FAULT-TOLERANT AND REAL-TIME WIRELESS SENSOR NETWORK FOR CONTROL SYSTEM

Transcription

1 FAULT-TOLERANT AND REAL-TIME WIRELESS SENSOR NETWORK FOR CONTROL SYSTEM by Wenchen Wang Bacheor of Engineering, Northeastern University, China 2013 M.S. in Computer Science, University of Pittsburgh, 2017 Submitted to the Graduate Facuty of the Kenneth P. Dietrich Schoo of Arts and Sciences in partia fufiment of the requirements for the degree of Doctor of Phiosophy University of Pittsburgh 2018

2 UNIVERSITY OF PITTSBURGH DEPARTMENT OF COMPUTER SCIENCE This dissertation was presented by Wenchen Wang It was defended on Juy 27, 2018 and approved by Dr. Danie Mosse, Department of Computer Science, University of Pittsburgh Dr. Rami Mehem, Department of Computer Science, University of Pittsburgh Dr. Youtao Zhang, Department of Computer Science, University of Pittsburgh Dr. Danie Coe, Department of Mechanica Engineering and Materias Science, University of Pittsburgh Dissertation Director: Dr. Danie Mosse, Department of Computer Science, University of Pittsburgh ii

3 Copyright by Wenchen Wang 2018 iii

4 FAULT-TOLERANT AND REAL-TIME WIRELESS SENSOR NETWORK FOR CONTROL SYSTEM Wenchen Wang, PhD University of Pittsburgh, 2018 Wireess contro systems (WCSs) enabe severa advantages over traditiona wired industria monitoring and contro systems, incuding sef-organization, fexibiity, rapid depoyment, and ower maintenance. However, wireess network deay and packet oss can resut in two main chaenges for the contro system: instabiity and performance degradation. This dissertation aims at soving the instabiity and performance degradation chaenges by deveoping faut-toerance and rea-time approaches for a WCS in two wireess transmission scenarios: one-way and two-way wireess transmission. For one-way wireess transmission, we first deveoped a faut-toerant network design and a nove mode to meet the contro system stabiity requirement in terms of network deay and packet oss with the minimum number of active nodes. The evauation resuts show that our mode is accurate with average 4.1% difference from the simuation resut. We then expored a hybrid offine-onine network reconfiguration framework with time-varying ink faiures to improve contro system performance for the WCS. Accordingy, a precise network imperfection mode and six reconfiguration agorithms have been deveoped to quantify and improve the performance, respectivey. The case study resuts show that our network imperfection mode is accurate with Pearson correation and our network reconfiguration approach performs better than the state-of-the-art static scheme with ess error and onger network ifetime. For two-way wireess transmission, we anayzed the worst-case network end-to-end deay to achieve the contro system stabiity. We carried out an anaysis to cacuate the maximum iv

5 number of conficts that coud happen during one message transmission, and then derive the worst-case end-to-end deay. The simuation resuts show that our end-to-end deay anaysis is accurate within 4.2% of reaistic simuation resuts. To improve the overa contro system performance for the WCS with mutipe physica systems, we studied a dynamic packet assignment approach. Our approach has two steps: packet priority assignment and network path seection. The case study resuts demonstrate that our approach is effective in improving the overa contro system performance. v

6 TABLE OF CONTENTS PREFACE xv 1.0 INTRODUCTION Background Probem Description Research Overview Contributions Dissertation Outine RELATED WORK Faut Toerance Technique Faiures in WCSs Network ony Soutions Contro and Network Co-design Soutions Rea-time Technique Network Deay in WCS Network ony Soutions Contro and Network Co-design Soutions Summary BACKGROUND AND ASSUMPTIONS Background Primary Heat Exchanger System Ridesharing Protoco Assumptions and Definitions vi

7 4.0 FAULT-TOLERANT NETWORK DESIGN Introduction Network Node Pacement Design k-connected Region Reay Region A Network Topoogy Set Generation TDMA Scheduing A Mode for Quantifying NH Deivery Ratio Cacuation Worst-case End-to-end Deay and NH Cacuation Performance Evauation The Mode for Quantifying NH Resut Simuation Resuts Summary DYNAMIC NETWORK RECONFIGURATION FOR WCS WITH ONE PHYSICAL SYSTEM Network Reconfiguration Framework Offine Optima Network Configuration Network Imperfection Mode Optima Network Configuration Determination Onine Network Reconfiguration Network Reconfiguration Process Network Average Link Success Ratio Estimation Reconfiguration Not Considering Consecutive Losses Reconfiguration Considering Consecutive Losses Case Study Case Study Resuts Offine Optima Network Configuration Resuts Onine Network Reconfiguration Resuts Summary vii

8 6.0 WORST-CASE END-TO-END DELAY ANALYSIS Network Mode Confict Anaysis Confict Anaysis for Case p s Confict Anaysis for Case 3 p s Confict Anaysis for Case p s Worst-case End-to-end Deay Determination Worst-case End-to-end Deay Anaysis Vaidation Summary DYNAMIC PACKET ASSIGNMENT FOR WCS WITH MULTIPLE PHYSICAL SYSTEMS Introduction Probem Formuation and Soution Probem Formuation Soution Overview Packet Priority Determination Static RMSE Dynamic RMSE PID Network Path Seection Network Path Quaity Mode Case Study Case Study Resuts Network Reiabiity Resuts PQmode Approach Resuts End-to-end Worst-case Deay Approach and PQmode Approach Comparison Packet Priority Determination Method Comparison Summary CONCLUSION viii

9 9.0 BIBLIOGRAPHY ix

10 LIST OF TABLES 1 Comparison of mode and simuation resuts Parameters and Vaues The tota stas of m 0 and m 1 (i.e., d 0 and d 1 ) when m 0 and m 1 confict with higher priority messages ( ps = 5) The tota stas of m 0 and m 1 (i.e., d 0 and d 1 ) when m 0 and m 1 confict with higher priority messages ( ps = 6) Simuation parameters and vaues Parameters and vaues of the simuation of SMR-based NPP x

11 LIST OF FIGURES 1 Wired contro system Wireess contro system The reationship between the probems and soutions of our dissertation Ridesharing protoco exampe iustration Faut-toerant reay nodes pacement design for a singe contro system (2- connected region and 3 ines of backup nodes in reay region) Three exampe states of eve h generated from one of the states of eve h The Mode of quantifying NH resuts Iustration of the probabiity of a message sent from previous eve is handed by the ast node of a eve. Red nodes do not receive messages and green nodes hande messages The reationship between RSSI and average LSR Simuation resuts Histogram of LSR difference distribution for RSSI = 64, RSSI = 76 and RSSI = Network reconfiguration framework for the contro system with dynamic network interference Network deay and deivery ratio trade-off iustration, when network deay is greater than contro samping period (p = 0.1s and D current = 0.2s) Time-varying RSSI variation exampe xi

12 15 (a) The number of active nodes of the offine estimated optima topoogy with different LSR vaues; (b) tota induced deay resut for RSSI vaues of -64, -70, -76, -82 and -84 that correspond to average LSR vaues of 0.93, 0.88, 0.82, 0.77, and 0.72, respectivey; (c) power output RMSE for different number of active nodes in the network Contro system power reference functions Power output IAE for different reference functions (average RSSI: -82dBm; LSRI: 2s (20 sampes)) (a) Power output IAE and (b) network ifetime (c) network ifetime / IAE resuts for different RSSI vaues (LSRI: 2s; α: 0.1) (a) Average number of nodes in the network, (b) average induced deay and (c) average RMSE over 20 experiments changing over time (LSRI: 2s; average RSSI: -82dBm; α: 0.1) (a) Network deivery ratio; (b) network deay for different average RSSI vaues (LSRI: 2s; α: 0.1) (a) Power output IAE and (b) network ifetime (c) network ifetime / IAE resuts for different LSRIs (average RSSI: -82dBm; α: 0.1) Comparison of estimated and rea LSRs (a) LSRI is 2s (b) LSRI is 8s (c) LSRI is 16s (average RSSI: -82dBm) (a) Average number of nodes in the network, (b) average induced deay and (c) average RMSE over 20 experiments changing over time (average RSSI: -82dBm) (a) Network deivery ratio; (b) network deay for different LSRIs (the average RSSI vaue: 82dBm; α: 0.1) Power output IAE resut comparison of AC and CL-AC for different apha vaues (average RSSI: -82dBm; LSRI: 2s) (a) Average number of nodes in the network, (b) average induced deay and (c) average RMSE over time for AC (α=0.1), CL-AC (α=0.9) and AC (α=0.9) (average RSSI: -82dBm; LSRI: 2s) Network mode with one or more ines of reay nodes (a) (b) (c) confict situation and (d) no confict situation xii

13 29 The conficts of m i when the eve difference with m i+j is 5 (a) and 4 (b) Confict situation when p s = 4: (a) m0 starts conficting with m 1 and (b) the confict is resoved in 7 time sots if the subsequent messages do not exist The cacuation process of eve separations with higher priority messages of m 0 and m 1, when ps = The sta time for m 0 (ower segments) and m 1 (upper segments), when conficting with m The sta time for m 0 (ower segments) and m 1 (upper segments), when conficting with m The sta time for m 0 (ower segments) and m 1 (upper segments), when conficting with m j and m j The cacuation process of eve separations with higher priority messages for m 0 and m 1, when ps = The sta time for m 0 (ower segments) and m 1 (upper segments), when conficting with m The sta time for m 0 (ower segments) and m 1 (upper segments), when conficting with m Exampes of (a) the most recent message first scheme and (b) the odest message first scheme transmission process with p = 0.1s, p s = 10, = 2 and n = 10. Note that the symmetry of the odest message first scheduing scheme with the most recent message first scheduing scheme begins at the 275 th time sots Contro system power reference functions with contro samping period of 0.2s Power output RMSE for different reference functions with different network deays for a singe PHX (DR=0.9; random packet drop with probabiity of 0.1 for sensing and actuation, respectivey) Power output RMSE with different network deays and DRs for a singe PHX (reference function: ramp30) xiii

14 42 System overview: three SMRs transmit measurement messages via shared wireess network to the remote controer, and the remote controer transmits back contro signas backup via the same network Deivery ratio of three network paths under different RSSI vaues Percentage of consecutive osses (noss) for network path Percentage of consecutive osses (noss) for network path Percentage of consecutive osses (noss) for network path The best β vaue over different RSSI vaues for three huristic methods Path quaity order seections for different RSSI vaues (the size of the bubbe means the number of time steps a certain path order is seected) RMSE avg comparison of end-to-end deay approach and PQmode (best β vaues) over different network conditions with dynamic RMSE heuristic method RMSE avg comparison for three heuristic methods with best β vaue xiv

15 PREFACE In oving memory of my grandparents, two most important person in my ife, Mr. Keming Wang and Mrs. Renjuan Yu. xv

16 1.0 INTRODUCTION 1.1 BACKGROUND Traditiona contro systems rey on wires to connect controer, sensors, and actuators, where the controer is the centra point that can contro one or more physica systems (we ca them wired contro systems in this dissertation). Typicay, the controer is physicay separate from the physica pant, in a remote ocation. Figure 1 shows a genera wired contro system with a singe physica system. The sensors attached to the physica system send measurement packets to the remote controer periodicay and the remote controer cacuates the contro signa and sends back the contro signa to the actuator to actuate the physica system using the received contro signa. However, when a wired contro system with a singe physica system is scaed to contro a arge number of physica systems, it wi bring the depoyment and maintenance probems. Motivated by these probems, wireess contro systems (WCSs) are gaining rapid adoption in the industria process, because WCSs can overcome the probems of wired contro systems and have the advantages of sef-organization and fexibiity [Gungor and Hancke, 2009]. WCSs have been widey appied to domains of transportation, heath-care, manufacturing, agricuture, energy, aerospace and buiding. WCSs controed over muti-hop wireess sensor networks (WSNs) have especiay received significant attention in recent years [Han et a., 2011; Li et a., 2015, 2016; Pajic et a., 2011b,a; Wang et a., 2016; Kim and Kumar, 2010]. As shown in Figure 2, the wireess transmission has two directions: (1) up, sensors sending measurement messages to the remote controer; (2) down, the remote controer transmitting the messages with contro signas back to the actuators. In this dissertation, we say a message is sent up to the remote controer and down to the actuator. 1

17 Figure 1: Wired contro system Figure 2: Wireess contro system 1.2 PROBLEM DESCRIPTION Whie eary success of WSNs has been recognized, significant potentia remains in exporing WSNs as faut-toerance and rea-time networks for industria pants. Even though WSNs are good for depoyment, wireess network communications are imperfect in terms of packet oss and network deay. Most WSNs embedded in WCSs are depoyed and appied in industria environments, such as smart grids [Gungor et a., 2010], water tanks [Li et a., 2015] and even nucear power pants (NPPs) [Wang et a., 2016]. Harsh and compex eectric-power-system environments pose great chaenges in the reiabiity of WSN communications. Interference is the main factor of packet osses in WSN [Li, 2015], where wireess inks exhibit widey varying characteristics over time due to moving peope/obstaces and eectromagnetic and radio frequency interference (EMI/RFI) [Baccour et a., 2012; Kar and Moura, 2009; Baccour et a., 2012; Gungor et a., 2010; Ganesan et a., 2001]. The interference can make some inks/nodes inaccessibe and disconnected for a imited amount of time (e.g., if an obstace, ike a factory robot transporting materias, bocks the wireess transmission). Moreover, the time deay is another issue of WSN due to retransmissions and muti-hop characteristic. Rea-time scheduing has been studied in WSN to constraint network deays in [Saifuah et a., 2010; Gobrie et a., 2009b; Stankovic et a., 2003]. A WCS is a system with two subsystems, the wireess sensor network and the physica system. The performance of one subsystem wi affect the other. Network-induced imper- 2

18 fections [Zhang et a., 2013; Gupta and Chow, 2010], that is, packet oss and time deay (discussed above) can resut in two main probems for the contro system: instabiity [Zhang et a., 2001; Zhang and Yu, 2008; Jusuf and Joeianto] and performance degradation [Pant et a., 2015; Li et a., 2016]. When the physica system is unstabe, the pant or part thereof can be damaged and ead to serious safety issues and financia oss. On the other hand, even if the contro system is stabe under network-induced imperfections, WSN can introduce unreiabe/non-deterministic eves of service in terms of deays and osses and induce undesirabe additiona errors, that is, network-induced error. The smaer the network-induced error, the coser to the wired contro the system performance is. The contro system appication desired requirements can be categorized as hard and soft requirements, which are stabiity and performance, respectivey. The performance requirement comes after the stabiity requirements are met. This dissertation studies different faut toerance and rea-time techniques in WSN to sove the foowing two probems: P1 : contro system stabiity guarantee; P2 : network-induced error reduction. In a WCS, the contro samping period is the interva where the contro oop makes decisions. In practice, the contro samping period in a WCS and cyber-physica system (CPS) is 2 n seconds, where 2 n 9, that is, from 250 ms to approximatey 8 minutes [Han et a., 2011] and it depends on the pant being controed. After one knows the contro samping period, there are two cases for the network deay: (1) worst-case network deay is ess than or equa to the contro samping period; (2) worst-case network deay is more than the contro samping period. For the first case, the network reiabiity is the key effect on contro system performance. The higher the reiabiity, the better the contro system performance. To achieve high reiabiity, the network can be designed to be as reiabe as possibe, that is, a high eve of redundancy, which requires more nodes. A higher number of nodes typicay induces more deay for messages to be deivered (more traffic on the network), but a messages sti arrive within the contro samping period and, thus the deay has itte (if any) effect on the contro system performance. Recent research works mainy focus on this case [Saifuah et a., 2011; Li et a., 2015; Saifuah et a., 2015; Li et a., 2016]. 3

19 However, for the second case, there is a trade-off between network deay and packet osses for the contro system stabiity and performance, which is a more compex case that there is imited research insight on. Our dissertation focuses on addressing P1 and P2 covering the two cases above, that is, it is possibe that the worst-case network deay is more than the contro samping period, which is more genera and compicated than previous research. 1.3 RESEARCH OVERVIEW In this dissertation, there is a deicate interpay between network reiabiity and network deay for designing a WSN in the WCS. Redundancy requires an additiona deay to achieve network reiabiity. Conversey, it is easy to see that reducing the redundancy (e.g., backup sensors) in a WSN to reduce end-to-end network deay increases the probabiity of packet oss. The trade-off between faut toerance and rea-time network for the industria wireess network has been expored in the iterature [Han et a., 2011; Yu et a., 2014]. Limited insights have emerged with respect to how the wireess contro system appication s desired requirements affect and are affected by the faut toerance and rea-time communication. To this end, this dissertation aims at deveoping faut-toerance and rea-time approaches to address P1 and P2. Our goa is to study the viabiity of and provide the justification for the foowing dissertation statement: It is possibe to achieve stabiity and reduce network-induced error for contro systems, whie operating under packet osses and rea-time constraints in a wireess network. We seek to achieve this objective by studying two wireess communication scenarios in a wireess contro system: (1) one-way wireess transmission: transmitting messages up to the remote controer by assuming the messages are sent down on another wireess channe with a different radio frequency; (2) two-way wireess transmission: transmitting messages up to the controer and down to the actuator sharing a wireess network. The difference between the two scenarios is the worst-case end-to-end network deay anaysis. Specificay, 4

20 up messages can confict with down messages during the two-way transmission that can induce more network deay, whie there is no confict during the one-way transmission if the messages are scheduabe (wi expain ater in Section 4.3.2). For both scenarios, we first satisfy the contro system stabiity requirement and then reduce the network-induced error. Note that the contro system stabiity requirement in this dissertation is given by the contro engineering researchers (see Equation (4.1)), that is, an inequaity constraint of network deay and packet oss. For the one-way transmission, given a contro system stabiity requirement in terms of network deay and packet osses, we propose a faut-toerant network node pacement design and a mode to estimate the minimum number of active nodes in the network to meet the stabiity requirement (soution 1: S1 ). Based on the mode in S1, we expored a network reconfiguration framework with offine and onine parts to reduce the network-induced error for a WCS with a singe physica system (soution 2: S2 ). For the two-way transmission, we propose a worst-case end-to-end deay anaysis (soution 3: S3 ) to compement S1. We then study a dynamic packet assignment approach to reduce the network-induced error for a WCS with mutipe physica systems (soution 4: S4 ). Figure 3 shows the reationship between the probems and soutions. 1.4 CONTRIBUTIONS This dissertation consists of the foowing main contributions. Faut-toerant network design. Contro system stabiity is critica for physica pants, since system instabiity can resut in pant damage and severe safety issues [Zhang et a., 2001; Zhang and Yu, 2008; Jusuf and Joeianto]. In WCSs, network deay and packet oss are the potentia threats to contro system stabiity. Given a contro system stabiity requirement in terms of network deay and packet oss, we first propose a fexibe faut-toerant node pacement design. We then deveop a mode to meet the requirement and to determine the initia network topoogy with the minimum number of active nodes [Wang et a., 2016]. This contribution is S1 to sove P1, with the detai presenting in Chapter 4. 5

21 Figure 3: The reationship between the probems and soutions of our dissertation Offine-onine Network reconfiguration framework for a WCS with a singe physica system. The trade-off of network deays and packet osses affecting the WCS performance motivates us to find the optima network configuration to minimize the networkinduced error. Another main difficuty of having wireess networks for the contro systems is caused by interference and noise that produce time-varying faut patterns [Cerpa et a., 2005; Srinivasan et a., 2010], which motivates us to find a fast and effective way to carry out network reconfiguration at run time. We design and impement a new framework with offine and onine components to do network reconfiguration for the contro system with time-varying ink faiures [Wang et a., 2017a, 2018b]. We propose a network imperfection mode in the offine part and six network reconfiguration agorithms in the onine part. This contribution is S2 to sove P2, with the detai showing in Chapter 5. Worst-case end-to-end deay anaysis. Contro system deadine is a critica variabe to make sure the contro system stabiity. Worst-case end-to-end deay anaysis heps network design to guarantee meeting the contro system deadine. Since the two-way wireess communication wi incur communication conficts, we first carried out the confict anaysis 6

22 to get a message scheduabiity condition. Based on the condition, we then cacuate the maximum number of conficts that wi happen during one message transmission and derive the worst-case end-to-end deay [Wang et a., 2018a]. This contribution is S3 to sove P1, with the detai expaining in Chapter 6. Dynamic packet assignment for WCS with mutipe physica systems. Wireess contro system with mutipe physica systems wi be increasingy common due to the deveopment of IoT (Internet of Things) systems and IIoT (Industria IoT). In addition, network deay and packet oss wi impact each contro system performance differenty due to different appication demand. For the same deay and packet oss, we found that the physica system with more urgent appication demand wi have the more network-induced error than the one with ess urgent demand. Finay, the network paths within the wireess network can have different network characteristic in terms of deay and packet oss (e.g., the source routing and the graph routing in WireessHart[wir, 2007]). The facts above motivate us to assign urgent demand packets to network path with ow deay and high reiabiity. We propose a dynamic packet assignment approach to assign the packets from the WCS with mutipe physica systems to the network paths, in order to reduce the overa network-induced error [Wang et a., 2018a, 2017b]. This contribution is S4 to sove P2, with the detai introducing in Chapter 7. Nucear power pant case study. In order to evauate the performance of our proposed methods and modes for WCSs, we conducted case studies of one or more primary heat exchangers (PHXs) in nucear power pants (NPP) with a wireess sensor network. We combined a start-of-the-art cyber-physica system simuator (WCPS 2.0 [Li et a., 2015]) with an NPP simuator to mimic our wireess contro system. For the wireess network, we use the TOSSIM network simuator (embedded in WCPS) with wireess noise traces from a 21-node subset of WUSTL Testbed [tes, 2017] under a wide range of wireess conditions (e.g., different eves of noise/interference). For each case study, we evauate the network and contro system performance, that is, the network deay + reiabiity and network-induced error, respectivey. This contribution is spread from Chapter 4 to Chapter 7. 7

23 1.5 DISSERTATION OUTLINE The rest of this dissertation is organized as foows: Chapter 2 reviews existing faut toerance and rea-time techniques in WCSs. Chapter 3 introduces the background and assumptions of this dissertation. Chapter 4 presents the energy-aware faut-toerant network design approach and resuts. In Chapter 5, we buid a network reconfiguration framework for ink faiures varying over time for a WCS with a singe physica system. In Chapter 6, we do a worst-case end-to-end deay anaysis for two-way wireess transmission. Chapter 7 presents the dynamic packet assignment approach for a WCS with mutipe physica systems. Finay, Chapter 8 concudes the dissertation. 8

24 2.0 RELATED WORK The soutions for network deay and packet osses in WCS are typicay divided into three categories: contro ony, network ony, and contro and network co-design soutions. In this dissertation, we ony review the ast two categories of faut toerance and rea-time techniques. This chapter first reviews the iterature of faut toerance and rea-time soution from the WSN perspective ony, then presents the recent faut toerance and rea-time research works in WCSs considering the interaction between network and contro system, respectivey. 2.1 FAULT TOLERANCE TECHNIQUE Faiures in WCSs The faiures in WCSs have hierarchica characteristics due to the joint of two subsystems, contro system and wireess network. The highest eve of faiures of WCS is contro system instabiity and performance degradation. One of the main causes of the instabiity and performance degradation of WCSs is the unreiabiity of the wireess network, that is, packet oss. Packet oss in WSNs is caused by two categories of faiures, ink and node faiures due to various factors such as power depetion, environmenta impact, radio interference, asymmetric communication inks, disocation of the sensor node and coision [Kakamanshadi et a., 2015]. We mainy focus on ink faiures in this dissertation and the iterature review in the foowing subsections. 9

25 2.1.2 Network ony Soutions Radio ink quaity estimation (LQE) is the first step to toerate the ink faiures, which has fundamenta impact on the network performance and network protoco design [Baccour et a., 2012]. LQE is the statistica characterization of wireess inks through estimation theory. PRR (packet reception ratio)-based passive LQE agorithms are presented in [Woo and Cuer, 2003; Cerpa et a., 2005]. In [Gobrie et a., 2009a], the authors show how different faut-toerant, dupicate-sensitive, aggregation schemes for WSNs can take advantage of ink quaity information by an extensive simuation study. The faut toerance techniques for the ink faiures are typicay divided as static and dynamic soutions. For the static faut toerance soutions, faut toerance in-network aggregation protocos in WSNs have been studied on the tree-based [Gobrie et a., 2006], custer-based [Zhou et a., 2004; Mahimkar and Rappaport, 2004], mutipath [Nath et a., 2008], hybrid [Manjhi et a., 2005], and gossip-based [Boyd et a., 2006; Aysa et a., 2009] approaches. Their objectives are to extract usefu goba information by coecting individua sensor readings and sending the aggregated information to the sink node. They are appied to monitor a specific environment, which is different from the communication in a WCS with no need of information aggregation. On the other hand, faut-toerant node pacement agorithms for ink faiures, k edge-disjoint agorithms with the minimum number of nodes in the network to save network energy consumption have been investigated in [Frank and Tardos, 1989; Han et a., 2010]. As the adoption of the WSN in process contro system, reiabe routing agorithms are proposed from wireess sensor network perspective for the WCS in [Heo et a., 2009; Han et a., 2011]. Specificay, EARQ [Heo et a., 2009] provides rea-time, reiabe deivery of a packet considering network energy consumption. It cacuates the probabiity of seecting a path, using the estimates of the energy cost, deay and reiabiity of a path to the sink node. In [Han et a., 2011], the authors propose three routing graphs for different communication ways of transmitting messages up (sensing), down (actuation) and broadcasting messages. Based on the graphs, data ink ayer communication schedues are generated. However, a the aforementioned works focus soey on the network without considering the contro aspect of a WCS. We sove contro system instabiity issue by a fexibe faut-toerant node 10

26 pacement design and a mode to quantify the network-induced imperfections (see Chapter 4). Since the network interference is unpredictabe and varies with time, the ink quaity fuctuates over time [Cerpa et a., 2005; Srinivasan et a., 2010]. It is necessary to toerate the network ink faiures in a dynamic way. Interference can make the network disconnected and becomes inaccessibe for a certain amount of time and wi degrade the contro system performance. Network reconfiguration is an essentia part of the network faut-toerance technique. Based on the LQE agorithms, network reconfiguration schemes are expored in dynamic routing agorithms [Zhang et a., 2015]. In addition, severa agorithms [Li et a., 2003; Li and Hou, 2004] mitigate the impact of ossy inks by maintaining k-connectivity of the network. Topoogy contro is another active research area to dynamicay toerant ink faiures [Ramanathan and Rosaes-Hain, 2000; Santi, 2005]. Topoogy contro is achieved by adjusting the transmit powers of nodes, which brings the positive effect of reducing contention when accessing the wireess channe and making the network more reiabe. Unfortunatey, these works do not consider contro system performance. We design a network reconfiguration framework with a network imperfection mode, indicating the impact of network deay and packet oss on contro system performance (see Chapter 5) Contro and Network Co-design Soutions Faut-toerant co-design of the network and contro system is effective for WCSs. Most soutions of recent research works either extract the condition/requirements of the contro system or design a wireess network based on a contro requirement or both. A set of topoogica conditions is extracted for the controer, distributed over the nodes in the network that aows the contro system to be stabiized in [Pajic et a., 2011a]. A reiabiity anaysis that evauates a given configuration of an activey repicated networked contro system and quantifies its resiiency to eectromagnetic interference-induced transient fauts is presented in [Gujarati et a., 2018]. In [Mouradian and Augé-Bum, 2013], the authors propose a forma verification method to derive the property of correctness probabiity of a given network topoogy based on the WSN radio inks probabiity. This probabiity must meet the re- 11

27 quirements of the contro appication; otherwise, the system must be changed to increase the probabiity. Other co-design soutions are case studies to observe the interaction between the network dynamics and contro system performance. For exampe, a case study is conducted to see the interaction between the mode predictive contro and network routing schemes in [Li et a., 2016] with the observation of contro system having different eves of resiience to packet oss for sensing and actuation. However, none of these works address the tradeoff between network deay and packet oss in WCSs, nor present the interaction between the network reconfiguration and contro. We conduct a case study to show how the network reconfiguration affects the contro system performance (see Chapter 5). 2.2 REAL-TIME TECHNIQUE Network Deay in WCS There are mainy two kinds of message deays in WCSs: sensor-controer deay and controeractuator deay. The sensor-controer deay represents the time interva from the instant when the physica pant is samped to the instant when the controer receives the samped message; and the controer-actuator deay indicates the time duration from the generation of the contro message at the controer unti its reception at the actuator. In contro theory, these deays cause phase shifts that imit the contro bandwidth and affect cosed-oop stabiity and performance [Park et a., 2018] Network ony Soutions In order to guarantee the appication deadine of a WSN, worst-case end-to-end deay anaysis is an important research area to study. In recent research works [Saifuah et a., 2010, 2011, 2015], the worst-case end-to-end deay anaysis for source and graph routing based on wireesshart standard to guarantee the rea-time communication in WCSs are discussed. However, they a consider the network fow deadines are smaer than their periods. We focus on a genera case when it is possibe that the transmission deadines are greater than 12

28 their periods. To the best of our knowedge, no other works are studying this case before, but it is common in rea-time WCSs. We came up with a worst-case end-to-end deay anaysis, which heps a network design to guarantee the contro system deadine (see Chapter 6). Dynamic rea-time network scheduing is an effective soution to constrain network deays. Rea-time TDMA scheduing agorithms in WSNs are studied from many aspects to reduce the end-to-end network deays: parae transmission design [Gobrie et a., 2009b]; packet prioritization [Liu et a., 2006; Zhang et a., 2015]; and optimization with other constrains, such as energy consumption [Gu et a., 2009] and the number of packet drops [Hong et a., 2015]. However, the above works do not consider contro system appication demands. We propose a dynamic packet assignment approach considering dynamic contro system appication demands and network reiabiity + deay impact on the contro system performance (see Chapter 7) Contro and Network Co-design Soutions For the co-design of rea-time network and contro system, [Li et a., 2015] expores a data ink ayer rea-time communication protoco with sot steaing agorithm [Gobrie et a., 2009b] and event-based communication on top of the WireessHART protoco [wir, 2007] to reserve time sots for emergency packets. However, neither network-induced error minimization is considered, nor mutipe contro systems are invoved. Onine dynamic ink ayer scheduing agorithms have been proposed in [Hong et a., 2015; Zhang et a., 2017] to meet the deadine of a rhythmic fow and minimize the number of dropped reguar packets in a centraized and distributed way, respectivey, based on a rhythmic task mode proposed in [Kim et a., 2012]. Whie the impact of network dynamics on existing network fows is minimized, overa contro system performance (different contro system appication demands) is not considered,and there is no case study for rea-word appications. In [Gatsis et a., 2014], the authors first abstract the contro performance requirements as desired decrease rates of Lyapunov functions. Since the channe conditions on wireess medium not ony change unpredictaby overtime but aso differ among users, they present a framework for designing opportunistic channe-aware centraized scheduers for a WCS of mutipe contro tasks over a shared 13

29 wireess medium. In their ater work [Gatsis et a., 2016], they derive a sufficient decouping condition for the random access poicy empoyed by each node in the wireess network given contro dynamics. They then design a random access poicy that can adapt to the dynamic of the physica system onine. The end-to-end rea-time guarantee between interfaces of distributed components in WCS besides the wireess network is proposed in [Jacob et a., 2016]. A rea-time high-speed wireess protoco is expored in [Wei et a., 2013]. However, the above works ony consider the contro stabiity and not the overa contro system performance. To the best of our knowedge, a cross-ayer dynamic packet assignment has not been studied in a WCS with mutipe physica systems, which is our ast work in this dissertation (see Chapter 7). 2.3 SUMMARY This chapter reviews reated work in the fieds of faut toerance and rea-time techniques in WSNs and WCSs. We introduce the faiures in WCSs and state-of-the-art faut toerance techniques from ony the WSN aspect and contro and network interaction aspect. On the other hand, we discuss the network deay in WCSs and the rea-time soutions of network ony and contro and network co-design. Motivated by the WCS chaenges and shortcomings of existing work, this dissertation targets at the work that ies at the intersection of faut toerance and rea-time scheduing for WCSs. 14

30 3.0 BACKGROUND AND ASSUMPTIONS In this chapter, we first introduce the background for this dissertation with (a) the contro system we use to do our performance evauation and (b) the network protoco we appy to do wireess transmission. Then we discuss the definitions and assumptions we made for this dissertation before we go into more detais in the foowing chapters. 3.1 BACKGROUND Primary Heat Exchanger System The contro system we study in this dissertation is a remote controer controing one or more primary heat exchanger systems in a nucear power pant (NPP). A new trend in nucear power pants is to use severa Sma Moduar Reactors (SMRs) rather than a singe arge reactor [Greene et a., 2010], due to the fexibiity and cost-benefit of starting and stopping SMRs. Given the arge number of SMRs in a modern NPP, the cost and difficuty of cabing a sensors and actuators woud be prohibitive. Typicay there is one primary heat exchanger system (PHX) and two secondary heat exchangers in each SMR. Note that we ony mode the PHX in this dissertation, since the two secondary heat exchangers are backups for safety and woud foow a simiar approach with a different network. A PHX in an NPP is modeed as a noninear system and has as its main function the exchange of heat from inside of the reactor to the outside, which contros the pressure and the temperature of the reactor. A PHX makes many measurements, three of which are the focus of this dissertation, given its importance to the NPP contro, namey the outet hot eg temperature, the inet hot 15

31 eg temperature, and the mass fow rate. In our NPP, these measurements are periodicay sent via a wireess network to the remote controer ocating in the operator contro room. The remote controer wi compute the contro signa using the received measurements and then send back the contro signa to the actuators to actuate the PHX. When there are mutipe PHXs, they a share one wireess network to transmit the measurement packets to the centraized remote controer and send the contro signas back to each PHX. We use the contro system we discussed above to do case studies in this dissertation to evauate our modes and approaches. We conducted wireess contro case studies for one PHX in Chapter 4 and Chapter 5, and the case study for three PHXs in Chapter 7. Note that athough important for NPPs, safety issues are beyond the scope of this dissertation and we focus on the feasibiity of making contro system stabe and reducing network-induced error Ridesharing Protoco The network protoco we use in this dissertation is based on a TDMA protoco, ridesharing [Gobrie et a., 2006] to toerate ink faiures. Ridesharing is an in-network aggregation protoco, which is used to monitor a certain environment. We define reay nodes as the sensor nodes passing messages in between the source and destination. In ridesharing (shown in Figure 4), reay nodes are organized in a chidren-parent reationship. There is a direct wireess ink between the chid and parent node, where a chid node (e.g., C 1 ) is a transmitter, and a parent node (e.g., P 1 ) is a receiver of the message from its chid node. To make the network more reiabe, besides a reay node which is caed primary node, we pace one or more reay nodes as backups which are caed backup nodes. For exampe, P 2 and P 3 in Figure 4 are the backup nodes of the primary node P 1. The primary node and its backup nodes are caed sibing nodes (e.g., P 1, P 2 and P 3 are sibing nodes). Thus, a node has one primary parent and zero, one or more backup parents, and aso has zero, one or more sibings. If the backup parent finds out (whie overhearing) that the primary parent did not send out the vaues it shoud receive from their chidren, the backup parent wi compensate for the primary parent. For exampe, in Figure 4, C 1 has one primary parent P 1, two backup parents, P 2 16

32 Figure 4: Ridesharing protoco exampe iustration and P 3. The ink between C 1 and P 1 fais. When C 1 broadcasts its message in time sot 0, P 2 and P 3 receive the message. When P 1 broadcasts its message in time sot 1, P 2 overhears P 1 s message and knows that P 1 did not receive C 1 s message. At time sot 2, P 2 aggregates C 1 s measurement with the measurement it senses itsef and sends a message with an added fied indicating that it received C 1 s message. P 3 overhears P 2 s message knowing that P 2 aready handed C 1 s message and P 3 discards C 1 s message. In time sot 3, P 3 sends out a message with its own sensed measurement. In this way, the backup parent P 2 toerates the ink faiure between C 1 and P 1 and improves the network reiabiity. If P 2 fais to hande the faut (i.e., the ink between C 1 and P 2 fais), P 3 does so in a simiar manner. The more backup nodes, the more reiabe the network. In this dissertation, we modified the ridesharing protoco, by concatenating measurements into one message, instead of aggregating the measurements. We remove the measurement aggregation is because there are different types of measurements that cannot be aggregated in WCS appications. We choose not to send each measurement with one message is to save network energy and reduce the network contention, since more messages wi bring more chances of transmission conficts. But we ony concatenate the measurements sensed 17

33 at the same contro samping period due to the imited size of the message. Therefore, when a reay node receives mutipe messages before it sends out its own message, it wi first discard the dupicate messages, which were aready received by its sibings via overhearing its sibings messages; then it concatenates the measurements of the remaining received messages of the same contro samping period to the message it is going to send (note that the concatenated measurements are distinct, since the dupicate messages are discarded). 3.2 ASSUMPTIONS AND DEFINITIONS In this dissertation, we make definitions as foows. Link success ratio and deivery ratio. Links in wireess network fai independenty with a certain probabiity and we define ink success ratio (LSR) as the probabiity a message can be sent out successfuy on that ink. We use average LSR over a the network inks as the indication of the average network interference. We use network deivery ratio (DR) as the network reiabiity indicator, that is, the ratio of arrived measurements or signas or messages in the destination (DR [0, 1]). Typicay, the bigger the LSR vaue, the bigger the DR. Seep nodes and active nodes. Seep nodes are the reay nodes in seep mode that cannot receive and transmit messages, whie active nodes are the reay nodes that can receive and transmit messages. To save energy, we make reay nodes to seep for a whie. We aso wake up the seep nodes to be active as needed by sending reconfiguration messages periodicay. Thus, in this dissertation, the seep nodes wi wake up periodicay to isten to the reconfiguration messages to see whether they need to wake up. The reconfiguration messages are sent in reserved sots, as in many proposed TDMA agorithms [Yackovich et a., 2011]. Thus, active nodes in this dissertation isten to the messages of their chidren, overhear the messages of their sibings, isten to the reconfiguration messages and send out its own messages. Neighbors of a reay node. Neighbors of a reay node A are defined as the network nodes that are one hop from A. 18

34 We make assumptions as foows. There is no message retransmission in our wireess transmissions. Simiar to [Li et a., 2015], when a message gets ost during a transmission, the controer/actuator uses the ast received measurements/contro signa to carry out the contro agorithm/actuation, respectivey. A sensors attached to one physica system send out the measurements at the same period as the contro period (i.e., the sensing samping period is the same as the contro samping period). In a traditiona wired contro system, the packet oss and deay can be ignored. The reconfiguration messages to activate (i.e., wake up seep nodes) or deactivate (i.e, put active nodes to seep) reay nodes never get ost. The inks between parent nodes and chidren nodes can fai, but the inks between sibing nodes never fai. An active node ony overhears its sibing s messages if the sibing node is schedued to transmit messages before it. We ignore the time deay of the contro signa computation in the remote controer. 19

35 4.0 FAULT-TOLERANT NETWORK DESIGN Contro system stabiity is critica for physica pants, since system instabiity can resut in pant damage and severe safety issues [Zhang et a., 2001; Zhang and Yu, 2008; Jusuf and Joeianto]. In WCS, network deay and packet oss are the potentia threats to contro system stabiity. Given a contro system stabiity requirement in terms of network deay and packet oss, we first propose a faut-toerant node pacement design. We then deveop a mode quantifying the stabiity requirement for different network topoogies. We can determine the initia network topoogies with the minimum number of active nodes to meet the requirement for different average LSR vaues. Finay, we evauate our mode by simuating a WCS with one PHX and a 12-hop wireess network. 4.1 INTRODUCTION In physica systems, the stabiity of the pant depends on the contro system receiving sensor data in a timey fashion. In [Wang et a., 2016], the contro engineering researchers define network heath (NH) as the genera contro system stabiity requirement in terms of end-toend network deay D network and deivery ratio (DR). NH = p 1 Dnetwork 2 + p 2 D network + p 3 (1 DR) (4.1) where p 1, p 2, p 3 are characteristic constants for a specific controer. The worst-case end-toend deay D network is the worst-case time deay of any one message from the time it is sent out to the time it is received by the controer (for one-way wireess transmission)/actuator (for 20

36 two-way wireess transmission). We wi consider the D network of one-way wireess transmission in this chapter and two-way wireess transmission in Chapter 6. The contro engineers came up with a contro system stabiity requirement that when NH 0, the contro system is stabe. Given the NH in Equation (4.1), our goa is to design a faut-toerant wireess network to meet the requirement (NH 0) with the minimum active reay nodes to save network energy for one-way wireess transmission (messages sending up to the remote controer). In this chapter, we first design a faut-toerant network node pacement for WCS and propose a mode to quantify NH and determine the minimum number of active nodes to have in the network, to meet NH 0 requirement. 4.2 NETWORK NODE PLACEMENT DESIGN Since the remote controer is not on the same site (physicay separated) as the sensors and actuators, the periodic measurement messages wi be transmitted through reay nodes to the remote controer. As the first network design step, we pace reay nodes in between the measurement sensors and the remote controer. We divide the network area into two regions, namey k-connected region and reay region (see Figure 5). A virtua root demarcates the connection between the two regions. The reason why we have two regions is that a physica system coud be very arge and the sensors sensing different types of measurements coud be dispersed attached to it and we want to have the measurements sent to one ocation (virtua root) first, then pass them together to the remote controer. After we pace the reay nodes in the network area, we describe how we generate a network topoogy set that wi be used to determine the initia topoogy to meet the contro system stabiity requirement. Finay, we introduce the TDMA scheduing for each region based on the node pacement design. 21

37 4.2.1 k-connected Region Optima node pacement in a wireess sensor network has been shown to be NP-hard [Han et a., 2010]. Given that we ony consider ink faiures, we appy k edge-disjoint agorithms [Frank and Tardos, 1989; Han et a., 2010], instead of k node-disjoint agorithms [Zhang et a.; Bredin et a.]. We define a k-connected region as the nodes and inks having k edge-disjoint paths from each measurement sensor to the virtua root. In the k-connected region, we appy Han s agorithm to pace reay nodes [Han et a., 2010]. To get k edge-disjoint paths, we sove an optimization probem for finding a minimum-cost subgraph H of a digraph G = (V, E) such that H contains k edge-disjoint paths from a fixed node of G to any other node, which can be reduced to a weighted matroid intersection probem [Frank and Tardos, 1989]. A common basis of these matroids corresponds to a subgraph, that is, the union of k disjoint spanning trees. Therefore, finding k edge-disjoint paths of a graph is equivaent to finding the subgraph of k disjoint spanning trees with minimum cost (e.g., [Yang, 2005]). We aso add (k 1) backup nodes to the virtua root to improve reiabiity. Note that we ca the virtua root and its backup nodes as virtua roots and treat them as one node when generating the k edge-disjoint paths. The ast reay node of each path can reach a the virtua roots, as we pace virtua roots as cose as possibe together (wi expain the reason in Theorem 4.2.1). In k-connected region, for k edge-disjoint paths of each measurement sensor, the path with the minimum number of reay nodes is caed the primary path, the path with the second smaest number of reay nodes is caed the first backup path, and so on Reay Region In the reay region, primary reay nodes are paced in a straight ine between the virtua roots and the remote controer, caed the ine of primary reay nodes. The distance between two consecutive primary nodes is the same. In addition, we pace b ines of backup nodes (b 1), that is, each primary reay node have b backup nodes. For exampe, in Figure 5, A and B are the primary nodes, and D and C are the backup nodes. Horizontay, the eve where one primary node and its backup nodes are ocated is caed one eve. Each node in eve h is abe to isten to a the nodes in its ower eve h 1 (the eve coser to the physica 22

38 Figure 5: Faut-toerant reay nodes pacement design for a singe contro system (2-connected region and 3 ines of backup nodes in reay region) system) and its upper eve h + 1 (the eve coser to the remote controer). To ensure each node can hear a the nodes one hop from it with the minimum number of reay nodes, we pace the nodes in each eve as cose as possibe ( horizontay right next to each other), as proved beow. We wi aso pace a virtua root and its backups as cose as possibe for the same reason. Thus, we can assume the side ink between any two nodes (sibings) in the same eve (e.g., A D) never fais, given they are so cose (it is one of the assumptions mentioned in Section 3.2). Theorem Assuming fauts are independent events, adding backup nodes as cose as possibe to each primary reay node, minimizes the number of reay nodes in the reay region. 23

39 Proof. Referring to the inset in the upper eft corner of Figure 5, note that the distance between two consecutive primary nodes (e.g., A and B) is x, which is a function the radio technoogy used and the power eve each node transmits. The maximum distance between a primary node and its furthest backup node (e.g., B-C) is m. The maximum distance between the sender and any backup receivers (e.g., B-D) is r. We use an auxiiary imaginary point, E, that forms a right ange between D and the primary node B. θ is the ange DCE. Therefore, (m + cos θx) 2 + (sin θ) 2 x 2 = r 2 (4.2) 4r Soving Equation (4.2), x = 2 4(sin θ) 2 m 2 2 cos θm, r sin θm. To minimize the number of 2 primary nodes, we need to maximize x, the distance between two consecutive primary nodes. Therefore, m shoud be as sma as possibe (note the negative sign of factors containing m), which means primary and backup nodes in the same eve shoud be paced as cose as possibe, since θ and r are constant A Network Topoogy Set Generation After pacing the reay nodes in the network area, backup paths in the k-connected region and backup nodes in the reay region can be put to seep to save energy when the network condition is bad (LSR is ow), and some of the backup paths in the k-connected region or backup nodes in the reay region need to be activated when the network condition is good (the LSR is high). Thus, we generate a network topoogy set with the different number of active nodes based on the node pacement design. Specificay, we activate the primary paths for each measurement sensor in the k-connected region and the primary ine of reay nodes in the reay region to make sure the network is connected. Then, for each measurement sensor, we activate the backup paths in k-connected region from the first backup path (the shortest) to the ast backup path (the ongest) one path at a time. Meanwhie, we aso activate one node at a time in the first ine of backup nodes from the virtua roots to the remote controer, then add one node at a time in the second ine of backup nodes, etc. Thus, we can generate a network topoogy set with different number of active nodes (e.g., a topoogy with a 2-connected region and one and a haf ines of backup nodes in the reay 24

40 region or a topoogy with a 1-connected region and three ines of backup nodes in the reay region) TDMA Scheduing The TDMA scheduing in k-connected region is done first and then, after synchronizing at the virtua roots, the TDMA scheduing for the reay region. This is due to different node pacement design in the two regions. In the k-connected region, one reay node coud be shared by mutipe paths of different measurement sensors. Thus, we design a TDMA scheduing to make sure each reay node receives a the messages from its chidren before transmitting its own message. For exampe, in a 2-connected region, two measurement sensors (numbered as 0 and 1) send messages to a virtua root (numbered as 3) by 5 reay nodes (numbered as 2, 4, 5, 6, and 7). The two paths of sensor 0 are and and the two paths of sensor 1 are and One of the feasibe TDMA scheduings is The reay nodes in k-connected region ony isten to its chidren s messages and do not overhear the messages from other reay nodes. Thus, the virtua roots can (and probaby wi) receive dupicate messages, discard them and ony send out messages with the measurements of the remaining received messages. In the reay region, the reay nodes broadcast messages from the owest eve (where the virtua roots are ocated) to the highest eve (where the remote controer is ocated). Within each eve, the primary node wi broadcast first, then the first, second, and third active backup node (if any), in order. Each reay node wi overhear the messages of some sibings before it sends out its own message. Therefore, the more active backup nodes in the network, the more messages are sent, and thus the higher network deay. 25

41 4.3 A MODEL FOR QUANTIFYING NH We propose a mode to quantify the DR in terms of average LSR and the worst-case endto-end network deay, D network, in order to quantify NH for the network topoogy set with different number of active nodes. We can determine the network topoogy with the minimum number of active nodes to meet the requirement NH 0, for different LSR vaues Deivery Ratio Cacuation We cacuate the DR at the remote controer as the ratio of the expected number of measurements received at the remote controer and the tota number of measurements it shoud receive for the different number of active nodes in the network given an average LSR vaue. Specificay, we cacuate the probabiity of measurement reception at the virtua roots in k-connected region from the measurement sensors. We then design a dynamic programming agorithm to cacuate the probabiity of different measurement receiving situations eve by eve from the virtua roots to the remote controer for the reay region. For the k-connected region, we assume there are m measurement sensors and each measurement sensor sends out one message with one measurement vaue in every contro samping period. We denote the number of hops in the i th path from measurement sensor c to virtua roots is i c. The probabiity of the measurement sent from measurement sensor c and received by at east one of the virtua roots is LSR c 1, if k = 1 p c = k i 1 (4.3) k(lsr c 1 + LSR c i ( (1 LSR c j ))), k > 1 i=2 where LSR c 1 is the probabiity the primary path transmits the measurement sent from measurement sensor c successfuy over 1 c i 1 hops to one of the virtua roots; LSR c i ( (1 LSR c j )) is the probabiity the i th backup path transmits the measurement sent from measurement sensor c successfuy over j c hops and the primary path and i 1 previous backup paths fai. As mentioned in Section 4.2.1, if we have k edge-disjoint paths in the k-connected region, we have k virtua roots, each one can receive the ast nodes in a the paths. Thus, the j=1 j=1 26

42 probabiity that at east one of the virtua roots receives the measurement c shoud have the factor k as a mutipier. (a) (b) (c) Figure 6: Three exampe states of eve h generated from one of the states of eve h 1 For the reay region, each node sends one message with one or more measurements that it has received to its parent nodes in the next eve. According to the ridesharing protoco in Section 3.1.2, the number of measurements received by each node varies (due to network errors) from 0 to the number of sensed vaues, but the tota number of measurements of a the active nodes in current eve that are going to send out to the next eve cannot exceed the tota number of measurements (or sensed vaues), due to the overhearing mechanism. 27

43 We introduce the concept of state, which represents the measurement receiving situation of a eve. A state of eve h, s h is [c h,1, c h,2,..., c h,nh, m h, p h ], where n h is the tota number of active nodes in eve h, c h,i is the number of measurements that are going to send to eve h + 1 by the i th node in eve h; we define the array [c h,1, c h,2,..., c h,nh ] as the measurementsending array of eve h; m h = n h c h,i (m h m), which is the tota number of measurements i=1 that are going to pass to the next eve; p h is the probabiity of state s h occurring. We define x h,i as the number of received messages from eve h 1 that are going to be concatenated into one message by the i th node in eve h (i.e., the number of remaining messages, since the dupicated messages were aready discarded via overhearing mechanism), so x h,i messages of the i th node contain c h,i measurements. We define y h as the tota number of messages that are going to be used to do the measurement concatenation, y h = n h x h,i. For exampe in Figure 6(a), there are three nodes in eve h 1 and h, respectivey; 5 measurements are sent from eve h 1 to eve h; the rectange represents a message with one or more measurements and the circe represents a reay node; the rectanges beow the nodes represent the messages received from the previous eve; the rectanges above the nodes represent the messages received from previous eve that are used to do measurement concatenation; and the top rectanges represent the messages are going to send to the next eve. Figure 6(a) shows that n1 sends a message with two measurements, 1 and 2; n2 sends a message with two measurements, 3 and 4; and n3 sends a message with one measurement 5; n4 receives the messages from n1 and n2; n5 receives the message from n2; and n6 receives a the message from eve h 1. n4 concatenates the four measurements to its message from the received two messages (x h,1 = 2) and sends out the message. n5 and n6 overhear n4 s message, knowing that n4 aready got messages from n1 and n2, and discard the messages received from n1 and n2 (if any). n5 does not send a message (x h,2 = 0). n6 sends a message ony incuding measurement 5 from one received message (x h,3 = 1). The measurement-sending array of eve h is [4, 0, 1]. s h is one of the states cacuated recursivey from a state in the previous (ower) eve h 1, s h 1. For exampe, et the previous eve h 1 have n h 1 nodes, each node in eve h 1 sends one message to the upper eve h. Note that m h m h 1 and y h y h 1 (the reason is discussed above), where m h 1 is the tota number of measurements sent from ower i=1 28

44 eve h 1, and y h 1 is the tota number messages used for measurement concatenation of eve h 1. The probabiity of state s h can be computed recursivey as n h p h = p h 1 ((1 LSR) i 1 LSR) x h,i i=1 (4.4) ((1 LSR) n h ) y h 1 y h The above notation is a simpification of the probem, because there are many possibe states at eve h that can be derived from many possibe states at eve h 1. For exampe, Figure 6 shows three exampe states of eve h that generated from one state of eve h 1: the measurement-sending array of the state of eve h 1 in the exampe is [2, 2, 1]. From Figure 6(a) and 6(b), the measurement-sending arrays of eve h are [4, 0, 1] and [2, 2, 1], respectivey. Figure 6(c) shows that the measurement 5 is ost during the transmission and the measurement-sending array of eve h is [2, 0, 2]. Therefore, stricty speaking, we shoud treat each eement of the state representation with another superscript, as foows. A state k of eve h is represented as s k h = [ck h,1, ck h,2,..., ck h,n h, m k h, pk h ] computed from a state j of eve h 1, s j h 1 simiary defined. Note that the states of eve 0 (where virtua roots ocate) are computed by enumerating a possibe vaues in the measurement-sending array and cacuating the corresponding occuring probabiity from Equation (4.3). To cacuate the probabiity of a possibe number of measurements received by the remote controer, we need to enumerate a possibe states each eve coud have. For each eve, we carry out the cacuation with two phases, namey, a states-generating phase and states-combining phase. For the former, one or more states are generated by one of the states of the previous eve (ike the exampes shown in Figure 6). Formay, the new states, s k h of eve h that are generated by one state, state s j h 1 in eve h 1, are the combinations of a possibe vaues of c k h,i with the foowing conditions: mk h mj h 1, 0 ck h,i mj h (1 i n h). For the states-combining phase, the probabiity of states with the same measurement-sending array (generated from different states of eve h 1), [c k h,1, ck h,2,..., ck h,n h ] are summed up and combined into one state. Since we compute each state s probabiity iterativey from the measurement sensors to the remote controer, a possibe number of measurements wi 29

45 be accounted for at the remote controer. The deivery ratio at the remote controer is cacuated as DR = m (p RC (i) i) i=1 (4.5) m where m is number of measurements sent from the sensors, and p RC (i) is the combined state probabiity that the remote controer receives exacty i measurements. p RC (i) is cacuated recursivey from the eve of measurement sensors to the eve of the remote controer, where the states of each eve in reay region are cacuated during the phases of states-generating (using Equation (4.4) for each state probabiity cacuation) and states-combining Worst-case End-to-end Deay and NH Cacuation Based on the ridesharing protoco [Gobrie et a., 2006], which is a modification of TDMA scheduing, each active node is reserved one time sot for transmitting the measurement message. We focus on one-way wireess transmission in a WCS in this chapter and there is a pipeine of messages one after another 1 (periodic messages). Once the messages are scheduabe (messages can be deivered to the destination), it is not possibe that the messages of previous contro samping period are conficted by the messages of the current period, because previous messages are aways sent and arrive at the remote controer before the current message. Therefore, the worst-case network deay is D network = n active t (4.6) where n active is the number of the current active nodes and t is the time sot of TDMA scheduing. Therefore, for a given LSR, we can cacuate NH using Equation (4.1) for the topoogy set (generated in Section 4.2.3) with the different number of active nodes in the network, by cacuating DR from Equation (4.5) and D network from Equation (4.6). Then, we seect the 1 If the eve difference between the two messages from consecutive contro samping periods is ess than 3, there wi be message transmission confict. The messages are unscheduabe (messages cannot be deivered to the destination) and wi be stuck at a certain eve forever. We wi expain ater in the Lemma in Chapter 6 30

46 topoogy with the minimum number of active nodes that meets the constraint NH 0 for different LSR vaues. 4.4 PERFORMANCE EVALUATION We carried out a case study of a WCS with one PHX in an NPP to evauate our mode, with the contro system stabiity requirement as p 1 = 0.714, p 2 = 0.138, and p 3 = [Wang et a., 2016] (Equation (4.1)). We use the TOSSIM network simuator [Levis et a., 2003] with wireess noise traces from a 21-node subset of the WUSTL Testbed [tes, 2017]. Simiar to [Li et a., 2015], we use controed Received Signa Strength (RSSI) [Lee et a., 2007] with uniform gaps to simuate various LSR vaues. For the wireess network, we evauate a 12-hop (5 hops in the k-connected region and 7 eves in the reay region) network of both the mode resuts and simuation resuts. For our mode anaysis, we pace 3 ines of backup nodes in the reay region (b = 3) to avoid ong-running computations. For the simuation anaysis, we pace 7 ines of backup nodes in the reay region (b = 7) for sensitivity anaysis purposes. We set the maximum connectivity degree of k-connected region as 4 (i.e., k 4). Starting with one ine of primary nodes and fixed k-connected region, we activate ines of backup nodes from virtua roots to the remote controer (as discussed in Section 4.2.3). We assume the same time sot duration, t = 0.01s, of WireessHart [wir, 2007]. We evauate three metrics: DR, NH, and the minimum number of active nodes in the network for different LSRs with NH The Mode for Quantifying NH Resut The cacuated DR from Equation (4.5) at the remote controer is shown in Figure 7(a) for the average LSR 0.8 (other vaues of LSR show the same trend). Figure 7(a) represents the cacuated DR as a function of the number of added backup nodes in the reay region for different vaues of k-connected region. Three interesting observations are as foows. First, the infection points happen when a primary reay nodes have the same number of backup 31

47 Deivery Ratio k=4 k=3 k=2 k= Number of Nodes Added in the Reay Region (a) Deivery ratio at remote controer; average LSR = 0.8 (b) NH with different LSRs: 0.7, 0.8 and 0.9. Figure 7: The Mode of quantifying NH resuts nodes (every 7 nodes or a compete ine in this case). Second, whie adding the first ine of backup nodes, the DR exponentiay increases because the probabiity of sending a message successfuy from virtua roots to the remote controer is (2LSR(1 LSR) + 2LSR) b LSR 7 b = 2 b LSR 7 (2 LSR) b, where b is the number of backup nodes added in the first ine of backup nodes; (2LSR(1 LSR) + 2LSR) b means the probabiity of sending a message successfuy from the eve of virtua roots to the eve of the ast backup nodes added in the first ine of backup nodes. As b increases, the probabiity increases exponentiay. Third, the sope decreases when adding more ines of backup nodes. Figure 8 demonstrates the reason: the probabiity of using the ast active node in one eve handing a message decreases as the number of backup nodes in each eve increases, which expains why the sope of the first ine of backup nodes is the steepest. Figure 7(b) shows the average NH for different LSRs. The system shoud operate above N H 0, when the network meets the contro system requirements (above the horizonta ine in Figure 7(b)). From this resut, we are abe to seect topoogies with the minimum number of active nodes that meet NH 0 for different LSR vaues (more resuts are shown in Tabe 1). For exampe, given LSR vaue of 0.8, the minimum number of active nodes in 32

48 Figure 8: Iustration of the probabiity of a message sent from previous eve is handed by the ast node of a eve. Red nodes do not receive messages and green nodes hande messages a topoogy meeting the requirement is 34 (see Figure 7(b)). As the number of backup nodes increases, the NH increases, but the sope of the improvement decreases. When the LSR is 0.9 and 0.8, the NH starts to decrease after more than 40 nodes in the network. It is because the network deay increases faster than the network reiabiity and starts to have bad effect on NH Simuation Resuts In the simuation, we adjust the RSSI vaue to simuate various LSR vaues. Figure 9 shows how to correate RSSI and LSR based on 12,000 transmissions, where RSSI is between -64 dbm and -84dBm. As the RSSI increases, the average LSR increases, which indicates the network condition becomes better. The simuated average DR is shown in Figure 10(a) for different RSSI vaues as a function of the number of active nodes in the network. The DR increases when the number of active nodes increases, showing network gains in reiabiity. Obviousy, the higher the RSSI, the higher the DR; however, the difference in DR decreases as a function of the number of active nodes and RSSI becomes irreevant for networks with many nodes (backup nodes dominate then and network is very reiabe). Simuated vaues of NH are shown in Figure 10(b). From this resut, we can aso seect topoogies with the minimum number of active nodes that meet NH 0 (above the horizonta ine in Figure 10(b)) for different LSR vaues (we can correate the RSSI vaues with the LSR vaues from Figure 9). It is interesting to see that the NH increases at first as the number of active 33

49 Figure 9: The reationship between RSSI and average LSR Deivery Ratio RSSI=-64 RSSI=-70 RSSI=-76 RSSI=-82 RSSI= Tota Number of Nodes in the Network (a) Deivery ratio for different number of active nodes. (b) NH distribution for different number of active nodes. Figure 10: Simuation resuts nodes in the network increases, because the DR increases faster than the network deay. But the NH then decreases as the number of active nodes increases, because the network deay increases faster than the DR. 34

50 Tabe 1: Comparison of mode and simuation resuts RSSI (dbm) average LSR LSR stdv MinMR MinSR Diff % % % % % We compare our mode resuts (MR) with the simuation resuts (SR). Tabe 1 is the comparison of the minimum number of active nodes of MR (MinMR) and the minimum number of active nodes of SR (MinSR) when satisfying NH 0 for various vaues of RSSI. Diff is defined as the percentage difference between MinMR and MinSR, Diff = (MinMR MinSR)/MinMR, quantifying the difference between our mode and the simuation. The simuation resut demonstrates that our mode is accurate with average 4.1% difference from the mode resut (minimum and maximum difference is 0% and 8.7%, respectivey). The MinMR is different from the MinSR due to the foowing reason. MR uses a constant vaue of LSR to do the cacuation of the minimum number of active nodes in the network that woud meet NH 0, whie the distribution of LSR in our simuation foows the CPM mode [Lee et a., 2007] in TOSSIM. We conduct a simuation of 12,000 transmissions in a network and cacuate the average LSRs every 60 transmissions. In order to see the LSR distribution ceary, we normaize the LSRs by subtracting with the average LSR over the 12,000 transmissions. Figure 11 shows the histograms of the LSR difference distribution, for RSSI = 64, RSSI = 76 and RSSI = 84. They a have LSRs that are different from the overa average LSR, but the more concentrated around 0, the more LSRs cose to the overa average LSR, which matches the LSR standard deviation in Tabe 1. The LSR dispersion degree (Figure 11) is the highest for poor network (RSSI = 84), indicating that the LSR has the most variation and is the most different from the constant LSR of our mode, which expains RSSI = 84 shows the highest Diff. 35

51 4.5 SUMMARY In this chapter, we focused on designing a faut-toerant wireess network to meet contro system requirement with the minimum number of active nodes. We first propose a fauttoerant network node pacement design. We then present our mode to cacuate the contro system stabiity requirement, NH, and determine the minimum number of active nodes in the network to meet NH 0. For vaidation, we simuate a 12-hop wireess network on TOSSIM simuator, transmitting messages for a PHX in an NPP. The simuation resut demonstrates the correctness of our mode with average 4.1% difference from the mode resut. Furthermore, we find that the redundancy in the wireess network is not aways good for the contro system stabiity, which coud induce more network deay in the WCS. Figure 11: Histogram of LSR difference distribution for RSSI = 64, RSSI = 76 and RSSI = 84 36

52 5.0 DYNAMIC NETWORK RECONFIGURATION FOR WCS WITH ONE PHYSICAL SYSTEM In Chapter 4 we achieve the contro system stabiity requirement with minimum number of nodes in the network. However, ony making sure the system stabiity is not enough, since network-induced imperfections can sti degrade contro quaity comparing with the wired contro system and resut in equipment damage and serious economic osses [Yu et a., 2014]. Therefore, it is necessary to reduce the network-induced error to make the contro system performance as cose as the performance of the wired contro system. In this chapter, we discuss reducing network-induced error for a WCS with one singe physica system for oneway wireess transmission. We wi discuss reducing the network-induced error for a WCS with mutipe physica systems for two-way wireess transmission in Chapter 7. The trade-off between network deay and packet oss motivates us to find the optima network configuration to minimize the network-induced error for the contro system under different LSR vaues. Another main difficuty of having wireess networks for the contro systems is caused by the interference and noise that produce time-varying faut patterns [Cerpa et a., 2005; Srinivasan et a., 2010], which motivates us to find a fast and effective way to carry out network reconfiguration at run time. In this chapter, our objective is to reduce the network-induced error for a WCS with a singe physica system under time-varying network ink faiures. We design and impement a framework with offine and onine components to do network reconfiguration for the contro system to toerate LSR changing over time (caused by the time-varying ink faiures). To evauate the contro system performance with our network reconfiguration framework, we conduct a systematic case study with a WCS for a singe PHX in an NPP. 37

53 Figure 12: Network reconfiguration framework for the contro system with dynamic network interference 5.1 NETWORK RECONFIGURATION FRAMEWORK We propose a network reconfiguration framework that has as input a network configuration set, that is, a network topoogy set generated in Section based on the node pacement design discussed in Section 4.2. Different topoogies correspond to different number of active nodes in the network. Our framework contains two parts, offine and onine, as shown in Figure 12. For the offine part, to quantify the network-induced imperfection impact on contro system performance, we propose a network imperfection mode to transform network deay and DR to the tota induced deay on the contro system. We estimate the tota induced deay for each topoogy in the network topoogy set. We find an estimated optima network topoogy set for each LSR offine (optima means minimum network-induced deay), and store them at the controer node. For the onine part, at run time, the network notifies the controer what the estimated LSR is and the controer seects a network topoogy from the estimated optima topoogy set computed offine. The controer then broadcasts the new network topoogy to a the nodes in the network to carry out a reconfiguration. Therefore, the remote controer acts as a centraized network manager and decides which network 38

54 configuration shoud choose. 5.2 OFFLINE OPTIMAL NETWORK CONFIGURATION We first introduce a mode describing the network-induced imperfection impact on the contro system performance, which quantifies the trade-off between network deay and DR. We then show how to find estimated optima network topoogy set by using this mode Network Imperfection Mode Athough previous research discussed how the network reiabiity and network deay affect the contro system performance [Wang et a., 2016; Li et a., 2015], to the best of our knowedge there is sti no mode that buids the reationship between network performance (i.e. network deay and message oss) and contro system performance (i.e. network-induced error). We define the deay induced into the contro system by the wireess network as T used T sensed, where T used is the time the measurement signa is used by the controer and T sensed is the time the sensor sends out the sensor measurement. The tota deay induced into the contro system is cacuated dynamicay every time it is needed: D = ( Dcurrent p + n oss )p (5.1) where D current is the current end-to-end network deay, p is the contro samping period, n oss is the number of consecutive packet osses. For exampe, as shown in Figure 13, the contro samping period is 0.1s, but when the network deay is 0.2s and measurement M 2 gets ost, the induced deay D 2 is 0.3s and the controer wi use measurement M 1 instead. When the measurement M 3 aso gets ost, the induced deay D 3 is 0.4s and the controer wi (re-)use measurement M 1. Note that n oss is computed from the contro system perspective, that is, if a message is received by the controer every contro samping period, n oss = 0. D is reated to both network deay and the number of consecutive packet osses. n oss is estimated by the expected vaue of the network oss ratio (1-DR). We assume message 39

55 Figure 13: Network deay and deivery ratio trade-off iustration, when network deay is greater than contro samping period (p = 0.1s and D current = 0.2s) osses foow the uniform distribution, since DR can be viewed as the probabiity a message received by the controer. Thus, n oss = n i(1 DR) i DR, (1 DR) i DR c (5.2) i=1 where (1 DR) i DR is the probabiity of i consecutive osses. When the probabiity is ess than a threshod (c), we assume that the probabiity can be ignored to avoid ong-running computations. For exampe, for DR = 0.9 and c = , the probabiity of getting 1, 2 and 3 consecutive osses are 0.09, 0.009, and , respectivey. Therefore, the expected number of consecutive osses is 1 (1 0.9) (1 0.9) (1 0.9) = The situations of 4 or more consecutive osses are ignored, since the probabiity of 4 consecutive message osses is (1 0.9) = < c Optima Network Configuration Determination Our offine agorithm discovers the set of estimated optima network topoogies that wi be saved and used ater during the onine portion. The goa of the offine agorithm is to minimize the network impact (network deay and packet oss) on the contro system, using the network imperfection mode above. By appying the worst-case network deay (D network ) cacuation in Equation (4.6) and DR cacuation in Equation (4.5) (so that n oss can be estimated from Equation (5.2)), we are abe to estimate the tota induced deay D for the 40

56 network topoogy set for different LSR vaues. For each LSR vaue, our agorithm searches a the network topoogies and finds the one with minimum estimated induced deay, D. Thus, we find a set of estimated optima network topoogies with minimum tota induced deay D for each LSR vaue and store them in a ook-up tabe indexed by LSR vaue. 5.3 ONLINE NETWORK RECONFIGURATION Wireess networks, especiay in radiation-prone ocations, suffer from varying eectromagnetic interference, which causes some inks, some of the time, to fai. Ceary, static configurations do not adapt to the time-varying noise and interference that can cause time-varying ink faiures, that is, the average LSR remains constant over a period of time. We devised an onine dynamic network reconfiguration to improve the contro system performance by reducing the tota induced deay D. The controer carries out both the contro and network reconfiguration agorithms, given that it has a the information needed to decide the new configuration (i.e., network topoogy). The controer detects a reconfiguration is needed (for exampe, due to interference/noise), and computes and propagates a new network configuration to a the nodes by broadcasting reconfiguration messages. To dea with packet re-ordering, we discard od messages (i.e., the time stamps of the messages are oder than the received messages) at the remote controer. In this dissertation, we restrict network configuration to the network topoogy, even though our offine agorithm (Section 5.2) is genera and the offine agorithm can be designed to dea with network configuration variabes ike data ink ayer schedue, network routing, etc. We first introduce the network reconfiguration process. Since our onine network reconfiguration is based on the offine ook-up tabe given the current LSR, we then propose an agorithm to estimate the average LSR at run time. Finay, we propose six onine network reconfiguration agorithms, that is, three origina agorithms with two variations each, namey considering or not consecutive packet osses. 41

57 5.3.1 Network Reconfiguration Process Reca that the network topoogy set is generated foowing the process discussed in Section When we do network reconfiguration, that is, changing the network topoogy from topoogy A to topoogy B, there are two cases: (a) topoogy B has more active nodes than topoogy A; and (b) topoogy A has more active nodes than topoogy B. For the first case, we need to activate the seep nodes to be active to get topoogy B by activating backup nodes in the reay region or/and the backup paths in the k-connected region. For the reay region, we activate the backup nodes from the owest eve to the highest eve starting with the ine of inactive backup nodes that is cose to the primary ine of reay nodes, then from the owest eve to the highest eve in the second ine of inactive backup nodes that is cose to the primary ine of reay nodes and so on. For the k-connected region, we activate the backup paths in the order of the shortest inactive path, then the second shortest inactive path and so on. For the second case, opposite behaviors occur to put the active nodes to seep to get topoogy B: deactivating the active nodes from the highest eve to the owest eve in the reay region starting with the ast ine of active backup nodes; or/and deactivating the backup paths from the ongest active backup path. The speed and how many nodes to activate/deactivate at a time wi be expained ater in Section and Section Network Average Link Success Ratio Estimation Since our onine network reconfiguration is based on the offine ook-up tabe for each LSR vaue, we need a way to estimate the average LSR when the reconfiguration agorithm is executed. To estimate the LSR at run time, we propose a jumping window in-network aggregation method. During a certain amount of time, that is, the LSR estimation interva (LSRI), each node counts the number of messages it receives (NMR), n rev and the number of messages it shoud receive (NMS), n shoud (knowing the period of message arriva). At the end of the LSRI, each node concatenates the two numbers, n rev and n shoud to its message, and sends the message to its parent nodes. Then, the parent nodes wi sum their own NMR and NMS with their chidren s NMRs and NMSs, respectivey; this repeats unti getting 42

58 Initiaization: n shoud = 0, n rev = 0, LSRCounter=0; whie true do if LSRCounter == LSRI then ese end if it is time to receive a message then end get the n i rev and n i shoud from the received message m i ; n rev = n rev + n i rev ; n shoud = n shoud + n i shoud ; if it is time to transmit a message then end Attach n shoud and n rev to its message that is going to send; Send out the message; n rev = 0 ; n shoud = 0 ; LSRCounter=0; if it is time to receive a message then end n shoud ++; if receive a message then end n rev ++; LSRCounter++; end Agorithm 1: LSR estimation agorithm running on one active reay node 43

59 to the controer. Eventuay, the remote controer wi compute the fina overa network average LSR by its received n rev and n shoud as agorithm running on one reay node in more detai. n rev n shoud. Agorithm 1 shows the LSR estimation Reconfiguration Not Considering Consecutive Losses The intuition behind the onine agorithm is to find the estimated optima topoogy according to the current estimated LSR cacuated by the remote controer, and then adjust the current network topoogy to the estimated optima topoogy. We expore three options to reach the estimated optima topoogy, given that the reconfiguration depends on the LSR, which cannot be computed instantaneousy. We first discuss three agorithms not considering consecutive message osses, which are DirectJump to Optima (DO), Mutipicative Increase and Conservative Decrease (MICD), and Adaptive Contro (AC). The inputs to these agorithms are the offine ook-up tabe and the LSR computed in Section 5.2 and Section 5.3.2, respectivey. DO (Direct Jump) The controer sends out a message to a participating nodes to adjust the network topoogy to instantaneousy have the estimated network topoogy whenever the LSR estimation vaue changes according to the offine ook-up tabe. Agorithm 2 shows the detai. MICD (Mutipicative Increase and Conservative Decrease) Inspired by [Sankarasubramaniam et a., 2003], with a focus on network reiabiity, the number of seep nodes is mutipicativey (i.e., very quicky) activated when the number of active nodes in current topoogy is ess than the number of active nodes in the estimated topoogy based on a changed LSR vaue (converse of TCP/IP protocos window reduction [Chiu and Jain, 1989]). When the number of active nodes in current topoogy (curr node ) is more than the number of active nodes in the estimated topoogy (est node ), the number of active nodes is conservativey deactivated (in our case, we deactivate one active node at a time). Agorithm 3 shows more detai: every LSRI, a certain number of nodes (change nodes ) is activated or deactivated on top of the current topoogy to achieve reconfiguration. AC (Adaptive Contro) Inspired by adaptive contro theory [Hovakimyan and Cao, 44

60 Initiaization; LSRCounter=0; whie true do if LSRCounter == LSRI then estimate current LSR, curr LSR ; ook up the offine tabe and get the new network topoogy, T based on curr LSR ; change the current network topoogy to T; LSRCounter=0; end LSRCounter++; end Agorithm 2: Direct jump to optimum (DO) 2010], the arger the difference between the number of active nodes in estimated topoogy (getting from the offine tabe based on the estimated LSR) and the number of active nodes in current topoogy, the faster we activate or deactivate number of nodes in the network. That is, curr node = α curr node +(1 α) est node. Parameter α guides the speed of activation or deactivation of the reay nodes in the network (0 < α < 1). When α = 0, AC behaves ike DO and the speed of activating or deactivating nodes is maximum. When α = 1, the current number of nodes does not change, that is, it is a static network. In essence, smaer α impies higher speed to change the current number of active nodes. Agorithm 4 shows more detai Reconfiguration Considering Consecutive Losses From Equation (5.1), the tota induced deay is proportiona to the number of consecutive osses n oss. However, in the agorithms above, we did not consider n oss. Since the LSR estimation is not competey accurate, it takes time to reconfigure and the network conditions vary over time, there coud be consecutive message osses, which wi degrade the contro 45

61 Initiaization; LSRCounter=0, est node =0, increment = 1; whie true do if LSRCounter == LSRI then end get the number of active nodes in current topoogy, curr node ; estimate current LSR, curr LSR ; ook up the offine tabe and get the new network topoogy, T based on curr LSR ; est node =T.node; if curr node < est node then change node = increment; increment = increment 2; ese if curr node > est node then ese end change node = 1; increment=0; Activate or deactivate change node nodes on the current network topoogy to get a new topoogy; LSRCounter=0; LSRCounter++; end Agorithm 3: Mutipicative Increase and Conservative Decrease (MICD) 46

62 Initiaization; LSRCounter=0, est node =0, curr node = min node ; whie true do if LSRCounter == LSRI then get the number of active nodes in current topoogy, curr node ; estimate current LSR, curr LSR ; ook up the offine tabe and get the new network topoogy, T based on curr LSR ; est node =T.node; new node = α curr node + (1 α) est node ; Activate or deactivate curr node -new node nodes on the current network topoogy to get a new topoogy; LSRCounter=0; end LSRCounter++; end Agorithm 4: Adaptive Contro (AC) 47

63 Figure 14: Time-varying RSSI variation exampe system performance. In other words, when there are consecutive message osses, we need to make the network more robust (we choose to activate more nodes). As a first experimenta step, whenever n oss q, we add g more nodes in the network. g and q are user-seected parameters. Considering consecutive osses, we devise three more onine agorithms: CL-DO, CL- MICD, and CL-AC. 5.4 CASE STUDY We conducted a case study to show and experiment with our wireess network reconfiguration framework for one PHX of one-way wireess transmission. We depoy the same network in the case study as the one in Chapter 4, that is, a network with 12-hop and up to 50 nodes. We use a state-of-the-art cyber-physica system simuator (WCPS 2.0 [Li et a., 2015]) to combine TOSSIM network simuator [Levis et a., 2003] and the PHX simuink mode together. The ridesharing protoco is impemented in the TOSSIM simuator with wireess noise traces from a 21-node subset of the WUSTL Testbed [tes, 2017]. The onine reconfiguration agorithms mentioned in Section 5.3 are impemented on the controer. To simuate time-varying ink faiures, we propose a network faut mode as foows. We hod RSSI constant for a period of time and change RSSI to another vaue for the next period 48

64 Tabe 2: Parameters and Vaues Parameters Vaues Contro samping period (p) 0.1s TDMA time sot ( t) 0.01s Simuation time 300s RSSI range (-60 dbm, -85 dbm) time range (0, 20s) LSRI vaues 2s, 4s, 8s, 12, 16s, 20s Reference functions ramp30, ramp60, ramp90, ramp120 α vaue 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 of time (the duration is based on the noise traces mentioned above). We adjust each reay node s RSSI to change LSR within the range (0.5, 1.0), depending on the foowing three quantities: RSSI duration: the time interva at which the RSSI is fixed (after that, the RSSI may be changed); RSSI range and time range: the vaue and time range the RSSI duration is chosen from. We randomy choose RSSI from RSSI range with a uniform distribution and randomy choose RSSI duration from time range aso with a uniform distribution. Figure 14 shows an exampe of the generated RSSI over time using our faut mode with RSSI range of (-60 dbm, -85 dbm) and time range of (0, 20s). To evauate the performance of the contro system (in this case the PHX), we adopted two metrics: Integra Absoute Error (IAE) [Li et a., 2016] and Root Mean Square Error (RMSE), which is the RMS error measured between the cosed-oop responses using wired contro and wireess contro under consideration. These metrics quantify the quaity of the WCS: the ess (error), the better. We aso measure three more metrics, the tota induced deay D (to anayze IAE and RMSE) of the network imperfection mode, the number of active nodes that are used in the network, and the network ifetime. Tabe 6 shows our simuation parameters and vaues. 49

65 5.5 CASE STUDY RESULTS Offine Optima Network Configuration Resuts Number of optima nodes in the network optnodes Link Success Ratio Tota induced deay (s) rssi=-64 rssi=-70 rssi=-76 rssi=-82 rssi= Number of nodes in the network power output RMS error (MW) rssi=-64 rssi=-70 rssi=-76 rssi=-82 rssi= Number of nodes in the network (a) (b) (c) Figure 15: (a) The number of active nodes of the offine estimated optima topoogy with different LSR vaues; (b) tota induced deay resut for RSSI vaues of -64, -70, -76, -82 and -84 that correspond to average LSR vaues of 0.93, 0.88, 0.82, 0.77, and 0.72, respectivey; (c) power output RMSE for different number of active nodes in the network. By appying the agorithm in Section 5.2.2, we can get the ook-up tabe containing the estimated optima topoogy for each LSR vaue. Figure 15(a) shows the number of active nodes of the estimated optima topoogy for different LSR vaues. The higher the LSR, the higher the percentage of packets that get deivered, and the more robust the network wi be, and therefore the fewer reay nodes needed. The optima number is aways a mutipe of 10 due to the ceiing operation in our network imperfection mode (see Equation (5.1)). In detais, D current = n active t (from Equation (4.6)) is mutipe of time sot duration t = 0.01s; when n active = 10x (x 1), where x is an integer, the network is more reiabe (ess n oss ) than the network of n active = 10(x 1)+y (y = 1,.., 9) but with the same vaue of the term (p = 0.1). For exampe, a network with 25 active nodes (network deay D current p 50

66 Figure 16: Contro system power reference functions is 0.25s, but is considered as 0.3s due to the ceiing operation) wi definitey have more tota deay D than the network with 30 active nodes (network deay is aso 0.3s), since 30 nodes is more reiabe and has fewer n oss than 25. To see the correation of the network imperfection mode from Section and the contro system performance, we run the simuation with static RSSI vaues. Figure 15(b) shows the tota induced deay for different number of nodes and different RSSI vaues. Note that when the number of nodes is 20, the network is not robust (deivery ratio is ess than 0.6 when RSSI = 64 and ess than 0.1 when RSSI = 84 according to the resuts in Figure 10(a)) and has more consecutive message osses, thus has more induced deay even though the actua network deay is the owest (for the messages that are actuay deivered), since it has the smaest number of nodes. When the number of nodes is 50, the network is the most robust and amost does not have consecutive message osses (DR is above 0.9 when RSSI = 84 according to Figure 10(a)), but sti has induced deay due to the highest network deay. Figure 15(c) shows the power output RMSE of the PHX. Comparing Figure 15(b) and Figure 15(c), we can see that our network imperfection mode is accurate visuay and statisticay (Pearson correation r = 0.993, p < 0.001) correating we to the power output RMSE. 51

67 power output IAE (MW) ramp30 ramp60 best-static MICD DO CL-DO AC ramp90 Different reference function CL-AC CL-MICD ramp120 Figure 17: Power output IAE for different reference functions (average RSSI: -82dBm; LSRI: 2s (20 sampes)) Onine Network Reconfiguration Resuts To simuate time-varying ink quaity modes, we varied the RSSI range and time range to get different representative network faut modes (Section 5.4) with different average RSSI vaues over the simuation time. We simuate our system on five faut modes with average RSSI vaues (in dbm) of -65, -70, -74, -78 and -82. In this section, we present resuts of contro system performance (RMSE and IAE) and network ifetime; and the number of nodes, tota induced deay and RMSE changing over time for different onine reconfiguration agorithms. Heat exchanger system power reference function To study the behavior of the PHX, we consider the case when an operator changes the power output for the reactor. We set the power reference function (i.e., the required power output of a nucear reactor), to reduce power from 42 MW to 37.8 MW (typica vaues for NPPs) as shown in Figure 16 (sampe time is time/p). Ramp30 means that it takes 30 seconds to reduce the power from 42 MW to 37.8 MW. We consider four reference functions in this chapter: ramp30, ramp60, ramp90 and ramp120. As shown in Figure 17, the steeper the reference function, the arger the IAE. This is because when the reference function is steep, it requires the contro system to reduce its power output more aggressivey, and thus it wi have more transient response, causing arger IAE. In the figure, best-static is the best fixed number of active nodes in the 52

68 network, as foows. For each reference function, we tested the number of nodes 20 to 50 for each faut mode and chose the static scheme with minimum average IAE over a the faut modes (in our case it is the static scheme with 40 active nodes). As shown in Figure 17, onine agorithms a perform better than the best-static with the average improvement of 16%, 23%, 19% and 20% for ramp30, ramp60, ramp90 and ramp120, respectivey. Note that the onine network reconfiguration agorithms have simiar trends for a reference functions as shown in Figure 17. We ony present the resuts for ramp30 in the foowing sections. Comparison of Onine Reconfiguration Agorithms Figure 18(a) shows the power output IAE of the PHX for different average vaues of RSSI and different onine network reconfiguration agorithms; RMSE resuts are simiar to the IAE resuts and are thus omitted. For the first study, in this case study, we add 3 more nodes (g = 3) in the CL-* agorithms when 3 consecutive message osses (q = 3) happen. As the average RSSI vaue decreases, the power output IAE increases, since the network has more interference. As expected, our dynamic agorithms perform typicay better than the static scheme for a faut modes. CL-DO and CL-AC agorithms perform better than the other dynamic agorithms, because they add more nodes ony when needed, that is, when the network has consecutive message osses. But CL-MICD aways perform worse than CL-DO and CL-AC on average by 7.8% and 7.4% over five faut modes, respectivey. Figure 19 shows the comparison of CL-MICD and CL-AC on 20 experiments over 3,000 sampes. The reason CL-MICD aways performs the worst among CL-* agorithms is because the speed of reducing the number of nodes is sow (reduce one at a time) and the speed of adding nodes is fast (exponentia increase), which often overshoots the number of actuay needed nodes and thus causes more induced deay (induced deay of CL-MICD is aways higher than CL-AC) and degrades the contro system performance. We cacuate the average network ifetime to measure the network energy consumption. We define our network ifetime as the average reay node ifetime, and cacuate the average network energy consumption over different topoogies experiencing in the onine schemes for one round of measurement transmissions from the measurement sensors to the controer. For simpicity, we assume a genera battery capacity is 8640J, which is the typica capacity of two AA batteries. Figure 18(b) shows the network ifetime for different reconfiguration 53

69 Power output IAE (MW) best-static DO AC MICD CL-DO CL-AC CL-MICD -74 RSSI (a) Network ifetime (days) best-static DO -74 RSSI AC MICD CL-DO CL-AC -78 CL-MICD -82 (b) Network ifetime / IAE best-static DO AC MICD CL-DO CL-AC CL-MICD RSSI (c) Figure 18: (a) Power output IAE and (b) network ifetime (c) network ifetime / IAE resuts for different RSSI vaues (LSRI: 2s; α: 0.1) 54

70 Figure 19: (a) Average number of nodes in the network, (b) average induced deay and (c) average RMSE over 20 experiments changing over time (LSRI: 2s; average RSSI: -82dBm; α: 0.1) 55

71 (a) (b) Figure 20: (a) Network deivery ratio; (b) network deay for different average RSSI vaues (LSRI: 2s; α: 0.1) 56

72 agorithms. Agorithms considering consecutive message osses (CL-DO, CL-AC and CL- MICD) consume more energy than their counterparts not considering consecutive message osses (DO, AC and MICD). This is because CL-* agorithms are more aggressive activating additiona nodes when there are consecutive osses. In addition, from Figure 18(b), we found that when there is more interference in the network, the network consumes more energy, since the network needs more backup nodes to hande ink faiures. For network performance resuts, see Figure 20(a) and Figure 20(b). As the average RSSI vaue decreases, indicating more interference in the network environment, the DR decreases, but the network deay increases since more active nodes are reconfigured participating. To consider both contro system performance and network energy consumption together, we normaize network ifetime by IAE (i.e., network ifetime / IAE; the more normaized vaue, the better) in Figure 18(c) for different average RSSI vaues. The static scheme is significanty worse than the dynamic agorithms, because it consumes the most network energy consumption, and it causes the most power output IAE, demonstrating that our reconfiguration agorithms are necessary and work we. Note that we seected the beststatic scheme to be conservative in our evauation, but in reaity it woud be hard to seect a good static configuration a priori, since the network interference is unpredictabe. Sensitivity Anaysis of LSR Estimation Interva Since LSR is estimated periodicay, the ength of the LSR estimation interva (LSRI) wi affect the contro system performance. Figure 21(a) shows the resuts of the power output IAE for different LSRI vaues. When the LSRI increases, the IAE of agorithms DO, MICD and AC increases because our estimation is ess accurate at high LSRI vaues. Figure 21(b) and Figure 21(c) show the network ifetime and network ifetime normaized by IAE, respectivey. In Figure 22, the green ine is the rea LSR; the back ine (LSRI of 2s) in Figure 22(a) tracks the rea LSR better than the LSRI of 8s in Figure 22(b) and the LSRI of 16s in Figure 22(c). Therefore, the contro system performance has ess error when the LSR estimation is accurate. Figure 23 shows the comparison of the DO with LSRI of 2s and 20s (AC and MICD have simiar resuts). From sampe 600 to 800, the DO with LSRI of 20s runs with 30 nodes in the network because the LSR is estimated high averaged over the ast 200 sampes (from 400 to 600). However, from sampe 600 to 800, the LSR is ow (network has more interference) and 57

73 Power output IAE (MW) best-static DO AC 4 MICD CL-DO 8 CL-AC CL-MICD LSRI (s) (a) Network ifetime (days) best-static DO 4 AC MICD 8 CL-DO CL-AC LSRI (s) 12 CL-MICD (b) Network ifetime / IAE best-static DO AC MICD CL-DO CL-AC CL-MICD Link success ratio estimation interva (s) (c) Figure 21: (a) Power output IAE and (b) network ifetime (c) network ifetime / IAE resuts for different LSRIs (average RSSI: -82dBm; α: 0.1) 58

74 (a) (b) (c) Figure 22: Comparison of estimated and rea LSRs (a) LSRI is 2s (b) LSRI is 8s (c) LSRI is 16s (average RSSI: -82dBm) 59

75 Figure 23: (a) Average number of nodes in the network, (b) average induced deay and (c) average RMSE over 20 experiments changing over time (average RSSI: -82dBm) 60

76 30 nodes cannot hande the ink faiures, which makes the consecutive message osses happen (induced deay D is high) and negativey affects the contro system performance. The IAEs of the CL-* agorithms are not affected by the LSRI vaues because, even though the LSR estimation may not be accurate, CL-* agorithms activate additiona nodes to compensate to make the network robust. However, the side-effect is that CL-* agorithms consume more energy (see Figure 21(b)). For network performance (DR and deay), see Figure 24(a) and Figure 24(b). Adaptive contro agorithm with different α vaues Reca that the AC agorithm has a variabe α (0 < α < 1), which determines the speed to activate or deactivate nodes in the network (sma α, fast node activating/deactivating). The α vaue can aso affect the contro system performance. Figure 25 shows the IAE of AC and CL-AC agorithms for different α vaues. First, ooking at the resuts without consecutive osses, when α > 0.5, the contro system performs worse. This is because the speed of adding or removing nodes is sow that it cannot react to the LSR variation on time. Figure 26 shows the reason more ceary. From sampe 600 to 800, when the network has more interference, the speed of activating nodes in AC with α = 0.9 is sower than α=0.1, causing consecutive message osses and more induced deay. From sampe 800 to 1300, when the network has ess interference, the speed of AC (α=0.9) of deactivating nodes is aso sow and induce more deay (network deay is high) into the contro system. When considering consecutive osses, from Figure 25, we find that CL-AC aways performs better than AC. Athough the speed to activate or deactivate nodes is sow for AC with α=0.9, considering consecutive osses can compensate with 13.5% IAE reduction. Figure 26 shows more detais. From sampe 600 to 800, when the network has more interference (consecutive message osses happen), CL-AC (α=0.9) activates more nodes in the network than AC (α=0.9), which improves the contro system performance. But CL-AC consumes more network energy than AC (see Figure 25), due to activating additiona nodes when there are consecutive osses. 61

77 (a) (b) Figure 24: (a) Network deivery ratio; (b) network deay for different LSRIs (the average RSSI vaue: 82dBm; α: 0.1) Power output IAE error AC CL-AC Apha vaue Figure 25: Power output IAE resut comparison of AC and CL-AC for different apha vaues (average RSSI: -82dBm; LSRI: 2s) 62

78 Figure 26: (a) Average number of nodes in the network, (b) average induced deay and (c) average RMSE over time for AC (α=0.1), CL-AC (α=0.9) and AC (α=0.9) (average RSSI: -82dBm; LSRI: 2s) 63

79 5.6 SUMMARY In this chapter, we focus on the objective of reducing the network-induced error (i.e., RMSE and IAE) of a WCS with one physica system, as the LSR changes over time. We demonstrate that network reconfiguration is capabe of achieving this goa. To assess the performance of our proposed network reconfiguration framework with offine and onine parts, a systematic case study is conducted to see the in-depth interaction between the network reconfiguration and the contro. The simuation resuts show that our network imperfection mode is accurate with Pearson correation 0.993, that network reconfiguration works better than the static scheme showing ow error and onger network ifetime. Furthermore, we find that consecutive message osses can degrade the contro system performance, but onine agorithms can compensate for them dynamicay. 64

80 6.0 WORST-CASE END-TO-END DELAY ANALYSIS End-to-end network deay is critica to contro system stabiity in WCS according to our contro system stabiity requirement (Equation (4.1)) and recent research works [Yu et a., 2014; Saifuah et a., 2011, 2015], which require network packets transmitting within a certain contro system deadine to make the contro system stabe. Thus, it is necessary to quantify the worst-case end-to-end network deay, which can be used to test, both at design time and for onine admission contro, whether a set of rea-time transmissions can meet a their deadines. Compared to extensive testing and simuations, anaytica deay bounds are highy desirabe in wireess contro system appications that require rea-time performance guarantees [Saifuah et a., 2011]. As mentioned in Chapter 1, there is no transmission confict during the one-way wireess transmission in WCS if the messages are scheduabe. We quantify the associated worst-case end-to-end deay in Equation (4.6). However, for the two-way wireess transmission, the messages going up wi confict with the messages going down, which induce more deay than the one-way wireess transmission. This chapter focuses on anayzing the worst-case end-to-end deay for the two-way wireess transmission in a WCS. In this chapter, we first introduce the network mode we study. We then anayze the conficts that coud happen during the message transmission and get the scheduabiity condition (the condition that messages can be deivered to the destination within the bounded amount of time) from the anaysis. Based on the scheduaabiity condition, we then compute the worst-case end-to-end deay by cacuating the deay without confict, the maximum number of conficts during one message transmission and maximum time to resove the conficts. To the best of our knowedge, this is the first work that discusses the end-to-end deay anaysis for the network deadine greater than the contro samping period in the rea-time WCS with 65

81 traffic in both directions. 6.1 NETWORK MODEL In this chapter, the network mode we study is the reay region of the network we proposed in Chapter 4 (for the network topoogy pease see Figure 5). Our network mode is shown in Figure 27: there is one primary ine of reay nodes (marked as back) and zero or more ines of backup reay nodes (marked as grey). The reay nodes broadcast messages eve by eve towards the controer, then back to the actuator. Within each eve, the primary node wi broadcast first, then the first, second, and third backup nodes, in order. Therefore, the more reay nodes in the network, the more messages are sent, and thus the higher network deay. Every contro samping period, we assume there is one message containing a the measurement data sent out via the wireess network to the remote controer, which runs the contro agorithm and then sends a message back via the same network again to the actuator. The worst-case end-to-end deay anaysis is the worst-case time deay of any one message from the time it is sent out to the time it is received by the actuator. We aso assume there is no measurement concatenation for measurements sensed from different time steps. We assume that there are n hops from the sensors to the remote controer controer and ines of reay nodes, that is, it takes time sots at each eve to transmit messages (one sot per node). To be reiabe, the controer wi send out dupicate messages to the reay nodes (i.e. takes time sots). We denote the current time sot as t (t = 0, 1, 2,...), the current eve as h (h = 0, 1,..., n), and contro samping period as p. The number of time sots during one samping period is p s = p, where t is the duration of the time sot. Thus, t with the time deay (i.e., sta time) caused by conficting with other messages, d 0 (in terms of the number of time sots), message m 0 sent at time t = 0 up to the controer is at eve h(m 0 ) = t d 0 (0 t d0 < n) and the same message on its way down to the actuator is at eve h(m 0 ) = 2n t d 0 ( n t d0 2n 1). More generay, with the time deay caused by conficting with other messages, d i, a message m i sent out at time t = ip s, (i = 0, 1,...) traveing up is at eve h(m i ) = t d i ip s (0 t di ip s < n) and traveing 66

82 Figure 27: Network mode with one or more ines of reay nodes down is at eve h(m i ) = 2n t d i ip s to denote the time message m i starts conficting with m j. (n t di ip s 2n 1). We aso use tc (m i, m j ) 6.2 CONFLICT ANALYSIS We want to determine the worst-case end-to-end deay for periodic messages in a genera case, when the network deay is greater than the contro samping period (as discussed in Chapter 1). We focus on the deay anaysis for fixed priority scheduing where message transmissions are schedued based on the most recent message first and the odest message first schemes. We ony do our proof based on the most recent message first scheme, given that the derivation for the odest message first scheme first is symmetric, which wi be discussed in Section 6.4. We denote the priority of a message m i as pri(m i ). The deay without conficts for transmitting one message up to the remote controer is n and the same amount of deay for going down. Thus, the deay without confict is 2n. When 2n p s, there wi be no confcts, given that the messages wi go up and down before the next message is sent out. When 2n > p s, the current message m i wi confict with the message m j with higher 67

83 priority (pri(m i ) < pri(m j )) and induce more network deay. In this section, we wi do the confict anaysis of the message transmission. (a) (b) (c) (d) Figure 28: (a) (b) (c) confict situation and (d) no confict situation A node cannot both transmit and receive in the same time sot and two transmissions that have the same intended receiver interfere each other. If two transmissions are conficting, they cannot be schedued in the same sot, which induces more time deay to the ower-priority transmission. There are three canonica situations that two messages wi confict with each other. As usua in wireess networks, conficts arise when simutaneous transmissions arrive at the same node. The three scenarios are shown as confict situations 1, 2 and 3 in Figure 28(a), 28(b) and 28(c), respectivey, for a singe ine of reay nodes (no backups). Confict situation 1 shows the scenario when a message going up is at a ower eve than the other message going down. Confict situation 2 and 3 show the scenarios when two messages are going in the same direction but very cose together. But for the situation shown in 28(d), when the message going up is at a higher eve than the message going down, there is no 68

84 confict (even though the eve difference is 1), since their receivers are separated apart. Thus, the two messages start to confict at the eve difference, h is 1 or 2, ony under the three confict situations. When the h 3, the two messages wi not confict with each other, since it is not possibe that one receiver istening to the messages coming from more than one transmitters at the same time. (a) (b) Figure 29: The conficts of m i when the eve difference with m i+j is 5 (a) and 4 (b) For confict situation 1, when the h = 1, it wi take 2 time sots to resove the confict, given that the high-priority message wi go up two eves whie the ow-priority message waits. At this time the confict is resoved. Simiary, when the h = 2, the confict wi be resoved in 3 time sots. In genera, when message m i starts going down, the eve difference between m i and m i+j, h(m i, m i+j ) can be odd or even. When h(m i, m i+j ) = h(m i ) h(m i+j ) is odd (as shown in Figure 29(a)), each of the two messages wi make progress on one eve at a time, unti they are separated by exacty 1 eve, at which time the confict happens and wi be resoved in 2 time sots. Simiary, when h(m i, m i+j ) is even (as shown in Figure 69

85 29(b)), they wi make progress unti they are separated by exacty 2 eves, at which time the confict happens and wi be resoved in 3 time sots. For confict situations 2 and 3, it wi take 4 or 5 time sots to resove the confict, when the eve difference is 1 or 2, respectivey. Let us consider consecutive messages, m 0, m 1, m 2,..., m i that are sent at t = 0, t = p s, t = 2p s,..., t = ip s, respectivey. Since we appy the most recent message first message priority scheduing scheme, where pri(m 0 ) < pri(m 1 ) <... < pri(m i ). We define eve separation of two messages m i and m i+j, s(m i, m i+j ) as the number of eves m i+j needs to go through to be at the same eve and in the same direction of m i if m i stays sti. The eve separation of two consecutive messages before any conficts is s(m i, m i+1 ) = p s, which describes how separated the two consecutive messages are. Intuitivey, the more p s, the fewer conficts wi happen. Note that eve separation is different from eve difference of two messages, when two messages go in opposite directions (e.g., if there are 5 hops in the network and m i is going down at eve 4 and m j is going up at eve 0, h(m i, m j ) = 4 and s(m i, m j ) = 6). Reca that if p s 2n, there wi be no conficts, given that the message wi go up and down before the next message is sent out. Thus, three cases under the condition of 2n > p s are discussed in the foowing sections: (1) p s 2, (2) 3 ps 4 and (3) 5. ps Confict Anaysis for Case p s 2 Lemma When p s 2, no message can be deivered to the destination. Proof. For the base case of m 0 and m 1, when both m 0 and m 1 go up, their eves are h(m 0 ) = t and h(m1 ) = t p s ( t < n), respectivey. The eve difference of m0 and m 1 is h(m 0, m 1 ) = p s 2. Confict situation 2 happens, since m0 and m 1 are separated by ess than 3 eves. At time t = p s, h(m 0 ) = p s, m1 is sent out, and m 0 needs to wait unti m 1 is at eve h(m 1 ) = p s + 3 at time t = ps + 3. However, at time t = 2p s < p s + 3 (i.e., before the confict of m 0 and m 1 is resoved), m 2 wi be transmitted and aso bock m 1. Since the confict of m 0 and m 1 cannot be resoved, m 0 wi never move past eve p s. In genera, the situation of any two consecutive messages m i and m i+1 is simiar to 70

86 the situation of m 0 and m 1, where at time t = (i + 1)p s, m i+1 wi start transmission and interrupt m i at eve p s, creating a chain reaction. Therefore, a messages wi be bocked by messages with higher priority and no message can be deivered to the destination. Since a messages are bocked at eve p s when going up, we do not need to consider conficts situation 1 and 3 because they wi never occur if p s Confict Anaysis for Case 3 p s 4 Lemma When 3 p s 4, no message can be deivered to the destination. (a) (b) Figure 30: Confict situation when p s = 4: (a) m0 starts conficting with m 1 and (b) the confict is resoved in 7 time sots if the subsequent messages do not exist Proof. Let us first consider the best case (the argest separation between two consecutive messages): p s = 4. For the base case, when both m 0 and m 1 go up ( t 71 < n), h(m0, m 1 ) = p s 3 with

87 no confict. When m 0 is aready going down ( t n) and m1 is sti going up ( t p s < n), h(m 0, m 1 ) = 2n t t ps 2n 2 t + ps ps = 4. Let us consider the best case (the argest separation of m 0 and m 1 ) with h(m 0, m 1 ) = 4. As shown in Figure 30(a), the confict happens when h(m 0 ) = n 1 on the way down (grey arrow represents m 0 ) and h(m 1 ) = n 3 on the way up (back arrow represents m 1 ). As shown in Figure 30(b), the confict invoves confict situations 1 and 3: (1) during the confict situation 1, m 0 is bocked by m 1, whie m 1 goes up to the remote controer; (2) when m 1 reaches remote controer, the confict becomes confict situation 3 and is resoved unti m 1 reaches eve n 3. So the confict is resoved in 7 time sots if m 2 and the foowing messages do not exist. However, after 4 sots of the confict of m 0 and m 1, where m 1 is on the way down at eve n 1, m 1 wi confict with m 2 (ike the situation in Figure 30(a)) and the previous confict of m 0 and m 1 wi never be resoved. m 0 wi be bocked at eve n 1 forever. For genera case of m i and m i+1, when m i goes down, h(m i ) = 2n t ip s ( t ips n); and when m i+1 goes up, h(m i+1 ) = t (i+1)ps ( t (i+1)ps < n). Since h(m i, m i+1 ) = 2n t ip s t (i+1)ps 2n 2 t ip s + ps 4, with the best case of the argest eve difference of 4, m i wi confict with m i+1 as the same situation of m 0 and m 1 above. After 4 of the confict of m i and m i+1 (the confict takes 7 to resove), m i+1 conficts with m i+2, and the confict of m i and m i+1 cannot be resoved. Therefore, a the messages wi be bocked by higher priority messages at eve n 1 with p s = 4. Ceary, if the best case of p s = 4 causes indefinite bocking, the case of ps = 3 wi come to the same concusion Confict Anaysis for Case p s 5 We consider two cases for p s 5: the case of odd vaue of ps in Lemma and the case of even vaue of p s in Lemma Lemma When p s 5, a messages wi be deivered, if ps is odd. Proof. We prove this Lemma by showing that it is true for the worst case (smaest separation of two consecutive messages) when p s is odd, that is, p s = 5. We show the Lemma is true 72

88 Figure 31: The cacuation process of eve separations with higher priority messages of m 0 and m 1, when ps = 5 for the base case of m 0 and m 1, and then generaize to any two consecutive messages, m i and m i+1. There are three cases: (1) When both m 0 and m 1 go up ( t there is no confict. t < n), h(m0, m 1 ) = t t ps = p s = 5 3, (2) When m 0 goes down ( t n) and m1 goes up ( t p s < n), h(m0, m 1 ) = 2n t ps = 2n 2 t + p s. The confict ony invoves the confict situation 1. Since we are deaing with the case of ps = 5, which means eve separation is odd, so is h(m 0, m 1 ), the confict happens with h(m 0, m 1 ) = 1 and can be resoved in 2 time sots. By soving h(m 0, m 1 ) = 2n 2 t + p s = 1, we get t = n + 2. After this confict, m0 stays at the same eve as the confict before (staed), h(m 0 ) = 2n t = n 2; m1 goes up 2 eves and h(m 1 ) = t p s + 2 = n 1. Athough the eve difference is 1, m0 and m 1 are in the situation shown in Figure 28(d), there is no more confict between m 0 and m 1. Figure 31 shows the eve separation of m 0 and m 1 is 5 to start with (before confict), going down to 3, after the confict (because m 1 advances 2 eves whie m 0 stas). 73

89 Tabe 3: The tota stas of m 0 and m 1 (i.e., d 0 and d 1 ) when m 0 and m 1 confict with higher priority messages ( ps = 5) m 1 m 2 m 3... m j m 0 2 (2 + 3) ( ) 2 + 3(j 1) m 1-2 (2 + 3) 2 + 3(j 2) (3) When both m 0 and m 1 go down, m 0 and m 1 wi confict with higher priority messages, m 2, m 3,... m j. These conficts invove the confict situation 1, given that m 2, m 3,..., m j are going up. For both m 0 and m 1, ony the first confict starts with an odd eve separation (for m 0 see case (2) above) and the rest of conficts are a even. Therefore, as shown in Figure 31, conficts after the first confict are resoved in 3 time sots. A simiar process can be foowed for m 1. Tabe 3 shows the tota stas in terms of the number of time sots when m 0 and m 1 confict with m 2, m 3,..., m j under the condition ps = 5. In addition to confict situation 1, we aso need to consider confict situation 3, given that when both m 0 and m 1 go down and m 0 is ahead of m 1, m 0 wi sta first given the confict, causing m 1 to approach m 0, further causing situation 3 confict. Beow, we discuss three subcases to show how these conficts are resoved: (3A) m 0 and m 1 conficting with m 2, (3B) m 0 and m 1 conficting with m 3 and (3C) m 0 and m 1 conficting with m j (j 2). Case 3A: m 0 and m 1 confict with m 2. During the confict of m 0 with m 2, m 0 wi go down 1 eve, and during the confict of m 1 with m 2, m 1 wi go down 2 eves, as foows. The eve of m 0, m 1 and m 2 is h(m 0 ) = 2n t 2 (as shown in Tabe 3, d0 = 2 due to the confict with m 1 ), h(m 1 ) = 2n t p s and h(m2 ) = t 2p s, respectivey. When m0 starts conficting with m 2, h(m 0, m 2 ) = 2n t 2 t 2ps = 2, and we get t = n + p s, so t c (m 0, m 2 ) = n + p s (as mentioned earier, it is the time m 0 and m 2 starts conficting) and h(m 0 ) = 2n t 2 = 2n t + 2 = n p s + 2. When m 1 starts conficting with m 2, h(m 1, m 2 ) = 2n t p s t 2ps = 1, and we get t ps = n + 1 p s 1, 2 2 so t c (m 1, m 2 ) = n p s 1 2 and h(m 1) = 2n t p s 74 = n 1 p s + 1. Given that 2 2

90 h(m 1, m 0 ) = n 1 p s + 1 ps (n + 2) = 1 p s = 1 < 3 (i.e., the eve difference between m 0 and m 1 when m 0 and m 1 start conficting with m 2 ), m 0 and m 1 wi confict again with each other (this time under confict situation 3). To expain how ong m 0 gets staed before m 1 starts its confict with m 2, we turn to Figure 32, which shows the sta time of m 0 from I 0 to I 2 and m 1 from I 2 to I 3. The ength of I 0, I 1, I 2 and I 3 is, the time to transmit a message for one eve. Since m 0 stas for 3 and t c (m 1, m 2 ) t c (m 0, m 2 ) = 1 2 p s 1 2 = 2, the overap of m 0 and m 2 is, that is, I 2. During I 0 to I 1, m 0 conficts with m 2 (and stas), whie m 1 keeps going down 2 eves and m 2 goes up 2 eves. During I 2, both m 0 and m 1 confict with m 2 and ony m 2 (highest priority) goes up 1 eve. During I 3, m 1 conficts with m 2, aowing m 0 to go down 1 eve and m 2 to go up 1 eve. m 0 and m 1 wi not confict with m 3, since during I 3 ( t = n + p s m 1 and m 3 is h(m 0 ) = n ps + 2, h(m 1 ) = n 1 p s and h(m 3) = t 3p s + 3), the eve of m 0, = t 3p s = n 2ps + 3, respectivey, with h(m 0, m 3 ) = 4 and h(m 1, m 3 ) = 5 both greater than 3. From I 0 to I 2, the eve of m 0 and m 1 are both higher than their eves during I 3 and the eve of m 3 is ower than its eve of I 3. Since there is no confict with m 3 during I 3, there is no confict from I 0 to I 2. Thus, m 0 and m 1 wi not confict with m 3 and wi not confict with other messages (i.e., higher priority messages of m 3 ) either during I 0 to I 3. Figure 32: The sta time for m 0 (ower segments) and m 1 (upper segments), when conficting with m 2 75

91 Case 3B: m 0 and m 1 confict with m 3. m 0 and m 1 wi not be competey bocked during the conficts with m 3 : m 0 and m 1 wi both go down for 1 eve. The eve of m 0, m 1 and m 3 is h(m 0 ) = 2n t 5 (as shown in Tabe 3, d0 = 5 due to the conficts with m 1 and m 2 ), h(m 1 ) = 2n t p s 2 (as shown in Tabe 3, d1 = 2 due to the conficts with m 2 ) and h(m 3 ) = t 3p s, respectivey. When m0 starts conficting with m 3, h(m 0, m 3 ) = 2n t 5 t 3ps = 2, and we get t = n + 3 p s + 3, so t 2 2 c(m 0, m 3 ) = n + 3p 2 s and h(m 0 ) = 2n t 5 = 2n t + 5 = n 3 p s + 7. When m starts conficting with m 3, h(m 1, m 3 ) = 2n t p s 2 t 3ps = 2, and we get t ps = n + ps, so t c (m 1, m 3 ) = n + 2p s and h(m 1 ) = 2n t p s 2 h(m 1, m 0 ) = 1 p s 2 = 2n t ps + 2 = n p s + 2. Thus, 3 2 = 1 > 3, which means m 0 and m 1 have confict (confict situation 3). The start conficting time difference is t c (m 1, m 3 ) t c (m 0, m 3 ) = 1p 2 s 3 =. Figure 33 2 iustrates the sta intervas for m 0 conficting with m 1 and m 3. During I 0, m 0 conficts with m 1 and m 3, aowing both m 1 and m 3 to go down and up for 1 eve, respectivey. During I 1 to I 2, m 0 conficts with m 1 and m 3, and m 1 conficts with m 0 and m 3, aowing ony m 3 to go up 2 eves. During I 3, m 1 conficts with m 0 and m 3, aowing m 0 to go down for 1 eve and m 3 to go up 1 eve. Even though m 0 and m 1 confict, each gets a chance to move further by 1 eve when the other one is staed with m 3. Simiar to case 3A, m 4 cannot confict with m 0 and m 1 during the confict from I 0 to I 3. Since during I 3 ( t = n + 3 p s + 9), the eve of m 2 2 0, m 1 and m 4 is h(m 0 ) = n 3 p s + 7, 2 2 h(m 1 ) = n ps + 2 and h(m 4 ) = n 5 p s , respectivey, with h(m 0, m 4 ) = 4 and h(m 1, m 4 ) = 5 both greater than 3, m 4 wi not confict with m 0 and m 1 during I 3. Therefore, m 4 wi not confict with any messages from I 0 to I 3 and thus no confict of m 1, m 2 with other messages (i.e., the higher priority messages of m 4 ) aso. Case 3C: m 0 and m 1 confict with m j (j 2). m 0 and m 1 wi not be competey bocked during the confict and can both go down 1 eve. The eve of m 0, m 1 and m j is h(m 0 ) = 2n t (2+3(j 2)) (as shown in Tabe 3, d 0 = (2+3(j 2)) due to the conficts with m 0, m 1,..., m j 1 ), h(m 1 ) = 2n t ps (2+3(j 3)) (as shown in Tabe 3, d 1 = (2 + 3(j 3)) due to the conficts with m 1,..., m j 1 ) and h(m j ) = t jp s, respectivey. In genera, when m 0 starts conficting with m j, h(m 0, m j ) = 2n t (2+3(j 2)) t jp s = 2, and we get t = n + 3 (j 2) + j p s, so t 2 2 c(m 0, m j ) = n + 3(j 2) + j p 2 2 s and h(m 0 ) = 76

92 Figure 33: The sta time for m 0 (ower segments) and m 1 (upper segments), when conficting with m 3 2n t (2+3(j 2)) = 2n t + (2 + 3(j 2)) = n j p s + 3(j 2) + 2. When m starts conficting with m j, h(m 1, m j ) = 2n t ps (2+3(j 3)) t jp = 2, and we get t p s = n + 3 (j 3) + 1 (j 1)ps, so t 2 2 c (m 1, m j ) = n + 3(j 3) + j p 2 2 s + 1p 2 s and h(m 1 ) = 2n t ps (2+3(j 3)) = 2n t p s + (2 + 3(j 3)) = n 1 ps (j 1) (j 3). 2 2 Thus, h(m 1, m 0 ) = 1 p s 3 = 1 and m and m 1 are sti conficting with each other. The start confict time difference is t c (m 1, m j ) t c (m 0, m j ) = 1p 2 s 3 =. The sta time for 2 both m 0 and m 1 is the same as Figure 33: during the confict, m 1 can go down 1 eve during I 0 ; and m 0 can go down 1 eve during I 3. Aso, m j+1 wi not confict with confict with m 0 and m 1 from I 0 to I 3. Since during I 3 ( t = n + 3 j + j p s ), the eve of m 2 2 0, m 1 and m 4 is h(m 0 ) = n j p s 2 h(m j+1 ) = n j ( j 2 + 3(j 2) + 2, h(m 2 1) = n 1 ps (j 1) (j 3) and 2 + 1) ps, respectivey. With h(m 0, m j+1 ) = 4 and h(m 1, m j+1 ) = 5, m j+1 and other higher priority messages wi not confict with m 0 and m 1 from I 0 to I 3. This pattern wi repeat itsef indefinitey in the worst case. No deay caused by the confict of m 0 and m 1 for Case 3A, 3B and 3C According to the Case 3A, Case 3B and Case 3C, m 0 and m 1 aways confict with each other. However, the confict does not induce more deay is because the duration between the start time of the confict of m 0 with m j (j 2) and the start time of the confict of m 0 with m j+1 is t c (m 0, m j+1 ) t c (m 0, m j ) = n + 3 j+1 (j 1) + p 2 2 s (n + 3(j 2) + j p 2 2 s) = 3 + 1p 2 2 s = 4. 77

93 Figure 34: The sta time for m 0 (ower segments) and m 1 (upper segments), when conficting with m j and m j+1 As shown in Figure 34, the duration between the start time of the two conficts equas to the duration of the conficts among m 0, m 1 and m j, which means that the new confict of m 0 and m j+1 starts when the conficts among m 0, m 1 and m j finishes. There is no rest time between the conficts among m 0, m 1 and m j and the conficts among m 0, m 1 and m j+1. So, the confict of m 0 and m 1 aways happen during the conficts with other higher priority messages and wi not induce more sta time aone. For any two consecutive messages, m i and m i+1, we can show the message progress, simiar to the process above. Conficts aways happen when the ower priority messages are going down (confict situation 1). Even though the two messages going down confict with each other (confict situation 3), each gets a chance to make progress when the other one is staed due to the conficts with higher priority messages; both messages finay can reach to the destination. The proof above is for the worst case for odd separation ( ps = 5). Outside the worst case, the message density is ower, and therefore fewer conficts and stas wi happen, which comes to the same concusion. Lemma When p s, a messages wi be deivered, if ps is even 78

94 Figure 35: The cacuation process of eve separations with higher priority messages for m 0 and m 1, when ps = 6 Proof. Simiar to odd vaue of p s 5, we first consider the worst case of the smaest separation of two consecutive messages when p s is even, p s = 6. We show the emma is true for the base case of m 0 and m 1, and then generaize to any two consecutive messages, m i and m i+1. There are three cases: (1) When both m 0 and m 1 go up ( t there is no confict. t < n), h(m0, m 1 ) = t t ps = p s = 6 > 3, (2) When m 0 goes down ( t n) and m1 goes up ( t p s < n), h(m0, m 1 ) = 2n t ps = 2n 2 t + p s ps. The confict ony invoves the confict situation 1. Since = 6 is even ( h(m 0, m 1 ) is even), the confict happens with h(m 0, m 1 ) = 2 and can be resoved in 3 time sots. By soving h(m 0, m 1 ) = 2n 2 t + p s = 2, we get t = n + 2. After this confict, m 0 stays at the same eve as the confict before (staed), h(m 0 ) = 2n t = n 2; m 1 goes up 2 eves and h(m 1 ) = t p s + 3 = n 1. Athough the eve difference is 1, m 0 and m 1 are in the situation shown in Figure 28(d), there is no more confict between m 0 and m 1. Figure 35 shows that the eve separation of m 0 and m 1 is 6 to start with (before 79

95 Tabe 4: The tota stas of m 0 and m 1 (i.e., d 0 and d 1 ) when m 0 and m 1 confict with higher priority messages ( ps = 6) m 1 m 2 m 3... m j m 0 3 (3 + 2) ( ) 3 + 2(j 1) m 1-3 (3 + 2) 3 + 2(j 2) confict), going down to 3, after the confict (because m 1 advances 3 eves whie m 0 stas). (3) Simiar to the case of ps = 5, when both m 0 and m 1 go down, both m 0 and m 1 wi confict with higher priority messages, m 2, m 3,..., m j. These conficts invove the confict situation 1, given that m 2, m 3,..., m j go up. For both m 0 and m 1, ony the first confict starts with an even eve separation (for m 0 see case (2) above) and the rest of conficts are a odd. Therefore, as shown in Figure 35, conficts after the first confict are resoved in 2 time sots. A simiar process can be foowed for m 1. Tabe 4 shows the tota stas in terms of the number of time sots when m 0 and m 1 confict with m 2, m 3,..., m j under the condition ps = 6. Beow, we separate this into three subcases to show how these conficts are resoved: (3A) m 0 and m 1 conficting with m 2, (3B) m 0 and m 1 conficting with m 3 and (3C) m 0 and m 1 conficting with m j. Case 3A: m 0 and m 1 confict with m 2. m 0 and m 1 wi not be competey bocked during the conficts with m 2 : m 0 wi go down for 2 eves, and m 1 wi go down for 1 eve. The eve of m 0, m 1 and m 2 is h(m 0 ) = 2n t 3 (as shown in Tabe 4, d0 = 3 due to the confict with m 1 ), h(m 1 ) = 2n t p s and h(m2 ) = t 2p s, respectivey. When m0 starts conficting with m 2, h(m 0, m 2 ) = 2n t 3 n + p s + and h(m 0 ) = 2n t 3 with m 2, h(m 1, m 2 ) = 2n t p s t c (m 1, m 2 ) = n p and h(m 1) = 2n t p s t 2ps = 1, and we get t = n+ ps +1, so tc (m 0, m 2 ) = = 2n t + 3 = n p s + 2. When m 1 starts conficting t 2ps = 2, and we get t ps = n + 1 ps 2 1, so = n 1 p s + 1. h(m 2 1, m 0 ) = 1 p s 1 = 2, 2 which means m 0 and m 1 wi confict again (confict situation 3) with each other given that m 0 got staed before m 1 conficts with m 2. t c (m 1, m 2 ) t c (m 0, m 2 ) = 1 2 p s 2 =. Figure 80

96 Figure 36: The sta time for m 0 (ower segments) and m 1 (upper segments), when conficting with m 2 36 represents the sta time for m 0 and m 1. During I 0, m 0 conficts with m 2 (and stas), whie m 1 keeps going down for 1 eve and m 2 goes up for 1 eve. During I 1, m 0 conficts with both m 1 and m 2 ; m 1 conficts with m 2 ; ony m 2 (the highest priority message) goes up 1 eve. During I 2 to I 3, m 1 conficts with m 2, aowing m 0 to go down 2 eves and m 2 to go up 2 eves. m 0 and m 1 wi not confict with m 3, since during I 3 ( t m 1 and m 3 is h(m 0 ) = n ps + 2, h(m 1 ) = n 1 p s 2 = n+ ps +4), the eve of m0, = t 3p s = + 1 and h(m 3 ) = t 3p s n 2ps + 4, respectivey, with h(m 0, m 3 ) = 4 and h(m 1, m 3 ) = 6 both greater than 3, m 3 wi not confict with m 0 and m 1. Thus, m 3 and its other higher priority messages wi not confict with m 0 and m 1 during I 0 to I 3 (see Figure 36). Case 3B: m 0 and m 1 confict with m 3. m 0 and m 1 wi not be bocked during the conficts with m 3 : m 0 wi go down for 2 eves, and m 1 wi go down for 2 eves. The eve of m 0, m 1 and m 3 is h(m 0 ) = 2n t 5 (as shown in Tabe 4, d0 = 5 due to the conficts with m 1 and m 2 ), h(m 1 ) = 2n t p s 3 (as shown in Tabe 4, d1 = 3 due to the confict with m 2 ) and h(m 3 ) = t 3p s, respectivey. When m0 starts conficting with m 3, h(m 0, m 3 ) = 2n t 5 t 3ps = 1, and we get t = n + 3 ps 2 + 2, so t c (m 0, m 3 ) = n+ 3p 2 s+2 and h(m 0 ) = 2n t 5 = 2n t +5 = n 3 p s +3. When m 2 1 starts conficting with m 3, h(m 1, m 3 ) = 2n t p s 3 t 3ps = 1 and get t ps = n+ ps +1, 81

97 Figure 37: The sta time for m 0 (ower segments) and m 1 (upper segments), when conficting with m 3 so t c (m 1, m 3 ) = n+2p s + and h(m 1 ) = 2n t p s 3 = 2n t ps +3 = n p s +2. The eve difference between m 1 and m 0 is h(m 1, m 0 ) = 1 p s 1 = 2, which means m 2 0 and m 1 confict with each other again. The start conficting time difference is t c (m 1, m 3 ) t c (m 0, m 3 ) = 1 p 2 s = 2. Figure 37 iustrates sta intervas for m 0 and m 1. During I 0 to I 1, m 0 conficts with m 3, aowing both m 1 and m 3 to go down and up for 2 eves, respectivey. During I 2 to I 3, m 1 conficts with m 0 and m 3, aowing both m 0 and m 3 to go down and up for 2 eves, respectivey. Even though m 0 and m 1 confict, each can move further by 2 eves when the other one conficts with m 3. Simiar to case 3A, m 4 cannot confict with m 0 and m 1 during the confict from I 0 to I 3 in Figure 37. Since during I 3 ( t = n + 3 ps 2 + 5), the eve of m0, m 1 and m 4 is h(m 0 ) = n 3 p s 2 + 3, h(m 1 ) = n ps + 2 and h(m 4 ) = n 5 p s 2 + 5, respectivey, with h(m 0, m 4 ) = 4 and h(m 1, m 4 ) = 6 both greater than 3, m 4 wi not confict with m 0 and m 1. Therefore, m 4 and its other higher priority messages wi not confict with any messages from I 0 to I 3. Case 3C: m 0 and m 1 confict with m j (j 2). m 0 and m 1 wi not be bocked during the confict and can go down by 2 eves. The eve of m 0, m 1 and m j is h(m 0 ) = 2n t (3+2(j 2)) (as shown in Tabe 4, d 0 = (3 + 2(j 2)) due to the conficts with m 1, m 2,..., m j 1 ), h(m 1 ) = 2n t ps (3+2(j 3)) (as shown in Tabe 4, d 1 = (3 + 2(j 3)) due 82

98 to the conficts with m 2,..., m j 1 ) and h(m j ) = t jp s, respectivey. In genera, when m 0 starts conficting with m j, h(m 0, m j ) = 2n t (3+2(j 2)) t jp s = 1, and we get t = n+ j ps 2 +j 1, so tc (m 0, m j ) = n+ j p 2 s +(j 1) and h(m 0 ) = 2n t (3+2(j 2)) = 2n t + (3 + 2(j 2)) = n j p s + j. When m 2 1 starts conficting with m j, h(m 1, m j ) = 2n t ps (3+2(j 3)) t jp = 1, and we get t ps = n+ j 1 ps 2 +j 2, so tc (m 1, m j ) = n + j+1 p 2 s + (j 2) and h(m 1 ) = 2n t ps (3+2(j 3)) = 2n t p s + (3 + 2(j 3)) = n 1 ps (j 1) + j 1. The eve difference between m 2 1 and m 0 is h(m 1, m 0 ) = 1 p s 1 = 2, 2 which means m 0 and m 1 wi confict again (confict situation 3). The start confict time difference is t c (m 1, m j ) t c (m 0, m j ) = 1 2 p s = 2. The sta time for both m 0 and m j is the same as Figure 37: during the confict, m 1 can go down for 2 eves during I 0 to I 1 ; and m 0 can go down for 2 eves during I 2 and I 3. j 2 ps Aso, m j+1 wi not confict with m 0 and m 1 from I 0 to I 3. Since during I 3 ( t = n + +j+2), the eve of m0, m 1 and m 4 is h(m 0 ) = n j p s +j, h(m 2 1) = n 1 ps (j 1) +j 1 2 and h(m j+1 ) = n ( j 2 + 1) ps + j + 2, with h(m 0, m j+1 ) = 4 and h(m 1, m j+1 ) = 6, m j+1 and its higher priority messages wi not confict with m 0 and m 1 from I 0 to I 3. This pattern wi repeat itsef indefinitey in the worst case. Simiar to the reason of the genera case of ps = 5, there is no deay caused by the confict of m 0 and m 1 for Case 3A, 3B and 3C above. For any two consecutive messages, m i and m i+1, even though they confict with each other during the downside transmission, each gets a chance to make progress and finay reaches to the destination. The proof above is for the worst case of ps obviousy come to the same concusion. = 6. For the other even vaues of p s wi 6.3 WORST-CASE END-TO-END DELAY DETERMINATION Based on Lemmas 6.2.1, 6.2.2, and 6.2.4, we have the message scheduabiity condition: 5. We assume that a message aready conficted with (Q 1) higher priority messages. ps The upper-bound of the tota stas is 3(Q 1) (given that each confict can be resoved in 83

99 at most 3 time sots for confict situation 1). The foowing formua shows the difference in eves between m i and m Q+i, which is h(m i, m Q+i ); if that vaue is 1 or 2, the Q th confict wi happen: t ips 3(Q 1) t ips Qp s 1 h(m i, m Q+i ) = 2n 2 (6.1) Based on properties of the foor operation, we can get Then, t ips t ips Qps 1 2n + 3(Q 1) + 1 h(m i, m Q+i ) t ip t ips Qps 2n + 3(Q 1) + 2 Therefore, we get: t ips t ips Qps 2n + 3(Q 1) + = 2 (6.2) t ips = n (Q 1) + 1 Qp 1 (6.3) 2 Since the conficts happen ony when a message is transmitted down, the foowing condition hods about the eve of message m i : n t 3(Q 1) ips 2n 1, so n + 3(Q 1) t ips 2n 1 + 3(Q 1). Put the Equation (6.3) into the above condition, we get Q 2n 3 2n 3 p s 3 and derive the maximum Q as p s 3. After cacuating the maximum 3 p s number of conficts, we can estimate the worst-case stas in terms of the number of time sots caused by conficts, D confict = 3Q = 3. Recaing that the deay without 2n 3 p s 3 confict, D pure = 2n, the worst-case end-to-end deay in terms of the number of time sots is 2n 3 D sots = D pure + D confict = 2n + 3 p s 3 To determine the worst-case end-to-end deay, we mutipy D sots by t, and obtain D network = (2n + 3 ) t. 2n 3 p s 3 (6.4) 84

100 Tabe 5: Simuation parameters and vaues parameters vaues p 0.05s, 0.1s, 0.15s, 0.2s, 0.25s, 0.3s p s 5, 10, 15, 20, 25, 30 1, 2, 3, 4 n 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, WORST-CASE END-TO-END DELAY ANALYSIS VALIDATION To vaidate our worst-case end-to-end deay anaysis, we impement a simuation to simuate the process of the dynamic message transmission. Reca that the scheduabiity condition ( p s 5) is to determine whether a message can be deivered to the destination within a imited amount of time. We carried out a set of tests on our simuation with different vaues of p, and n, as shown in Tabe 5, where each test corresponds to a vaue of p, and n. Our test set can be divided into two test sets, test set 1, where a the tests meet the condition and test set 2 where a the tests do not meet the condition. We test the scheduabiity condition on the test set and cacuate the test accuracy by summing the percentage of the tests that can deiver the messages within a imited amount of time for test set 1 and the percentage of the tests that cannot deiver the messages within a imited amount of time for test set 2. We get 100% accuracy for the scheduabiity condition test, demonstrating the correctness of our scheduabiity condition. Under the test set 2, the worst-case deay anaysis overestimates the deay by 4.2% compared with the reaistic simuation resuts (aways pessimistic, but a very tight pessimism). Figure 38 shows the exampes of message transmission process of the most recent message first (Figure 38(a)) and the odest message first scheduing schemes (Figure 38(b)) with p = 0.1s, p s = 10, = 2 and n = 10. For the most recent message first scheme, as discussed above and shown in Figure 38(a), the ower priority messages confict with higher priority 85

101 (a) (b) Figure 38: Exampes of (a) the most recent message first scheme and (b) the odest message first scheme transmission process with p = 0.1s, p s = 10, = 2 and n = 10. Note that the symmetry of the odest message first scheduing scheme with the most recent message first scheduing scheme begins at the 275 th time sots. 86

102 messages and are deayed when traveing down. As anayzed in Section 6.2, when a message traveing down, it is deayed at every eve starting with eve n 2 (eve 8 in this exampe) but can sti move down by 1 eve unti it reaches to the destination. Regardess, they sti arrive at the controer within the deadines, because the condition p s 5 is satisfied. For the odest message first, as shown in Figure 38(b), the conficts happen when ower priority messages (ater messages) traveing up. The message transmissions are unstabe 1 at first. It is because for the first few messages, there are not many higher priority messages ahead, so the deay is ess than the ater ower priority messages. The transmissions get stabe 2 after the 275 time sots and the transmission process is symmetric with the most recent message first scheme. Thus, the proof process for the odest message first scheme is exacty the same as the most recent message first scheme, that is, starting with the first two owest priority messages, which are the ast two messages for the odest message first scheme. Note that if the scheduabiity condition is not met, the odest message first scheme wi be aways unstabe, but can sti deivery messages to the destination which is different from the most recent message first scheme. However, the end-to-end network deay is unbounded (becomes arger and arger), since more and more conficts are accumuated to be unresoved. 6.5 SUMMARY In this chapter, we carried out the worst-case end-to-end deay anaysis for the two-way wireess transmission in a WCS with one singe physica system. From the transmission confict anaysis, we get the scheduabiity condition, 5. Based on the condition, we cacuate the maximum number of conficts during one message transmission as 2n 3 p s 3. With the maximum number of conficts, we derive the worst-case end-to-end deay as D network = (2n + 3 ) t. The simuation resuts show 100% accuracy for 2n 3 p s 3 the scheduabiity condition test. ps With the scheduabity condition satisfied, the simuation resuts show that our end-to-end deay anaysis is accurate within 4.2% of the reaistic 1 It is not the stabiity concept as mentioned for the contro system. Unstabe means the end-to-end deays of the messages are not the same. 2 The end-to-end deays of the messages are the same. 87

103 simuation resuts (aways pessimistic, but a very tight pessimism). 88

104 7.0 DYNAMIC PACKET ASSIGNMENT FOR WCS WITH MULTIPLE PHYSICAL SYSTEMS In Chapter 5, we introduce the network-induced error reduction for a WCS with one singe physica system. However, the situation of mutipe physica systems utiizing one shared wireess network wi be common, especiay in IoT (Internet of Things) systems and IIoT (Industria IoT). It is necessary to study the contro system performance improvement for a WCS with mutipe physica systems, which is the focus of this chapter. To the best of our knowedge, it is the first study on dynamic packet assignment for a WCS with mutipe physica systems. 7.1 INTRODUCTION We consider a WCS of mutipe contro systems with one shared wireess network, controed by a centraized remote controer. In a shared network, a rea-time wireess network typicay has mutipe network paths 1 to transmit messages in parae (some paths may have redundancy). Each path may have different characteristic in terms of deay and reiabiity (e.g., in WireessHart Protoco [wir, 2007], one can choose between more reiabe and higher deay and ower deay but ess reiabe paths, which refer to graph routing and source routing, respectivey). Aso, different contro systems may have different appication demands. For exampe, one contro system has urgent demand, such as reducing temperature by 10 C within 10 minutes in a room whie another system has ess urgent demand, such as increasing 1 The network paths can be physicay separated or frequency separated (transmit messages in different channes) 89

105 Figure 39: Contro system power reference functions with contro samping period of 0.2s the temperature by 2 C within one hour. Our soution foows our intuition: to get better overa contro system performance, we shoud assign the messages of the contro system with the urgent demand to fast and reiabe paths and assign the messages with the ess urgent demand to sower or ess reiabe paths. To test our intuition, we simuate a PHX system in Simuink. Figure 39 shows 8 different reference functions (ramp functions) of a PHX when the controer decides to reduce the output power from 42MW to 32MW within different amount of time. For exampe, ramp30 means to reduce the power from 42MW to 32MW within 30s. The contro system appication demand urgency order of the 8 reference functions is ramp15 > ramp30 > ramp45 > ramp60 > ramp75 > ramp90 > ramp105 > ramp120. To motivate how important packet oss and deay are to different contro system appication demands, we inject packet osses and time deay into the PHX system. We assume in this chapter the DR from measurement sensors to the remote controer (i.e., sensing) is the same as the DR from the remote controer to the actuator (i.e., actuation), since we appy the same network routing scheme for both sensing and actuation in this dissertation. We inject random packet drop with the same probabiity of (1-DR) and inject the same deay for both sensing and actuation. Note that the DR in this chapter refers to the haf-way network reiabiity (i.e., sensing or actuation), but the network deay refers to the tota deay for both sensing and actuation. We measure system performance through power RMSE (the same 90

106 Power output RMSE (MW) ramp15 ramp30 ramp45 deay=0.2s deay=0.4s deay=0.6s ramp60 ramp75 Reference functions ramp90 ramp105 ramp120 Figure 40: Power output RMSE for different reference functions with different network deays for a singe PHX (DR=0.9; random packet drop with probabiity of 0.1 for sensing and actuation, respectivey) Power output RMSE (MW) deay=0.2s deay=0.4s deay=0.6s DR Figure 41: Power output RMSE with different network deays and DRs for a singe PHX (reference function: ramp30) 91

107 metric used in the case study in Chapter 5). Figure 40 shows the effect of network deays and power output reference functions (from Figure 39) with DR=0.9 (other vaues of DR show simiar trends of the RMSE). Figure 41 shows the power output RMSE with different network deays and DRs when the reference function is ramp30 (simiar trends for the other reference functions). We have two observations: 1. As shown in Figure 40, for the same network deay and DR, the steeper the reference function, the arger the RMSE. This is because when the reference function is steep, it requires the contro system to reduce its power output aggressivey (in much ess time), and thus it wi have a more transient response, causing arger RMSE. However, if the time required to change the power output is onger than 60 seconds (i.e., ramp60), the contro system has approximatey the same error due to the sow reaction required by the NPP. 2. As shown in Figure 41, for the same reference function, the higher the network deay and ower DR, the arger the RMSE. For the same contro system appication demand, different network deay and deivery ratio can ead to different contro system performance. Based on the two observations above, network imperfections wi impact each contro system differenty, depending on the contro system s appication demand (e.g., a reference function in case of a PHX). Thus, our goa is to reduce the overa contro system RMSE caused by network-induced imperfections. We propose an approach to dynamicay assign packets of different physica systems to the appropriate network paths (with redundancy or not). Our approach has two parts: (1) priority determination of the packets of different physica systems (highest priority for the most urgent physica pant); (2) network path seection. For the second part, we study two cases: (2a) consider network deay ony Based on the worst-case end-to-end deay anaysis in Chapter 6, we assign the highest priority packets to the fastest network path. (2b) consider both network deay and packet oss We propose a more genera mode to describe the network path quaity combining the impact of network deay and packet oss on the contro systems together, based on the network imperfection mode proposed in Section Quaity here is from the perspective of the 92

108 contro system: higher quaity brings higher performance (smaer RMSE) to the contro system. After a, the highest priority packet is assigned to the highest quaity path. To evauate our approach, we first carried out a case study on three PHXs in a modern, SMR (Sma Moduar Reactor)-based NPP. Note that our approach is genera and can be appied to other WCSs. The resuts demonstrate that our packet assignment approach is effective and abe to compensate for deay and packet oss incurred by the network during the transition between steady states of mutipe physica systems when they vary their demands simutaneousy. This approach is abe to create a WCS with the performance cose to a wired network. 7.2 PROBLEM FORMULATION AND SOLUTION Probem Formuation There are N physica systems that share one wireess network. We define a series of time steps T = {t 0, t 1,..., t w }, where T is the interva of w time steps and the time between two consecutive time steps is the contro samping period. During T any physica system is in transition (the system is in non-steady state). We have a set of N reference functions R = {r 1 (T ), r 2 (T ),.., r N (T )} that define different physica system appication demands. Simiar to [Saifuah et a., 2010], there are e choices of network paths/fows P = {p 1, p 2,..., p e } (e N), each path associated with a different deay and deivery ratio, which depends on the redundancy in the path as we as the scheduing and routing scheme. In this chapter, each network path deivers one message with the measurements of one physica system to the remote controer and deivers back one message with the associated contro signa to the actuator periodicay. For each physica system i, we can compute RMSE i, defined in Equation 7.1, where wired i (t j ) and wireess i (t j ) are the wired (no osses, no deay) and proposed wireess contro system power output of physica system i at time step t j, respectivey. Our objective is to minimize the RMSE avg, defined in Equation 7.2. Our scheme produces the network 93

109 path seection for physica systems over a time steps 2, P S = {[ps 1 (t 0 ), ps 2 (t 0 ),..., ps N (t 0 )], [ps 1 (t 1 ), ps 2 (t 1 ),..., ps N (t 1 )],..., [ps 1 (t w ), ps 2 (t w ),..., ps N (t w )]}, where ps i (t j ) is the seected network path number for the i th physica system transmission at time t j. RMSE i = 1 w (wired i (t j ) wireess i (t j )) w 2 (7.1) j=0 RMSE avg = 1 N RMSEi 2 (7.2) N i= Soution Overview In essence, our soution is to determine which network path to transfer which physica system s measurement over T (i.e., P S) to achieve the objective of RMSE avg minimization, at the side of the centraized remote controer. Let us first assume that the packet oss and network deay on a network paths are predictabe. We consider a brute-force way to sove the probem. At each time step, we try a possibe combinations of network paths C(e, N) and choose the best path seection, that is, P S that has minimum RMSE avg over w time steps. The compexity of our probem is O(C(e, N) w ), which is exponentia. Even if we assume the network is predictabe, it is impractica due to its high computation time and storage costs. When we consider the reaistic case that network deay and oss are unpredictabe, the optima soution does not exist. Therefore, we need soutions to make decisions at run time. We propose to sove the probem in two steps. We first propose three heuristic methods to determine which physica system has the most urgent appication demand and impose a priority order for the packets (Section 7.3). We then study two cases: (1) considering network deay ony: based on the anaysis of the worst-case end-to-end network deay, we assign the most urgent packet to the network path with the shortest deay (Section 7.4); (2) considering both network deay and packet osses: we propose a network path quaity mode to consider both the end-to-end deay and reiabiity of a network path. We assign the most 2 Note that RMSE of each physica system can change from one time step to the next, thus necessitates recacuation of the path seection 94

110 urgent packet to the network path that can deiver the measurement as high reiabiity and as short deay as possibe (the highest quaity path) to resut in sma RMSE avg (Section 7.4). Note that both the packet priority and the path quaity cacuation are done in the remote controer. 7.3 PACKET PRIORITY DETERMINATION The basic idea of priority determination of packets is to give high priority to the packet of the system that woud yied ow performance, to avoid increasing RMSE and thus RMSE avg. To determine the packet priority, we propose three heuristic methods with different perspectives. For each heuristic method, we propose a metric to cacuate the urgency of the packets, we then sort the urgency for each packet and get the packet priority (ow urgency, ow priority) Static RMSE Simiar to the anaysis in Figure 40, we carried out a thorough offine anaysis for each physica system for a possibe reference functions (e.g., different sopes of the ramp functions) by injecting the same amount of time deay but no packet oss into the contro system. Thus, for each contro system, we can get a ist of reference functions, each with a RMSE resut over the same period of time (when the system is in non-steady state). According to the offine anaysis, we can estimate each physica system performance (meaning the RMSE resut with the same reference setting, e.g., the same ramp function). This heuristic gives the highest priority to the packets of physica system with the highest estimated RMSE obtained from the offine anaysis. But the priority determination of packets is fixed and is not dynamicay changed at run time. Note that static RMSE is the baseine of our packet priority determination methods. 95

111 7.3.2 Dynamic RMSE Since our objective is to minimize the contro system RMSE avg, the heuristic is based on the foowing: the higher RMSE, the more necessary to transmit its message as soon and reiaby as possibe (thus reducing the RMSE). Since we cannot get the RMSE comparing with the wired contro system output at run time, we track each system s rrmse, that is, RMSE comparing with its reference function at run time. Equation 7.3 shows the rrmse of i th physica system, rrmse i (t x ) comparing with its reference function r i from time step t 0 to t x. At current time step t x, we cacuate rrmse of each physica system at the remote controer (the system output wireess i (t x ) needs to sent with the measurements to the remote controer), sort the rrmses of N physica systems and assign the highest priority to the packet of the system with the highest current rrmse, max 1 i N rrmse i(t x ). rrmse i (t x ) = 1 x x (r i (t j ) wireess i (t j )) 2 (7.3) j= PID Our third heuristic method is inspired by the PID feedback contro oop mechanism. We determine a proportiona term (P-term) as K p e i (t x ), where K p is a constant and e i (t x ) is the difference between the i th physica system output at time t x and the desired setpoint r i (t x ), i N; in our case, the setpoint is determined by the reference function. The P-term describes how far the current system performance is from what it shoud be (i.e., the reference x function). We define the integra term (I-term) as K i e i (t j ), where K i is a constant and x e i (t j ) is the integra error from time t 0 to t x. j=0 j=0 The I-term denotes the overa system performance from the beginning. The D-term is defined as K d (e i (t x ) e i (t x 1)), where K d is a constant. This term approximates the trend of error in the future (e.g., if this term is negative, it means the system error tends to reduce). The pid i (t x ) function is shown in Equation 7.4. We use pid i (t x ) to describe the i th system performance and track pid i (t x ), i N for each physica system at run time. We assign the highest priority to the measurement of the physica system with highest pid i (t x ) vaue at time t x. As usua in contro systems, since 96

112 K p, K i and K d are constants, we tune these constants by manua tuning in Section 7.6. pid i (t x ) = K p e i (t x ) + K i x e i (t j ) + K d (e i (t x ) e i (t x 1)) (7.4) j=1 7.4 NETWORK PATH SELECTION After we determined the priority of the packets, we need to determine which path to transmit the message of which contro system. We focus on a wireess network disjoint with mutipe network paths that can transmit messages in parae. Each network path has one ine of primary nodes and zero or more ines of backup nodes, as shown in Figure 27 in Chapter 6. Thus, each path has different ines of reay nodes and has the different characteristic in terms of network deay and DR. Every contro samping period, each path transmits one message with a the measurements of one physica system up to the controer, and transmits one message with one or more contro signas associated to the same physica system back to the actuators. We first consider network deay ony for path seection. Based on the worst-case end-toend deay anaysis of the network path in Chapter 6, we assign the highest priority packet to the network path with the smaest worst-case deay Network Path Quaity Mode Now we determine which network path to transmit messages when considering packet osses. Based on the network imperfection mode we proposed in Section 5.2.1, we propose a more genera network path quaity mode, the PQmode, as described by Equation 7.5, that quantifies how much the network affects the contro system. P Q = ( Dcurrent p + βn oss )p (7.5) where β is a constant. The vaue β is static during the path seection in this dissertation. Since our PQmode quantifies the network imperfection impact to the contro system, thus 97

113 a smaer PQ vaue means the better quaity of the network path. We use β to adjust the importance between network deay and network reiabiity. When β = 1, network deay and network reiabiity have the same importance to the contro system performance. β is set according to different WCSs we are deaing with. When the worst-case network deay is smaer than the contro system samping period (e.g., ike the water tank system in [Li et a., 2015]), β is set to a very arge number since network reiabiity is the ony factor that affects the contro system performance. When the contro samping period is smaer than the network deay, a more common scenario, β is a number coser to 1. For instance, when the contro system uses kaman fiter or any other technique to compensate for message osses, we can reduce the network reiabiity importance and set β to be sma. β aso can be adjusted under different network situations for the same contro system. We wi discuss the vaue of β under different network situations ater in Section CASE STUDY As shown in Figure 42, we conduct a case study of an NPP with three SMRs (three PHXs, each of which transmits and receives messages via a shared wireess network). Given that there are severa SMRs in an NPP, the power output of each SMR may differ and the controer may decide to change the power output of each SMR dynamicay, based on energy requirements, efficiency, and power baance that is required to achieve a certain eve of power output. The PHXs in SMRs are identica systems except for the reference functions, which are set by the nucear engineer/operator based on the NPP requirement. In our case study, a reference function is a ramp function, defined (1) power change amount (PCA) as the amount of power required to change; (2) power change duration (PCD) as the interva of time the power finishes changing; (3) start interva (SI) as the time duration from time 0 to the time the power starts to change. For exampe, ramp30 in Figure 39 is with PCA=10MW, PCD=30s and SI=40s. The parameters in a set of reference functions are 3 PCAs, 3 PCDs and 3 SIs. Each reference function is randomy chosen from the range of vaues of PCA, PCD and SI isted in Tabe 6. 98

114 Figure 42: System overview: three SMRs transmit measurement messages via shared wireess network to the remote controer, and the remote controer transmits back contro signas backup via the same network In order to incude a the PCDs, we choose simuation time as 300s, taking into account the system setting time (even after the PCD, the system sti needs sometime to sette down to the setpoint). Each PHX wi generate one packet (with its three measurements) and send out the packet by wireess network periodicay at the samping period 0.2s. Based on the deadine of one PHX system (0.586s [Wang et a., 2016]), we design a wireess network with three paths, each of 6 hops: path 1 (p 1 ) has no backups (worst-case round-trip deay: 0.12s); path 2 (p 2 ) has 1 ine of backup nodes (worst-case round-trip deay: 0.3s); path 3 (p 3 ) has 2 ines of backup nodes (worst-case round-trip deay: 0.54s). Each path satisfies the scheduabiity condition, p s 5 (ps =20 with contro samping period 0.2 as shown in Tabe 6). The reiabiity reationship of the three paths is p 1 < p 2 < p 3. Each network path can transmit messages independenty from the others, that is, a 3 paths can transmit messages in parae, without interfering with each other. We appy the most recent message first scheme. We combined a state-of-the-art cyber-physica system simuator (WCPS 2.0 [Li et a., 2015]) with an NPP simuator to mimic the WCS we consider. Our simuator aows mutipe wireess network paths running together with mutipe PHXs. We impement the heuristic methods proposed in Section 7.3 and the network quaity mode from Section at the 99

115 Tabe 6: Parameters and vaues of the simuation of SMR-based NPP Parameters Vaues Contro samping period 0.2s Simuation time 300s TDMA time sot duration 0.01s PCA vaues 2MW, 4MW, 6MW, 8MW, 10MW PCD vaues 15s, 30s, 45s, 60, 75s, 90s, 105s, 120s SI range: [20s, 300s] β vaue range: [ ] remote controer. Simiar to the case study in Chapter 4, we use the TOSSIM network simuator (embedded in WCPS) with wireess noise traces from a 21-node subset of the WUSTL Testbed [tes, 2017]. We controed the Received Signa Strength with uniform gaps to simuate various wireess signa strength (RSSI) vaues to change the LSR. As shown in Figure 9, we adjust the RSSI vaues for the average LSR to be in the range (0.71, 1.0). 7.6 CASE STUDY RESULTS Based on the wireess contro system for the NPP introduced above, we first compare the reiabiity of the three network paths for different network conditions (Section 7.6.1). We then evauate our network path quaity mode (Section 7.6.2). Specificay, we did a sensitivity anaysis of β vaues and anayze the network path seection for different network conditions. Additionay, we compare RMSE avg for both end-to-end deay approach and PQmode approach (Section 7.6.3). Finay, we compare the RMSE avg among the three heuristic methods of packet priority determination (Section 7.6.4). In order to determine the constants K p, K i and K d of the PID heuristic method, we ran 100

116 Deivery Ratio p1 p2 p RSSI Vaues (dbm) Figure 43: Deivery ratio of three network paths under different RSSI vaues 100 experiments (each experiment corresponds to one set of reference functions) for each set of constant vaues of K p, K i and K d with no message oss (to make sure the path quaity order is fixed by the network deay. We choose the set of constant vaues (K p =1, K i = 2 K p /t and K d = 0) that has the average minimum RMSE avg over a the experiments. Note that K p, K i and K d vaue may be different with different types of contro systems (e.g., K d =0 in our case, but can be nonzero in other types of WCS) Network Reiabiity Resuts Figure 43 shows the DR of three network paths under different RSSI vaues. The DR increases as the number of backup paths increases. Since p 1 has no backup path, the DR is ony about 0.6 when the RSSI vaue is -64 (good network condition). At the other extreme, the DR of p 3 (two backup paths) is above 0.8 with the RSSI vaue -84 (poor network conditions). The percentage of the number of consecutive packet osses for paths p 1, p 2 and p 3 are presented in Figures 44, 45 and 46 respectivey. As expected, for the same network interference condition, the more backup paths in the network, the fewer number of consecutive osses. For each network path, as interference in the network increases (ess RSSI vaue), the percentage of massive consecutive oss (noss 6) increases (e.g., the topmost region is much arger for -84 than for -60 in Figure 44). 101

117 Figure 44: Percentage of consecutive osses (noss) for network path 1 Figure 45: Percentage of consecutive osses (noss) for network path 2 Figure 46: Percentage of consecutive osses (noss) for network path 3 102