to the first cycle. Figure 5.4 b) lots the exact serving rectangles SR) after cuts. Bounded by the sloes of minimal green and maximal green a signal lan is generated to travel through each SR with minimal delay starting from the origin which reresents the current time. In Figure 5.4 b) the cut is evaluated by a feasible signal lan with no delay meaning that the feasible lan is also an otimal lan. Therefore the hase time diagram also rovides the otimal signal timing lan when evaluating the cut grou { c 0 c 2 c 0 c 2}. The near-otimal lan can be imlemented with real vehicle actuations using the same concet of GEG develoed in Chater 4 section

154 153 Phase CSRs Phase R Time 12 R R R R R a) b) Time Figure 5.4 a) CSRs on the hase-time diagram b) Phase-time diagram evaluation of an assignment of serving R 22 in the second cycle Simulation results To evaluate the heuristic same numerical exeriments from Chater 4 Figure 4.10) were conducted. A simle two-intersection arterial was modeled in VISSIM on a short section of Seedway Blvd. in Tucson AZ bounded by from Cambell Ave. to Cherry Ave. Four conflicting bus routes were added in the model as shown in Figure The exeriments are configured as follows: 3 traffic volumes: low medium large.

155 154 Performance comarisons of 4 non-coordinated control methods: ASC free Determ free Robust free ASC-TSP free and Heuristic where ASC free is full actuated control; Determ free and Robust free reresents the deterministic formulation and robust formulation for non-coordinated riority control resectively; ASC-TSP free is fully actuated control with TSP enabled. Heuristic denotes the roosed algorithm in this chater. 10 runs er volume er method with different random seeds. Each run lasts 1 hour. A total of 150 simulation runs were conducted. ASC free Determ. free ASC-TSP free Robust free Heuristic Volume 1 Volume 2 Volume 3 a)

156 155 ASC free Determ. free ASC-TSP free Robust free Heuristic Volume 1 Volume 2 Volume 3 b) Figure 5.5 Performance comarisons of five different methods a) Average total vehicle delay; b) Average bus delay; Average total vehicle delay and average bus are measured at three volume levels. The erformances of five methods are shown in Figure 5.5. Some observations are as follows: 1. Every method erforms very well under low volume. It is exected that ASC free would have very large bus delay since bus riority is not considered in ASC free method. 2. Determ method has large variations. It can generate a large amount of delay esecially for large volume since a deterministic request that is not served due to random effects can result in very oor erformance.

157 ASC-TSP free doesn t work very well under large volume traffic with multile bus riority. 3. Robust free method outerforms other methods with very stable solutions under all traffic volumes. 4. Heuristic method shows close results comared with Robust method with the additional benefit that it canbe imlemented for real-time control. Table 5.1 Delay increment %) from Robust free to Heuristic Volume 1 Volume 2 Volume 3 Average Total vehicle delay -2.59% -2.53% 2.31% -0.94% Bus delay -7.24% 15.87% 5.31% 4.65% Furthermore delay increment ercentages of Heuristic are shown in Table 5.1 comared with Robust free. The average total vehicle delay is the same between these two methods. There is only about 5% delay increment in bus delay for using Heuristic algorithm. The results of the microscoic simulation study shows that roosed heuristic algorithm can successfully estimate the near-otimal sequence of serving requests in the existing request table. Therefore the roosed algorithm was coded in C++ and imlemented in an embedded Linux system on an RSE as a solver to roduce nearotimal signal lans for a table of request as received from OBEs as riority requesting vehicles aroach an intersection.

158 Field imlementation To imlement the roosed algorithm in the field for evaluation and demonstration it is necessary to have a basic v2x environment with OBEs RSEs and intersections. The multile riority control algorithm resented in this Chater was imlemented based the v2x environment rovided by Arizona E-IntelliDrive SM called E-VII before 2009) rojectthe goal of the Arizona E-IntelliDrive SM initiative is to develo and test advanced technologies and integrate roadway systems with emergency resonder vehicles to imrove emergency resonse efficiency as well as enhance resonder safety ADOT 2008) System structure The entire system of multile riority control was imlemented at a real intersection at Southern Ave. & 67 Ave and tested on February and March The intersection layout is shown in Figure 5.6. The intersection is a tyical signalized fourlegged two-way intersection. The traffic signal controller for this intersection is an Econolite ASC/3 Econolite 2010). The location of RSE and MAP wayoints are shown in Figure 5.6.

159 158 Figure 5.6 Test intersection layouts at Southern Ave. & 67 Ave. Phoenix AZ Google Earth) The system structure of imlementation is illustrated in Figure 5.7. The RSE was installed in the Cabinet connected with the Econolite ASC/3 traffic controller via Ethernet. The RSE reads traffic status using NTCIP objects from the signal controller and broadcasts the signal status intersection MAP Society of Automotive Engineers 2006) and current request table to the DSRC network. When receiving new riority request or udated riority request the RSE udates the request table and runs the heuristic algorithm to roduce a new near-otimal signal lan based on current signal status and hase-ring configurations. The new signal lan is then imlemented on traffic signal controller by NTCIP hase control objects including hase hold and hase forceoffs commands.

160 159 Priority requests DSRC networks MAP Request table Signal status Antenna GPS Cabinet GPS Antenna RSE OBE Commands WiFi Status Lato dislay Requests & Control Ethernet NTCIP Traffic Controller Status Vehicle side Infrastructure side Figure 5.7 System structure of field imlementation When aroaching intersection a vehicle equied with an OBE will receive the intersection MAP signal status and current request table through the DSRC network as it enters the communication range about 1km). Combining theintersection MAP current GPS osition vehicle heading and seed obtained from a GPS receiver) a simle algorithm running on the OBE is able to calculate the desired service hase and the relative arrival time at the sto bar. Using this information a riority request is sent from the OBE to the RSE including the requesting hase uer and lower bounds on when the vehicle will arrive and the time required to clear the front queue if the vehicle joints the queue detected as stoing some distance from the stobar).

161 RSE and OBE introductions The OBE and RSE hardware are rovided by Savari Networks Savari 2010). They are both embedded comuter systems with a 500Mhz rocessor 256MB of memory 4GB of comact flash disk sace multile networks WiFi DSRC bluetooth and Ethernet) and include an integrated USB GlobalSat BU-353 GPS receiver RSE configurations An RSE is usually mounted on a light or signal ole beside the traffic signal control cabinet or ut inside the cabinet with an external antenna as shown as Figure 5.8. There are three rograms running on RSE: RSE_BROADCASTER: reads controller status broadcasts intersection MAP signal status and the request table on DSRC network every half seconds. RSE_LISTENER: listens on a secific ort for riority requests manages the request table. RSE_SOLVER: solve the multile riority roblems if there are any changes to the request table and imlements the otimized signal lan on the controller via NTCIP.

162 161 a) b) Figure 5.8 RSE installnations a) Inside cabinet for demonstration uroses); b) On a ole OBE configurations The OBE is mounted on the dash of each vehicle as shown as Figure 5.9. There are three rograms running on OBE: OBE_LISTENER: listens on a secific ort for the intersection MAP signal status and request table. OBE_REQUESTER: sends a riority requests when it is either in range of an intersection sto bar or stoed in the queue. OBE_WEBDESIGNER: dynamically generate web ages for the webserver on OBE. This rovides an interface between the driver and OBE. The service of each OBE includes four states: 1). OBE aroaching anintersection; 2) receiving MAP

163 162 and request table 3) sending a riority request and 4) traveling through the intersection. The web ages corresonding to four stes are shown in Figure 5.10 a)-d).

164 163 Figure 5.9 OBE installation a)

165 164 b) c)

166 165 d) Figure 5.10 Web age dislays a) OBE aroaches a intersection; b) OBE receives MAP and request table; c) OBE sends a riority request; d) OBE travels through the intersection. GID is a former name of MAP in SAE J2735) NTCIP imlementation The National Transortation Communications for Intelligent Transortation System Protocol NTCIP) is a family of standards maintained by NEMA AASHTO and ITE. The NTCIP standards rovide the rules and vocabulary for electronic traffic equiment from different manufacturers to communicate and oerate with each other. NTCIP comliant devices must follow this standard. The NTCIP is the first rotocol for the transortation industry that rovides a communications interface between disarate hardware and software roducts. The NTCIP effort not only maximizes the existing

167 166 infrastructure but it also allows for flexible exansion in the future without reliance on secific equiment vendors or customized software Institute of Transortation Engineers 2010). It is necessary to understand tree structure of NTCIP objects. In order to read or wirte an object in the ASC controller the object identification number OID) should be located and secified in the NTCIP tree. An examle of reds grou 1 OID is The object in the left of each dot is the arent of the object in the right. This could be deicted in a tree structure shown as Figure The NTCIP set of standards defines the Point to Multi Point Protocol PMPP) for communication with traffic devices. PMPP is a secialization of the HDLC High-Level Data Link Control) rotocol which can use SNMP Simle Network Management Protocol) for the information field. The SNMP is already a widely acceted rotocol on the internet for remote devices. In the field test Net-SNMP is adated to erform communications between the RSE and the traffic controllers.net-snmp is a suite of alications used to imlement different version of SNMP through IPv4 or IPv6 Net-SNMP 2010).

168 167 ISO 1) Org ISO.3) Nema Enterrise.1206) Transortation Nema.1206) Device Transortation.2) ASC Device.1) Phase status grou reds Phase status grou entry.2) Phase status grou number Phase status grou reds.1) Figure 5.11 NTCIP tree structure of reds grou 1 in ASC controller DSRC field exeriences Dedicated Short-Range Communications DSRC) is 75 MHz of sectrum at 5.9 GHz allocated by the Federal Communications Commission FCC) to increase traveler safety reduce fuel consumtion and ollution and continue to advance the nation s economy

169 168 Federal Communications Commission 1999). The 2004 FCC ruling secifies DSRC will have six service channels and one control channel Federal Communications Commission 2004). The control channel is to be regularly monitored by all vehicles. The DSRC communication range was measured under both an urban intersection and a suburban intersection shown in Figure 5.12 a) and b) resectively. Both tests are configured with a data rate 3Mb/s in the control channel. The urban intersection is located at Mountain Ave. and Seedway Blvd. Tucson AZ. This intersection is on the camus of University of Arizona which is surrounded by large buildings and trees. The communication range is affected by the blockage. It varies from 300 meters to 600 meters. The suburban intersection is at Southern Ave. and 67 Ave. in Phoenix AZ. There is no any obvious blockage around this intersection. The DSRC communication distance falls in the range of 700 meters to 1100 meters. a)

170 169 Figure 5.12 DSRC communication ranges: a) A urban intersection; b) A suburban intersection Field tests With the suort of Maricoa County s Regional Emergency Action Coordinating REACT) team Three REACT vehicles were equied with OBEs shown as Figure 5.13 a) and b). Different scenarios were tested with single vehicle two vehicles and three vehicles. Multile test vehicles were ositioned and coordinated to arrive at the intersection according to the test lan. The test lan included the following tests: 1. Single vehicle aroaching intersection a. Crossing the desired service hase b. During the desired service hase

171 Two vehicles aroaching intersection a. Vehicles on conflicting movements b. Vehicle on concurrent movements 3. Three vehicles aroaching intersection: two vehicles on concurrent movements and one vehicle on conflicting movement. a. The timing hase is the same as two-vehicle requested hase. b. The timing hase is the same as one-vehicle requested hase. The detailed results of each scenario are described in Table 5.1. Table 5.2 Field test scenarios and results Number of test vehicles scenarios a b a b a Test descritions When the vehicle is less than 30 seconds away from the intersection the OBE sends a riority request to the RSE. A Force Off was observed on the status dislay of the traffic controller. When the vehicle is less than 30 seconds away from the intersection the OBE sends a riority request to the RSE. A Green Hold was observed on the status dislay of traffic controller. When both vehicles were sending requests to the intersection the traffic controller was able to show a Green Hold status for the hase that was timing when the requests were received essentially holding the hase to allow the vehicle to be served. After the serving vehicle in the controller dislayed a Force off status to terminate the current hase immediately and then changed to serve the remaining vehicle on the conflicting hase. Two cases were tested. In the first case two vehicles aroached during the green hase. When the requests were received a Green Hold was observed in the status dislay of traffic controller. The signal remained green until both vehicles assed through the signal. In the second case two vehicles aroached intersection during the red hase. A Force Off was observed in the status dislay of traffic controller and then Green Hold was observed after the controller switched to the desired service hase. A Green Hold was observed in the controller status dislay until two vehicles traveled through the intersection. After both vehicles were cleared a Force Off status was immediately dislayed until

172 171 b the hase changed. The third vehicle was then served and allowed to cross the sto bar. There was some delay for the third vehicle. A Green Hold was observed on the controller status dislay until the single vehicle traveled through the intersection. After the single vehicle was cleared a Force Off was immediately observed in the controller status dislay. The first vehicle of the two-vehicle grou was able to ass through sto bar with some delay and the second vehicle arrived just as the signal turned green.

173 172 a) b) Figure 5.13 Field tests a) REACT vehicles ready to test; b) A riority request is being served.