UNIVERSITY OF CALGARY. Variable Speed Limit: A Microscopic Analysis in a Connected Vehicle Environment. Bidoura Khondaker A THESIS

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1 UNIVERSITY OF CALGARY Variable Speed Limit: A Microscopic Analysis in a Connected Vehicle Environment by Bidoura Khondaker A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN CIVIL ENGINEERING CALGARY, ALBERTA APRIL, 2016 Bidoura Khondaker 2016

2 Abstract This thesis presents a novel proactive Variable Speed Limit (VSL) control algorithm to find a balanced trade-off among mobility, safety and environmental impact in a Connected Vehicle (CV) environment. The development of CV technology has the potential to provide essential data at the microscopic level to have an understanding of real time drivers' behavioural information. CVs also have the unprecedented ability to be used as mobile sensors able to capture the impact of control schemes on driver s behaviour and compliance rate. In addition, Connected/Autonomous Vehicle initiatives claim to serve three main purposes: improving safety, enhancing mobility and reducing emissions. In line with these initiative, this thesis develops a dynamic anticipatory VSL control strategy that attempt to meet the multi-criteria objective of improving travel time, safety, and emission/fuel consumption, while taking into consideration the likely responses of drivers. A microscopic car following model, IDM (Treiber et al., 2000) in conjunction with a microscopic lane changing model, MOBIL (Treiber and Kesting, 2009) are used to anticipate the lane changing and acceleration/deceleration decisions of drivers on multi-lane freeway. A system-wide optimization using a multi-objective function is formulated to obtain the VSL values that minimize: (i) Total Travel Time (TTT); (ii) Collision probability derived from Time to Collision (TTC); and (iii) Emission and/or Fuel Consumption. The proposed algorithm has been optimized using Genetic Algorithm(GA) via an integrated VISSIM-COM-MATLAB interface. ii

3 The results of the thesis suggested that the VSL strategies were able to result in fewer lane changing rate (LCR), which synchronized driver behaviour. Also, the developed algorithm was able to produce a smoother acceleration and deceleration pattern compared to the uncontrolled case, which corresponds to lower emission and fuel consumption. The sensitivity analysis results showed that at free flow condition, the VSL strategy outperformed the uncontrolled case up to 35% penetration rate. However, for higher demand levels, the safety component was highly sensitive to variation in % of CV and required more weight than the mobility and sustainability components. The result also indicated that 35% CV penetration rate was the minimum rate required to realize improvements in terms of safety, mobility and environmental improvements. Keywords: Variable Speed Limit, Connected Vehicle, Driver Behavior, Optimization, Macroscopic, Microscopic, Microsimulation, Driver Compliance, Optimization. iii

4 Acknowledgements This thesis has only been possible with the gracious help and support of many people. First, I would like to offer my enduring gratitude to my supervisor, Dr. Lina Kattan for the technical support and advice that she extended to me during the course of this research. I truly appreciate her support for enlarging my vision of engineering and providing coherent answers to my endless problems. As a supervisor she helped me to find out my hidden talents, refine them and made me capable of standing out among the crowd. I sincerely express my thankfulness for her guidance and encouragement not only in academic subject matters, but also for finding the right way, bring back the confidence and stay focused during many tough times in my life. I would like to express my sincere appreciation to my committee members, Dr. Alex de Barros, Dr. Chan Wirasinghe, Dr Chris Macnab and Dr. Chris Lee for reviewing the thesis and for their valuable suggestions in refining the quality of this dissertation. I would also like to acknowledge Natural Science and Engineering Research Council (NSERC) and Stantec for providing me financial support as NSERC-IPS scholarship while doing this research. I am also very fortunate to receive scholarship assistance from ITS Canada, Canadian Institute of Transportation Engineers (CITE) Michael Van Aerde Memorial scholarship, Transportation Association of Canada (TAC), University of Calgary Faculty Women's Club Graduate Scholarship, Teaching Assistantship, Urban Alliance Grant in Transportation System Optimization, Alberta Motor Association and Alberta Innovates technology Futures (AITF) iv

5 strategic grant in Smart Multimodal Transportation Systems, NSERC Discovery and Engage Grants during the course of my PhD research. I am truly grateful for their financial assistance as it helped me a great deal in focusing on my research. Finally, I would like to say that the process of earning a doctorate and writing a dissertation is long and arduous. Thanks a lot dear husband, Imran Matin, for sacrificing your job in Vancouver and starting a new life in Calgary just to support my PhD. Thanks a lot Zara, my daughter, for being so matured to let mommy spend so much time on her research. Finally, thanks a lot Zafir, my baby boy who was also born in this thesis 'birthing' process. My heartiest thanks to the three of you, for being truly supportive in all my endeavors. Since the very beginning and until the last moment, I dedicate every word that I typed in this thesis to you: Imran, Zara and Zafir. v

6 Table of Contents Abstract... ii Acknowledgements... iv Table of Contents... vi List of Tables...x List of Figures... xi CHAPTER 1: INTRODUCTION Background Why Variable Speed Limit (VSL) is Needed : Some Theoretical Background VSL to Resolve Traffic Breakdown Effect of VSL on Traffic Throughput Motivation and Problem Statement Contributions of the Thesis Organization of the Thesis...14 CHAPTER 2: LITERATURE REVIEW Introduction Impact of VSL on Traffic State Overview of Variable Speed Limit (VSL) Control Strategies Rule Based VSL Control Strategies Advanced Proactive VSL Control Strategies Advanced VSL Control Design with Traffic Prediction and Dynamic Speed Limit Models Impact of VSL on Traffic Safety...34 vi

7 2.5 Impact of VSL on Emission/Fuel Consumption Impact of VSL on Driver Behaviour VSL and Driver Compliance/Enforcement Summary...43 CHAPTER 3: METHODOLOGY Introduction Overview of The Methodology Microscopic Traffic Flow Model to Calculate Total Travel Time (TTT) Microscopic Lane Changing Model MOBIL to Estimate/Predict the Trajectory of Individual Vehicle Surrogate Safety Model to Calculate Time to Collision (TTC) VT-Micro Model to Calculate Emission/Fuel Consumption Implementation of The VSL Algorithm Formulation of a Multi-Objective Function VSL Trigger Condition Modeling Drivers' Compliance Solution Algorithm For Optimization SUMMARY...67 CHAPTER 4: CASE STUDY 1 - PROACTIVE VSL FRAMEWORK FOR A ONE LANE ROAD NETWORK Introduction Description of the Test Network...70 vii

8 4.3 Model Calibration Freeway Representation and Data Acquisition Estimation of the Parameters Simulation Results Case of 100% Market Penetration Rate Case of 50% Market Penetration Rate SUMMARY...88 CHAPTER 5: CASE STUDY 2 - VARIABLE SPEED LIMIT WITH ANTICIPATORY LANE CHANGING DECISIONS IN A TWO-LANE NETWORK Introduction Driver Behaviour with Anticipatory lane Changing Decisions Numerical Experiments Results on Impact of Driver's Behaviour in the Base Case Scenario SUMMARY CHAPTER 6: SENSITIVITY ANALYSIS Introduction Sensitivity Analysis Parameters Sensitivity Analysis Results: Case of 100% Penetration Rate Sensitivity Analysis Results: Case of Lower % Penetration Rate SUMMARY CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS viii

9 7.1 Context and Scope of Research Summary of Results Potential Implications of the Research Future Research Directions REFERENCES APPENDIX A ix

10 List of Tables Table 2.1: Models Used for VSL Design Table 4.1:Parameter Estimates for the Study Network Table 4.2:Scenario Description Table 4.3:Simulation Results for Different Scenarios Table 4.4:Simulation Results for 50% CV Penetration Rate Table 6.1:Scenario Description Table 6.2:Simulation Results for Different Demand Profiles (100% Penetration Case) Table 6.3:Simulation Results for Different Demand Profiles (50% Penetration Case) Table 6.4:Simulation Results for Different Demand Profiles (35% Penetration Case) Table 6.5:Variation of Weights in the Objective Function (for capacity demand and 35% penetration case) Table 6.6:Simulation Results for Different Demand Profiles (25% Penetration Case) x

11 List of Figures Figure 1.1: Hysteresis Phenomenon Caused by Traffic Breakdown (Kerner, 2009)... 4 Figure 1.2:Double Z Characteristics of Three Phase Traffic Theory (Kerner, 2007)... 5 Figure 1.3: Effect of VSL on Fundamental Diagram (Hegyi, 2005)... 8 Figure 2.1:Effect of VSL on Fundamental Diagram (Zackor, 1991) Figure 2.2:Various Models Describing The Variation Of Flow-Density Under The Effect of Figure 2.3: An Illustration of Closed Loop Control System Figure 3.1: Flow Chart of the VSL Algorithm Figure 3.2: A lane changing scenario, subject vehicle C considering lane change to the left (Treiber and Kesting, 2009) Figure 3.3: Flow Chart of The VSL Optimization Process Figure 3.4: VSL trigger algorithm Figure 3.5: Workflow of the simulation environment Figure 4.1: Layout of the freeway Figure 4.2: Regression Line for Free Flow Speed Figure 4.3: Estimation of Critical Density xi

12 Figure 4.4: Estimation of Jam Density Figure 4.5: Estimation of Capacity Drop Figure 4.6: Traffic flow (a, b) and speed (c, d) distribution under VSL control (S4) (right) and uncontrolled scenario (left) Figure 4.7: Flow-Density curve for VSL and No-VSL cases Figure 4.8: VSL Rates with Simulation Time (For scenario 1 only).86 Figure 5.1: Layout of the two-lane freeway...93 Figure 5.2: Lane Changing Rate With Time for Uncontrolled and VSL-Control Scenario Figure 5.3: Speed Profile in Both Lanes for Uncontrolled (a) and VSL-Control(b) Scenario Figure 5.4: Frequency Distribution of the Acceleration/Deceleration Rate Figure 5.5: Frequency Distribution of the Acceleration/Deceleration Rate Figure 5.6: Speed Contour Plot For the Uncontrolled Case (a) and VSL Control Case (b) 102 xii

13 CHAPTER 1: INTRODUCTION Background Over the past 20 years, traffic on our roads has increased by 60%, and the proportion of Canadians living in urban areas has been rising steadily with more than 81% living in urban areas (Gov of Canada, 2013). The cost of recurrent congestion in major urban areas in Canada is estimated between $3.1 billion to $4.6 billion annually (Urban Transportation Task Force, 2012). Taking into account for pollution, GHGs, noise, vehicle collisions and time delays from traffic congestion, road use in Canada is estimated to cost $27 billion per year. In Canada, the transportation sector is a major source of pollution, accounting for 24% of all GHG emissions (Statistics Canada, 2013). Our existing road transportation system is facing severe problems capacity shortage, poor safety, unreliability, inefficient fuel consumption and environmental pollution. Due to fiscal, land and environmental constraints, building more roads is often not a viable solution, especially in urban areas. Therefore, the future of Canadian transportation systems calls for a sustainable solution to alleviate these persistent problems. Recent advancements in Intelligent Transportation Systems (ITS) have shown that ITS strategies are able to effectively reduce congestion, incidents, travel time, money, fuel consumption and emissions. ITS capitalizes on emerging computer and communication technologies to proactively respond to the dynamic and random nature of traffic. This can be achieved through a variety of real-time management and control strategies. Hence, the future of our transportation system obviously depends on the application of ITS technologies that can be widely applied to numerous transportation problems. 1 Section 1.2 of this chapter has been taken from the paper: Khondaker, B., Kattan, L., Variable speed limit: an overview. Transportation Letters: The International Journal of Transportation Research, Volume 7, Issue 5. 1

14 Variable Speed Limit (VSL) systems are ITS solutions that enable dynamic change of posted speed limit in response to prevailing traffic, incidents and/or weather conditions. VSL systems utilize traffic speed and volume detection, road weather information systems to determine the appropriate speeds at which drivers should be traveling, given current roadway weather and traffic conditions. Changes in posted speed limits are indicated by displays on overhead or roadside variable signs. The main benefits of VSL installation can be summarized as follows: 1. Improvements of safety: This is achieved by the reduction of speed differences among vehicles travelling in the same lane and/or the reduction of speed differentiation among adjacent lanes. This reduction in speed variance synchronizes drivers' behaviour, discourages lane changing behaviour, and thus decreases the probability of collisions (Abdel-Aty et al., 2006). 2. Resolving traffic breakdown: When traffic is close to capacity, any disruption in the traffic stream can lead to traffic breakdown. VSL can restore freeway capacity by slowing down traffic that would otherwise enter bottleneck locations, thus delaying or in some cases preventing the occurrence of traffic flow breakdowns (Hegyi, 2005). 3. Improved throughput and environmental benefits: Since congestion is also associated with increased fuel consumption and emissions, the capability of VSL to improve traffic flow also results in environmental benefits (Zegeye et al. 2010). VSL system was first implemented in Germany more than three decades ago. Today, VSLs are widely used in European countries, USA, Korea and Australia. While variable speed limit systems are still not as common in Canada, they have the potential to make Canadian highways safer and more user-friendly. A coordinated network wide VSL control strategy has the potential to reduce congestion, shockwaves, and flow breakdowns on freeway networks and can significantly improve the efficiency of the infrastructure in terms of Total Time Spent. 2

15 1.2 Why Variable Speed Limit (VSL) is Needed : Some Theoretical Background VSL to Resolve Traffic Breakdown Congestion may occur from bottleneck formations resulting from a lane drop, a collision or other incidents, or near on-ramp with significant demand,. The onset of congestion is usually accompanied by an abrupt decrease in vehicular speed, which is known as traffic breakdown (Kerner, 2009). Traffic hysteresis and capacity drop are two widely observed traffic conditions associated with traffic breakdown (Gerelominis and Sun 2011; Saberi and Mahmassani 2013). Traffic hysteresis is a phenomenon characterized by various loops in the congested part of the speed-flow relationship. Capacity drop is mainly observed downstream of an active bottleneck and is associated with a drop in the average discharge flow compared to its pre-breakdown value for the same value of density at that particular bottleneck (Chung et al., 2007). However, due to the stochastic nature of observed free flow capacity, the concept of capacity drop is still somewhat controversial (Brilon et al. 2005, Kerner, 2009). Based on the spatiotemporal analysis of speed patterns, Kerner (2009) introduced the concept of "three-phase traffic theory" which consists of: 1) free flow (F), 2) synchronized flow (S), and 3) wide moving jam (J) phase. Based on this theory, traffic breakdown is mainly associated with a transition from phase F to S which is often accompanied by the hysteresis effect. As illustrated in Figure 1.1, Kerner (2009, 2013) has described the hysteresis effect as a phase transition from a free low to a synchronised flow (F S transition) and a return transition from synchronised flow to free flow state (S F transition). This hysteresis effect is closely associated with drivers' speed adaptation and lane changing behaviour. 3

16 Figure 1.1: Hysteresis Phenomenon Caused by Traffic Breakdown (Kerner, 2009) Kerner (2007) has described two different Z-characteristics depending upon F S or S J transition in a speed-density plane (Figure 1.2). The dashed line in Figure 1.2 between either states (i.e. S and F or S and J) describes the critical speed within speed disturbances. Based on the above double Z-characteristic of three-phase traffic theory, Kerner (2007) has studied the effect of speed limit control on a two-lane road section downstream of a freeway bottleneck. This study provided important insights about the role that speed control has on traffic breakdown and state transition. If there exists an on-ramp acting as an active bottleneck on a freeway and if the inflow entering the bottleneck is quite high, vehicles merging from the on-ramp onto the main line cause a considerable drop in speed. Kerner (2007) found that a traffic breakdown and the emergence of a wide moving jam might be rather induced at the bottleneck with the application of speed control downstream of the bottleneck. The main idea was that, if the speed within a disturbance is equal to or lower than the critical speed, it would lead to a phase transition causing traffic breakdown. If the disturbance grows, a wide moving jam (J) might also form. Nevertheless, this study was limited to examine the role of speed control at one fixed location downstream of the bottleneck. 4

17 Figure 1.2:Double Z Characteristics of Three Phase Traffic Theory (Kerner, 2007) In order to resolve the bottleneck, the inflow entering the bottleneck needs to be lower than the outflow from that bottleneck area, until the discharge capacity is restored. In other words, there should be freeway control measures upstream of the bottleneck section to be able to effectively limit the inflow to that section. Limiting inflow to the bottleneck can be achieved with several freeway traffic control measures, such as ramp metering that limits the number of vehicles entering the bottleneck, and/or VSL that reduce the speed of traffic to delay it from entering the bottleneck. Based on the fundamental traffic flow diagram, reducing speed of traffic inflow through VSL would also result in a reduced flow. Variable Speed Limit (VSL) control is thus considered an emerging inflow limitation technique that can be effective in such conditions Effect of VSL on Traffic Throughput For any applied traffic control measures, such as VSL, it is important to ensure that such control would not result in a large flow reduction elsewhere in the network and adversely affecting the overall network performance. For that purpose, VSL control can be formulated with the objective of maximizing network performance; or, alternatively, minimizing Total Time Spent (TTS) on the system, including delays for queues on ramps. 5

18 Papageorgiou et al. (2002) showed the existence of a direct relationship between the TTS and the inflow and outflow of a traffic network. If the number of vehicles in a network can be defined by a discrete time variable, n(k), where k is the time index and k = 0,1,2..., and T is the time interval, then TTS of all vehicles spend in the network over a time horizon, K, can be given by: = ( ) (1) If q in and q out denotes the total inflow and outflow of the network, respectively, then according to the conservation law of vehicles: ( ) = ( 1) + ( ) ( ) = (0) + ( ) (2) With the substitution of Equation (2) into Equation (1), the following relationship can be obtained: = (0) + ( 1) ( ) (3) With no-vsl control, q is equal to q due to congestion, whereas in presence of VSL, the outflow is restored to capacity and hence, q is equal to q. It is worth mentioning here that q in case of congestion will be 5% to 15% lower than q due to capacity drop (Hall et al., 1991). Thus TTS for both cases can be written as: ( ) = (0) + ( 1) ( ) (4) ( ) = (0) + ( 1) ( ) (5) 6

19 Since, VSL has the capability of limiting inflow and restoring capacity drop by creating discharge flow equal to capacity, hence the following relationship holds: ( ) < ( ) (6) < (7) By multiplying both sides of equation (7) by -1 and combining it with Equation (6), we obtain: ( ) < ( ) (8) Comparing Equation (4), (5) and (8), the following relationship can be deduced: ( )< ( ) (9) From Equation (9), it is clear that, if the inflow can be limited, it is possible to decrease the TTS considerably, which is a significant implication of VSL. Thus, the proposition of VSL is apparent. When traffic is in a nearly unstable condition, even very minor flow from an on-ramp or a vehicle changing lanes can create shockwaves and bring the traffic to a flow breakdown condition. VSL attempts to slow down traffic and limits inflow to the bottleneck. Therefore, changing the speed limit changes the shape of the fundamental diagram (FD) from state A in Figure 1.3 to somewhere between states B and C, thereby increasing the value at which the critical density occurs. 7

20 Figure 1.3: Effect of VSL on Fundamental Diagram (Hegyi, 2005) 1.3 Motivation and Problem Statement The VSL control strategies developed so far can be divided into two broad categories: reactive rule-based approaches and proactive approaches. Reactive rule-based VSL strategies have limited potential due to their reliance on simplistic localized control logic; whereas networkwide coordinated proactive VSL control strategies have the inherent capability of acting proactively, while anticipating the complex behaviour of dynamic systems. The majority of the developed proactive VSL strategies, however, have been based on the 2 nd order macroscopic traffic flow model and utilized aggregate data (such as average speed, flow, and density) from point detection technology. Deployment of such technologies corresponds to high installation, maintenance and communication costs, as well as high failure rates (Herrera et al., 2010). Moreover, this relatively coarse aggregation of data obscures many features of interest, such as any possible changes in the traffic state within the aggregation interval (Wu and Liu, 2014). In addition, these macroscopic models used for VSL design do not reflect the behaviour of individual drivers in a traffic stream. When traffic is in congested state, any disturbance in the 8

21 flow can create shockwaves that may result in traffic breakdown. Such shockwaves result from microscopic driver behaviour, such as sudden deceleration, merging or lane changing, leading to uneven headways. The use of a macroscopic traffic model cannot completely reflect the occurrence of such disturbances (Khondaker and Kattan, 2015). With current advancements in positioning, information and communication technologies, the transportation engineering community is having unprecedented access to such individual trajectory data that can be collected at the microscopic level (Khondaker and Kattan, 2015). Therefore, the current strategy of VSL design can be improved in a Connected Vehicle (CV) environment, where the wireless communication systems act as the next generation of new sensors. More specifically, Vehicle to Vehicle (V2V) and Vehicle to Infrastructure (V2I) communication initiatives (moving close to deployment) will provide a basis to detect individual vehicle trajectories. These emerging vehicles are equipped with electronic sensors capable of monitoring a vehicle's speed, position, and lateral and longitudinal acceleration. This data at a microscopic or individual vehicle level can be used as more accurate input in the design of advanced traffic control devices aiming to reduce congestion and enhance safety on roadways. The main advantage of using microscopic data is that the behaviour of drivers can be described in detail. For instance, the analysis of individual trajectory data is important in order to identify the location and magnitude of shock wave formation that can be created at the individual vehicle level, such as a vehicle changing lanes or coming to a sudden stop. This step is crucial to activating advanced traffic control devices in a timely fashion. Consequently, studies that focus on individual driver's behaviour (e.g. acceleration/deceleration, lane changing, over passing, etc.) 9

22 rather than aggregate behaviour are needed to develop the next generation of advanced and robust traffic control devices. Since lane changing and acceleration/deceleration behaviours are the primary driver s decision variables on a freeway, they have a significant effect on traffic control strategies such as VSL. According to previous studies, lane changing, in particular, has a considerable impact on traffic flow characteristics and freeway safety. In heavy traffic, lane changing is a key trigger to traffic breakdown, capacity drop, and traffic oscillations (Laval and Daganzo, 2006; Jin, 2010; Oh and Yeo, 2015 and Knoop et al., 2010). While the impact of acceleration and deceleration behaviours has received some attention; none of the published studies appears to account for the effect of lane changing behaviour in developing and evaluating freeway control strategies. In fact, traffic control and driver s behaviour mutually impact each other. For instance, lane changing behaviour is mainly triggered by speed differences between adjacent lanes, and drivers desire for travelling faster. The occurrence of a frequent lane changing manoeuvres might lead to shockwave formation which would activate freeway control schemes such as VSL. On the other hand, the presence of freeway management schemes such as VSL systems harmonize the travel speed by reducing speed differences among vehicles travelling in the same lane and/or adjacent lanes, which in turn discourages frequent lane changing behaviour. This interaction between driver s behaviour and control strategies suggests the need for an integrated framework where both anticipated driver behaviour and control strategies are modelled as mutually influencing each other to seamlessly optimize the efficiency of freeway facilities. 10

23 1.4 Contributions of the Thesis This thesis has taken a further step towards developing a VSL control strategy by using traffic data at the microscopic or individual vehicle level to achieve concurrent sustainability objectives. Recent Connected Vehicle/Autonomous Vehicle initiative claim to serve three main purposes: improving safety, enhancing mobility and reducing emissions (Zeng et al. 2012). In line with this initiative, this thesis incorporates driver behaviour (acceleration/deceleration, lane changing, compliance to posted speed limit etc.) from CVs in designing a proactive VSL system that is formulated as a multi-objective optimization function to find a balanced trade-off among mobility, safety and environmental sustainability. Throughout this thesis, the term 'Connected Vehicle' refers to any vehicle that can dissipate its location and speed information with high accuracy. Such positioning information is expected to be shared in the future between partial or fully autonomous vehicles or with the Road Side Equipment (RSE) within a certain range via DSRC. To develop this proactive VSL control strategy, Model Predictive Control, MPC (Maciejowski, 2002) technique was used in this research which has the capability of predicting future state of traffic so that traffic disturbances are anticipated before they even occur. In this research, the improvement of network efficiency has been measured in terms of minimizing Total Travel Time (TTT) of all the vehicles in the network. A surrogate safety measure, Time to Collision (TTC), has been used to capture the instantaneous safety between each individual pair of vehicles. For assessing the environmental benefit, VT-Micro model developed by Rakha et al. 11

24 (2004) has been used which has the capability to evaluate the environmental aspects of traffic management, operations and ITS strategies at microscopic level. Rather than using a fixed driver's compliance rate, the algorithm incorporates real-time driver compliance to adjust the optimal speed limit values. The developed approach has been tested in a synthetic two-lane freeway using the VISSIM microsimulation tool, via Genetic Algorithm (GA) as the optimization tool. The major contributions of this thesis are briefly described in the next section. In order to assess the traffic impacts considering mobility, safety and sustainability using data from CV, this thesis incorporated these three distinct components into a single VISSIM microsimulation framework These components were: (i) a microscopic traffic flow prediction model to minimize TTT (Total Travel Time) of all vehicles in the network, (ii) a surrogate safety model TTC (Time To Collision) to capture the instantaneous safety between each individual pair of vehicles, and (iii) a microscopic emission and fuel consumption model 'VT-Micro model' (Rakha et al., 2004) to measure Emission (E)/Fuel Consumption(FC). A microscopic car following model, IDM (Treiber et al., 2000) in conjunction with the microscopic lane changing model, MOBIL (Treiber and Kesting, 2009) are used to anticipate the lane changing and acceleration/deceleration decisions of the drivers on multi-lane freeway. Finally, a system-wide optimization using a multi-objective function was formulated to obtain the VSL values that: (i) minimized TTT; (ii) maximized safety as reflected in TTC; and (iii) minimized emission (E) and/or fuel consumption (FC). The developed approach has been tested using the VISSIM microsimulation tool via an integrated VISSIM-COM (Component Object Model) - MATLAB interface. 12

25 In summary the main contributions of this thesis can be outlined as follows: Development of a novel proactive VSL control strategy by incorporating driver behaviour (i.e. acceleration/deceleration, lane changing, compliance to posted speed limit) using traffic data at the microscopic/individual vehicle level from CV to formulate a multi-objective optimization function to find a balanced trade-off among mobility, safety and environmental sustainability. Using the power of Intelligent Driver Model (IDM, Treiber et al., 2000) and the kinematic motion equation of vehicles, to predict driver behaviour in a future horizon, as a function of the optimized variable speed limits. Also introducing a switching rule in the IDM model (i.e. whether vehicles are in 'car following' or 'free flowing' state) based on the minimum desired gap and actual gap between two consecutive vehicles. This switching rule is more realistic in the sense that, they are the function of individual vehicle's speed, relative speed difference and relative position in real time, therefore provide relatively more accurate information about the current state of vehicles. Development of the hypothesis that speed limit controls can be co-ordinated and optimized to reduce frequent lane changing and overall braking, thus to achieve greater traffic throughput, safety and sustainability by synchronizing driver behaviour. Thus, this research analyzes not only longitudinal interaction among vehicles, but also lateral interaction using the MOBIL lane changing model (Treiber and Kesting, 2009) to estimate/predict the likely trajectory of individual vehicle for a given prediction horizon. Using a unique VSL trigger condition to justify the initiation of VSL based on a 'speed drop' algorithm and using real time observed driver compliance rates to adjust the optimal VSL values. 13

26 Using an integrated VISSIM-COM (Component Object Model) MATLAB interface to facilitate the easy transfer of data between VISSIM and MATLAB. This allowed for data to be collected at the current time instant, transferred to MATLAB for systematic optimization, and return the optimized control values back to VISSIM to modify driver's behaviour. Considering the fact that modelling different levels of CV % penetration rate is important for examining their co-existence with manually and/or unequipped vehicles and their impact on the performance of the developed algorithm, a detailed sensitivity analysis was conducted considering different CV penetration rates and varying traffic demand. A sensitivity analysis of CV penetration rates is challenging due to the need for trajectory data of each individual vehicle, including the trajectories of unequipped vehicles. This research takes another step towards this by estimating the trajectory of unequipped vehicles based on the behaviour of two consecutive CVs using the algorithm developed by Goodall et al. (2014) and incorporating this with the developed VSL algorithm. 1.5 Organization of the Thesis The remainder of this thesis has been organized as follows. Chapter 1 provides a brief introduction of the thesis, including background, motivation, the problem statement and main contributions of this research. Chapter 2 presents a comprehensive literature review on VSL control strategies. Chapter 3 provides an overview of the adopted methodology, including the traffic flow model, safety model, VT-Micro model, objective function, and optimization method that have been used in this study. Chapter 4 demonstrates the application and performance of the 14

27 developed VSL algorithm using individual trajectory data from CVs in a simulation one-lane freeway. Chapter 5 extends the developed framework for a multi-lane freeway followed by Chapter 6 which describes a detailed sensitivity analysis of various CV % rates and varying traffic demands. Finally, Chapter 7 summarizes the research along with conclusions and recommendations for future studies. 15

28 CHAPTER 2: LITERATURE REVIEW Introduction This chapter provides an overview of various VSL strategies developed in the last two decades. First it describes the impact of VSL on traffic state. Next it discusses the traditional rule based VSL control strategies and the limitations associated with this approach followed by a discussion on the advanced coordinated network-wide VSL control strategies in coordination with traffic prediction and performance evaluation modeling. The potential safety and environmental benefits of VSL are also discussed along with impact of VSL on driver compliance. Finally this chapter summarizes the literature review, identifies the currently existing gap in the literature and recommends rationalization of the proposed approach of this thesis. 2.2 Impact of VSL on Traffic State The majority of the works in the literature that examined the impact of VSL on the flow-density diagram were based on theoretical assumptions, with very few works based on real observation data. According to Zackor (1991), VSL would decrease the slope of the flow-occupancy diagram at under critical conditions and enable higher flows at the same occupancy values at overcritical conditions (Figure 2.1). 2 The content of this chapter has been taken from the paper: Khondaker, B., Kattan, L., Variable speed limit: an overview. Transportation Letters: The International Journal of Transportation Research, Volume 7, Issue 5. 16

29 Figure 2.1:Effect of VSL on Fundamental Diagram (Zackor, 1991) Alessandri et al. (1999) developed a model that described different behavior at medium and high densities, indicating that when speed limit was applied, drivers' speed actually increased compared to the no control case (Figure 2.2a). In the model of Lenz et al. (1999), the effect of speed limit was reflected by a factor that just downscaled the fundamental diagram (Figure 2.2b). Therefore, these two models (i.e. Alessandri et al., 1999; Lenz et al., 1999) may have overstated the effect of speed limits. Later, the study conducted by Hegyi (2005) was not totally in agreement with Zackor (1991). Hegyi stated that the two curves met, but did not actually intersect. The main hypothesis in Hegyi s (2005) speed limit model was that the activation of VSL in under critical condition temporarily decreased the mainstream flow arriving at the bottleneck. This temporary flow decrease would occur because of the fact that critical density in VSL case was larger than that of the no VSL case (see Figure 2.2c). 17

30 (a) Alessandri's (1999) model (b) Lenz's (1999) model (c) Hegyi's (2005) model Figure 2.2:Various Models Describing The Variation Of Flow-Density Under The Effect of Speed Limits Papageorgiou et al. (2008) examined the impact of VSL on aggregate traffic flow behavior by analyzing 27 days of real-time field observations collected from a European freeway. They found that VSL decreased the slope of the flow-occupancy diagram in under critical traffic conditions, shifted the critical occupancy to higher values and enabled higher flows at the same occupancy values at over-critical traffic conditions. The analysis of the field data also showed that, when the VSL system was activated, it successfully lowered the average speed, thereby retaining the traffic inflow entering the jammed section and delaying the activation of a downstream bottleneck. These results indicate that efficient VSL control strategies can improve traffic flow for saturated and nearly saturated traffic conditions. However, the results from the study were not conclusive regarding the impact of VSL on the capacity of the facility. 18

31 A recent study conducted by Heydecker and Addison (2011) analyzed field data from a VSLmanaged freeway in the UK. The study described how introducing a VSL system induced greater road occupancy and increased capacity, leading to reduced congestion and, accordingly, decreased travel times. 2.3 Overview of Variable Speed Limit (VSL) Control Strategies VSL control strategies can be divided into two broad categories: reactive rule based approaches and proactive approaches. Earlier VSL studies were formulated as simple reactive rule based logic. In these approaches, real time VSL decisions were changed depending on pre-selected thresholds of traffic flow, occupancy or mean speed with the main objective of improving safety. On the other hand, recent VSL investigations have been mainly focused on more advanced control logic that works in a proactive fashion, meaning dynamically preventing a problem before it actually happens. These later approaches are formulated with the objective of minimizing TTS in the system with safety consideration included in the constraints. A detailed discussion on the theoretical background of both types of the approaches is discussed in the following subsections Rule Based VSL Control Strategies Early VSL studies were mainly formulated as simple reactive rule-based logic. As previously mentioned, real-time VSL decisions were changed based on preselected thresholds of traffic 19

32 flow, occupancy or mean speed. The main objectives of these approaches were harmonization of speed differences and stabilization of traffic flow. Examples of such systems are those developed by Zackor (1991), Smulders (1992), Smulders and Helleman (1998), Rama (1999), and Piao and McDonald (2008). These studies were successful in showing the effectiveness of VSL systems in harmonizing traffic and mainly improving safety. Van den Hoogen and Smulders (1994) developed a VSL strategy where the objective of which was not to reduce average speed, but to reduce speed variance within and between lanes. VSLs were only triggered when detected flows approached capacity. The result of the analysis showed that VSL system was efficient in reducing speed variation, which would contributed to reductions in crash frequency and severity. This study made important contributions in assessing the positive impact of VSL; however, the following issues were not considered: Interaction between changes in traffic flow and VSL activity, A quantitative analysis on the likely impact of VSL on capacity and throughput, and Empirical relationships between VSL and the resulting safety improvements. The literature on the effectiveness of VSL on the simultaneous improvement in both mobility and safety has been mixed (Lee et al., 2003; Abdel-Aty et al.; 2005, Allaby et al., 2006). The findings differed from one location to another based on congestion level and network topology. Lee et al. (2003) showed that real-time VSL systems could reduce crash potential, but at the expense of higher travel times. On the other hand, Abdel-Aty et al. (2005) indicated that VSL systems provided a significant reduction in crash probability only for non-congested conditions. 20

33 However, no substantial safety benefit was associated with the application of VSL for congested conditions. In addition to improved safety, Park and Yadlepati (2003), Lavansiri (2003), Pei-Wei et al. (2004) and Lyles et al. (2004) also showed the effectiveness of some rule-based VSL systems in improving throughput and reducing travel time for vehicles traveling through work zones. In a more recent study, Soriguera et al. (2013) demonstrated the effectiveness of VSL in reducing accident risk, emissions and fuel consumption, but at the expense of higher induced delays. The limitations of the above rule-based strategies can be mainly attributed to the reactive rather than proactive nature of the control. Due to the resultant time lag, reaction to real-time traffic measurements as a basis for real-time control is significantly inferior to the use of predictive information. By the time VSL actions are deployed, traffic conditions may have already reached breakdown, and VSL control is able to do little in resolving the situation Advanced Proactive VSL Control Strategies Advanced VSL control strategies have been developed to address the limitations of their rulebased counterparts. In most of the advanced VSL approaches, future traffic is predicted so that traffic breakdowns are anticipated before they even occur; and, remedial VSL strategies are injected into the system to reduce the inflow to the anticipated jammed area and resolve shockwaves before traffic reaches breakdown. This eliminates the time lag between prevailing traffic conditions and the time needed to optimize traffic signal variables. The VSL strategies should also be applied in coordination as any control action can influence flow in an adjacent 21

34 section of the network. To ensure coordination, control strategies are formulated to optimize the throughput from a system perspective and over a certain time horizon. To maintain consistency, this optimization is repeated after a specified time, with a newly collected data set to update the demand prediction based on the prevailing new traffic state. This type of closed-loop feedback control approach has the advantage of reducing the discrepancy between demand prediction and real demand. Figure 2.3 illustrates the components of such a closed-loop feedback control concept, typically consisting of monitoring, a state estimation/prediction, and an optimization process. Due to its prediction ability and its potential to prevent the problem instead of reacting to it, this type of control action is known as proactive or model predictive control (MPC). The sensors provide data about the current traffic state, which are inputs to a prediction system that, in turn, determines the appropriate action of the controller. Continuous monitoring is, therefore, important. For instance, if there is a deviation between the desired and actual measured system behaviors, the controller changes signals accordingly. Thus traffic control variables are injected in the system to respond to the likely prevailing traffic conditions rather than the previously detected conditions. 22

35 Figure 2.3: An Illustration of Closed Loop Control System Hence, the premises upon whichh MPC approaches are based are the robustness and reliability of the short-term traffic prediction model in representing future traffic states. This prediction is also the basis for triggering VSL and deciding what values of VSL should be adopted on the various sections of the network. The next sub-section discusses different traffic prediction models that were developed and used as part of this MPC approach Advanced VSL Control Design with Traffic Prediction and Dynamic Speed Limit Models Most traffic prediction models adopted in the literature are extensions of Payne's (1971) 2nd order model and consists of threee equations: 1. A conservation of flow relation, 2. A model describing the fundamental traffic flow relationship, and 3. A model describing temporal and spatial speed evolution. The main difference among the various models is based on how the drivers' desired speed (a variable used in the speed evaluation model) has been expressed. Table 2.1 summarizes the various traffic models used in designing a VSL system. 23

36 Alessandri et al. (1999) conducted a VSL study using a 2nd order macroscopic model to generate real time estimates of the dynamic behavior of traffic. The conservation law of vehicles in Equation 10 was used to predict the density. For speed prediction, evaluation of speed over time (Equation 11) was adopted where the external command of VSL was incorporated as a variable in the drivers' desired speed term V[ri (t)]. Equations 12 and 13 expressed the fundamental relationship to be used for a given controlled speed limit based on the parameter 'b'. In other words parameter 'b' described the shape of the fundamental diagram to be used depending on the adopted speed limit. Lenz et al. (1999) used a simple macroscopic spatio-temporal continuum model to predict the mean speed and density. The desired speed was incorporated in the evaluation of the speed model as shown in Equation 15 in Table 2.1, where u represents the control speed. The effect of the speed limit was reflected by a factor that just downscaled the fundamental diagram (see Figure 2.2b). The desired speed formulas described by Alessandri et al. (1999) and Lenz et al. (1999) may, therefore, overstate the effect of speed limits. 24

37 Alessandri et al. (1999) Mean density equation using the conservation law. Where r i (t)and s i (t) are the on and off ramp flows and d i is the section length. The mean speed is equal to the sum of mean speed at the previous time instant, a relaxation term, a convection term, and an anticipation term. Where z, n, k, and t are constants. Where the desired speed, V[ri (t)] is represented by a function of speed and density. Here l and m are positive real numbers. If variable speed limit is applied, the function V[ri (t)] becomes: Here, bi = displayed VSL divided by legal speed limit without VSL. Table 2.1: Models Used for VSL Design r ( + 1) = r ( ) + [ ( ) ( ) + ( ) ( ) ( + 1) = ( ) + t { r ( ) ( ) + z ( )[ ( ) ( )] n [r ( ) r ( ) t [r ( ) k] r ( ) = {1 r ( ) r ( ), = {1 r ( ) r r (10) (11) } (12) Where 0.5 b i 1. If b i = 1, there is no speed limit. If 0.5 b i < 1, speed limits are being applied. ( ) } (13) (14) Lenz et al. (1999) Hegyi et al. Desired speed V(r u) is expressed as a function of speed and density. Where: Fundamental relation between speed, flow and density. Where l m is the number of lanes. (r ) = ( ) ( r r ) (15) u is the speed control input and0.6 u 1,( ) = r, ( ),( )l (16) 25

38 (2005) Mean density using conservation law. r, ( + 1) = r, ( ) + l (, ( ),( )) (17) The mean speed by evolution relationship. Here h is the anticipation constant.,( + 1) =, ( ) + t ( (r, ( )),( )) +,( ), ( ),( ) h (r ( ) r,, ( )) t [r, ( ) + k] (18) Where the desired speed V(r m,i (k)) is: Carlson et al. (2010) Extensions to METANET model: This is a modification of the desired speed equation to incorporate speed limit. To reflect driver s reaction to varying downstream density, the anticipation constant h m,i (k) was divided into 2 terms. Driver's desired speed as a function of speed and density. Rendering the three parameters in the static speed density relationship (Eq. 21) as b m dependent using linear function. h, ( ) = h, r, ( )³ r, ( ) h, r, ( ) < r, ( ), [ ( )]=, [ ( )] r, [ ( )]= r, {1 + [1 ( )]} (19) (20) (21) a [ ( )]= a [ ( 1) ( )] (22) 26

39 Where: n * f,m, r* cr,m and a * m denotes the specific non-vsl values for these parameters while Am and Em are constant parametrs to be estimated based on real data. Also: bm = displayed VSL divided by legal speed limit without VSL. bm(k) = 1 when no VSL applied, otherwise bm(k)<1 For bm(k)=1 all parameters attain the respective non-vsl values. Lu et al. (2010) Wang and Ioannou (2011) Mean density using conservation law. mean speed, by evolution relationship. Where the speed control variable is denoted by u m,i (k). Here, i=segment index and M=link index. Switching rule to the speed limit tracking mode from the car following model. Here v i (k) and V R,i (k)are the speed of i th vehicle and imposed speed limit, respectively, in section i at time kt. r, ( + 1) = r, ( ) +,( + 1) =,l, (r, ( ), ( ) r, ( ),( ) + ( ) ( )),( ) + t (,( ),( )) +, (23),( ), ( ), 1t(,r,+1 r, r, + k) (24) ( + 1) = ( ) (25) ( ),, ( ) < ( ) >, ( ) ( ) < (, ( )) (, ( )), h (26) 27

40 Where: ( ) = [, ( ) ( )], ( ) = r ( r ( ) + 1) + c (27) ( )[ ( ) ( ) ( )] + t r ( ) ( ) m( ) t r ( ) r ( ) r ( ) + k l ( ) ( ) r ( ) + k The desired speed is V e (r i (k)). r ( ) =, r ( ) r ; r + r r, r ( ) r. r r r r r ( ) (28) (29) Hadiuzzaman and Qiu (2012) Demand (s) and Supply () functions. Here due to capacity drop, ' Q b = (1-) Q b where Q b is the bottleneck capacity and is the fraction of capacity drop. Flow (q) and density (r) s, ( ) =,r ( )l r ( ) r r ( ) > r, ( ) = r ( ) r, ( ) = (r r ( ))l r ( ) > r, (30) evaluation equations. ( ) = min {s ( ), ( )} (31) (32) Speed evaluation equation based on piecewise linear For cells with no VSL, 28

41 triangular FD. Here u i is the variable speed limit at cell i. = r ( + 1) ( r r ( ) 1) ( r r, 1) For cells with VSL control, ( + 1) = ( ) r ( + 1) r r, ( ) r ( + 1) r (33) (34) Zegeye et al. (2010) Prediction of i th vehicle's position x i (k) depending on acceleration function a i. ( + 1) = ( ) + ( ) ( ) (35) ( + 1) = ( ) + ( ) (36) Where, x i (t), v i (t) and a i (t) are the position, speed and acceleration of the i th vehicle at time t = k.t s. Here k is the simulation time step counter and t s is the sampling time. Where: If speed limit is applied, the acceleration is: ( ) = (,( s) ( s)) (37) where, is the speed limit of the ith vehicle and (s) s the reaction delay.otherwise, acceleration is determined using GHR car following model: ( ) = a ( ( s) ( s)) (38) ( ( s) ( s))) g Here, a,, g are the model parameters. 29

42 Hegyi (2005) used an extended version of the macroscopic traffic flow model METANET, which was an extension of Payne's model by Papageorgiou (1990) (Equations17-19). Hegyi introduced two major modifications to the original equations: incorporation of the speed limit (Equation 19), and introduction of two anticipation constants h high and h low to distinguish between spatially increasing or decreasing density respectively (Equation 20). Hegyi claimed that splitting the anticipation constant into two terms could better reproduce shock waves and capacity drop. Hegyi tested such models on a simulated transportation network in METANET and showed their ability to suppress and, in some cases, even eliminate the effects of shockwaves, resulting in safer traffic conditions. Although the models were not calibrated against real data, the authors claimed that the prediction models were successful in describing the dynamic behavior of real traffic and had the capability of reproducing all relevant phenomena. Later on Hegyi and Hoogendoorn (2010) proposed a VSL control strategy called "SPECIALIST", where VSL was triggered based on shockwave detection. The SPECIALIST algorithm consists of four steps: shock wave detection, control scheme generation, resolvability assessment and control scheme application. According to shock wave theory, six points on the fundamental diagram were chosen to represent how the shock waves would be resolved. They tested the algorithm on a 14 km freeway section on the Dutch A12. Evaluations of the VSL control algorithm indicated that 80% of the shock waves that were theoretically resolvable were resolved in practice. 30

43 Carlson et al. (2010) proposed a quantitative VSL model where the equation for the evaluation of the speed, density and flow followed the same process as the previously used macroscopic models. Although the drivers' desired speed (Equation 21) was same as Hegyi's, the incorporation of speed limits was done somewhat differently, as shown in Equations 22. Once again, Carlson s model attempted to modify the fundamental diagram by scaling the parameters of the curve, such as the free flow speed and the critical density, by the ratio of the imposed VSL and the original speed limit (b m ), as already seen in some of the previous studies. In another study, Lu et al. (2010) modified the previously developed 2 nd -order METANET model, which they then implemented into MATLAB simulator to evaluate its performance for VSL and ramp metering applications. The models were simplified METANET models that introduced two major modifications: There was no further parameterization of the speed control variable, and There was no assumption for the fundamental diagram (FD). Equations 23 and 24 were used to describe the evaluation of the mean density and speed. However, the speed control variable in Equation 25 was modelled as a linear approximation. The authors described that the advantage of this approach was the effective avoidance of model mismatch caused by discrepancies between field data and the FD curve. However, the simplification of the basic METANET model assumed that the control variable was linear as the speed variable was the designed VSL. This can only be justified if there is a strictly enforced VSL and where the practical observed speed is close to the designed VSL. 31

44 Another study in this area was conducted by Wang and Ioannou (2011), who stated that changing the speed limit for a freeway segment for a long time (e.g., in work zones) results in changes of the shape of the FD. They argued that most of the existing research work, such as the studies conducted by Alessandri (1999), Lenz et al. (1999) and Carlson et al.(2010), were based on modification of the equilibrium flow/density curve in modeling VSL. These models only considered the effects of VSL on steady-state speed values and ignored the transient effects of VSL. However, VSL systems are designed to control this transient effect of shock waves, in order to achieve smoother flow. Hence, the authors modelled the transient effects of VSL by proposing a new model derived from driver behavior when VSL is present. The authors proposed a speed limit tracking model in addition to the car following model (Equations 26-29). They described the basis of the proposed model as follows: When any VSL command is applied, drivers will follow the command and will ignore the downstream traffic condition; otherwise, they will follow the vehicle in front of them ignoring the VSL command. Once a safe gap distance is reached, drivers will consider following the VSL command if the vehicle speed is larger than the VSL display. The proposed model provided more accurate descriptions of the transient effects of VSL. However, the authors did not optimize the speed limits for the network, rather it was based on some preselected speed limit values. Hadiuzzaman and Qiu (2012) developed VSL control strategies by modifying the FD of the Cell Transmission Model's (CTM). The authors selected some fixed bottleneck locations on the freeway corridor of Whitemud Drive in Edmonton, AB, Canada. A triangular FD was used for each cell of the freeway, because the slopes of its two sides and apex are parameters in the CTM. 32

45 They defined the demand and supply functions (Equations 30), taking into consideration the capacity drop phenomena, and derived the density and speed dynamics for each cell (Equations 31-33). The authors used MPC approach; and, the adopted strategies were coupled with many important phenomena, such as capacity drop and shockwave formation. However, their approach was mainly suitable for recurrent congestion resulting from the presence of a fixed bottleneck. This study seems to have limited application for the case of non-recurrent congestions (e.g., incidents). Later on, Yang et al., (2013) claimed that the model used by Hadiuzzaman and Qiu (2012) made an approximation by assuming the speed-density relation as a liner function which might lead to inaccurate prediction. Therefore, they used an enhanced module by incorporating Kalman Filter method to eliminate prediction inaccuracy. In a more recent study, Kattan et al. (2014) used MPC approach and METANET model for developing a VSL system that takes as its only input the space mean speed (SMS) derived from vehicle probes constantly moving in the network. Overall, the findings from this paper indicate the efficiency of probe-based VSL in harmonizing speed for the examined range of traffic conditions. All of the above mentioned studies used macroscopic prediction models to describe the behavior of traffic. To date, only Zegeye et al. (2010) have used a microscopic traffic prediction model with VSL applications. The state variables of such models were acceleration, speed and position of each vehicle. Knowing the current position and speed, each vehicle's position was updated 33

46 using Equations 35 and 36. If VSL was applied, the acceleration was determined as a function of displayed speed limit (Equation 37); otherwise, the acceleration was determined using GHR (Gazis-Herman-Rothery) car following model (Equation 38). The authors used MPC approach for optimizing VSL using microscopic models which can better represent drivers' behavior. However, in the model only longitudinal behavior of drivers was considered for a single lane unidirectional road with no consideration for lane changing behavior on a multilane complex road network with ramps. 2.4 Impact of VSL on Traffic Safety The approaches discussed so far have commonly aimed at smoothing traffic by relieving congestion and enhancing throughput by minimizing travel time. The positive impact on traffic safety by VSL is mainly achieved from the homogenization of speeds, which decreased the probability of collisions. Thus, the reduction in speed variance was mainly used as a surrogate measure of improved safety. A more accurate evaluation of the safety benefits of VSL is, however, the assessment of model effectiveness in reducing the potential for freeway crashes. Most of the existing crash prediction models found in the literature used a static measure of traffic flow, e.g. average speed for the prediction of crash potential. However, these models are not appropriate for a real-time application to driver warning systems. Thus, it becomes necessary to develop crash prediction models that are able to relate real-time variation in traffic flow characteristics to crash potentials. 34

47 Lee et al. (2003) conducted a study to develop a statistical crash prediction model that estimated quantified crash potential on the basis of real-time traffic flow characteristics. The real-time crash prediction model developed by Lee et al. (2003) was able to estimate a dynamic measure of crash risk that was updated online as new traffic measurements became available, reflecting the fluctuation of traffic conditions. In addition, the model was able to capture any spatial or temporal changes in the crash risk that may have existed in adjacent road segments. However, the study used a predefined threshold of crash potential that was dependent on road geometry. Furthermore, the reduction in crash potential was higher for lower threshold values, but lower values generally resulted in increased travel times. Hence, it was necessary to evaluate a tradeoff between safety benefits and increased travel times. Allaby et al. (2006) used the model by Lee et al. (2003) to quantify the safety impacts of candidate VSL control strategies on an urban freeway in Toronto, Canada. This study differed from that of Lee et al. (2003) in the sense that, while Lee et al. (2003) attempted to intervene with VSL whenever the crash potential exceeded some threshold value, Allaby et al. (2006) designed a VSL control strategy based on threshold values of occupancy and volume conditions and then evaluated its impact by developing a categorical crash prediction model using microsimulation. The VSL strategies of Allaby et al. (2006) were shown to be efficient only for a limited range of traffic conditions. Abdel-Aty et al. (2006) conducted another study on I-4 in Orlando, Florida, USA using the same approach developed by Lee et al. (2003) but with slightly different VSL strategy. The control logic was entirely based on the detected average speed and used evaluation criteria that were 35

48 quite simplistic in nature, such as upstream lowering and downstream raising distance, rate of changing of speed limit values, and gap distance. The study concluded that VSL did not affect the crash likelihood at low-speed regimes, but was effective for high-speed regimes. These findings of the study seem counterintuitive, as it indicates that VSL would not be advised during congested periods (i.e. peak periods). Recently, Talebpour et al (2013) studied the impact of early shockwave detection on breakdown formation and safety using speed harmonization as a control strategy in a Connected Vehicle environment. A reactive algorithm based on drivers' cognitive risk showed significant improvement in traffic flow characteristics under congested conditions. In a more recent study, Yu and Abdel-Aty (2014) used an extension of the METANET model to optimize VSL values to minimize the total crash risk. The study concluded that the proactive VSL system was able to improve traffic safety by decreasing crash risk and enhancing speed homogeneity under both the high and moderate compliance levels. The review of the existing studies offered some initial insight into the relationship between the choice of control strategy parameter values and the resulting safety improvements. Unfortunately, no strategy could be identified that could provide improvements for traffic safety and travel time under all degrees of congestion. Hence, it is expected that some modification to the algorithm is necessary to obtain an optimal VSL system that is able to provide simultaneous safety and travel time benefits and be effective over a wide range of traffic conditions. 36

49 Recently, there has been considerable interest in using simulation based surrogate safety assessment models to assess the safety impact of future intelligent vehicles. For instance, Gettman and Head (2003) developed a widely used surrogate assessment model (SSAM) that could identify conflicts by analyzing each vehicle s interaction using vehicle trajectory records. Several traffic conflict techniques (TCT) have also been developed for traffic safety analysis. With the recent advancements in computer techniques, more detailed conflict information can be generated, which have enabled researchers in examining the capabilities of microsimulation models to support TCT for deriving surrogate safety measures for freeways. In TCT-based safety analysis, many objective measures have been developed by researchers which can be broadly classified into four groups, i.e., time-based, distance-based, deceleration-based and other composite measures (Yang et al., 2010). Although all of these TCT-based studies were aimed at evaluating highway safety measures, none of them examined at the applicability of these indicators in evaluating the impact of VSL in improving safety. It is expected that the introduction of Connected Vehicle technology will provide a basis to detect these individual vehicle trajectories which can be used as relatively high precision input data to derive such surrogate safety measures for freeways. 2.5 Impact of VSL on Emission/Fuel Consumption The review of the current practices of VSL has thus far been mainly focused on applications in freeway operations, work zones, and safety conditions. The environmental benefits of VSL have been largely ignored. A number of previous studies have shown that mobile emissions, especially nitrogen oxides, were highly correlated with high speeds and that these emissions 37

50 could be significantly reduced if traffic speeds were maintained at appropriate levels. In addition, greenhouse gas emissions are higher during stop-and-go and congested traffic conditions than in free flow conditions. Current vehicle emission/fuel consumption models can generally be classified as aggregate models (e.g., MOBILE6, COPERT III, MOVES etc) and microscopic models (e.g., CMEM, VT- Micro, POLY etc). Aggregate models which are based on the number of trips, vehicle miles traveled, number of stops per trip, average speed of vehicle etc. which do not include important parameters that can differentiate drivers' behavior such as the acceleration and deceleration manoeuvres of different drivers and vehicle types. On the other hand, dynamic or microscopic fuel consumption and emission models are able to assess environmental impacts of traffic control measures. These models use the second-by-second speed and acceleration of individual vehicles to estimate or predict emissions and fuel consumption and are more accurate than average-speedbased models. Rakha et al. (2004) developed the Virginia Tech microscopic energy and emission model (VTmicro model), which was based on experimentation with numerous polynomial combinations of speed and acceleration levels. Zegeye et al. (2010) used this VT-Micro model and MPC approach to assess the impact of the dynamic speed limit control in reducing CO2 emissions, fuel consumption and travel time. Their study concluded that a reduction of TTS alone could not meet the requirement of reducing emissions. Grumert et al. (2013) introduced a cooperative VSL system using Connected Vehicles to compare its performance with an existing VSL system. The cooperative VSL system resulted in a more harmonized flow, less varying speed pattern, and a 38

51 reduction of high acceleration and deceleration rates which reduced environmental impact. In order to evaluate the effectiveness of VSL system, Castro et al. (2014) developed a single indicator called Positive Accumulated Acceleration (PAA), which was based on accumulated acceleration in a section (or instantaneous speed variations). The results of the study showed slightly increased throughput and a positive impact on emission reduction, but increased TTS. Soriguera et al. (2013) demonstrated the effectiveness of VSL in reducing accident risk, emissions and fuel consumption, but at the expense of higher induced delays. Lee et al. (2013) developed a Cooperative Vehicle Intersection Control (CVIC) for urban intersection by optimizing vehicle trajectories to avoid crashes and examined positive impacts on mobility and environment. Wang et al (2015) developed a connected VSL control and vehicle acceleration control to resolve moving jam. In this study the link-level traffic controller regulates speeds through VSL systems to resolve stop-and-go waves, while the intelligent vehicles control accelerations through vehicle propulsion and brake systems to optimize their local situations. The simulation results showed that the connected VSL and vehicle control system improved total time spent in the network and average fuel consumption rate compared to the uncontrolled scenarios. These studies provided a good indication that a VSL system, if operated properly, may provide a promising solution to balance travelers' need for simultaneous mobility and conservation of the environment. 2.6 Impact of VSL on Driver Behaviour 39

52 Recent VSL research has so far been mainly focused on applications in freeway operations and safety condition, with some applications on reduction of vehicular emission and fuel consumption. The effect of VSL on driver behaviour such as; lane changing, sudden acceleration/deceleration was little researched so far. For example, Knoop et al., (2010) examined the influence of VSL on the distribution of lane usage near merging zones in the vicinity of an on-ramp. The study compared the lane usage distribution just upstream of the onramp with the distribution elsewhere. They concluded that VSL system significantly changed lane usage distribution, thereby increased the capacity in the underutilized right lane, which in turn increased the road capacity. Duret (2012) investigated the impact of VSL on lane distribution in French motorway and confirmed the results of the previous study by Knoop et al. (2010). They showed that VSL modified the lane distribution pattern, homogenized the usage of lanes, reduced underutilization of the slow lane, and accordingly increased the overall capacity of the section. Another study by Weikl et al., (2013) observed a similar homogenizing effect of VSL system as the previous two studies. Grumert et al. (2013) extended an existing VSL system by adding cooperative system functionality to compare its performance with the existing VSL system. The study used vehicle's acceleration rate to recommend speed limits which were communicated to vehicles via an onboard roadside unit. The developed cooperative VSL system resulted in a more harmonized flow, smaller speed variance and reduction of high acceleration and deceleration rates, which in turn resulted in reduced negative impact on the environment. Baskar et. al., (2008) proposed a MPC based VSL approach to determine optimal speed limits and lane allocations using intelligent vehicles. The approach was applied to a simple simulation example which showed that the 40

53 scenario with intelligent vehicles resulted in an improvement of total time spent of about 10% compared to the uncontrolled case. Roncoli et al. (2015a, 2015b) developed an integrated traffic control with ramp metering, VSL and lane changing control considering Vehicle Automation and Communication Systems based on a first-order multi-lane macroscopic model. The model was calibrated and validated with real data and showed benefits in terms of alleviating congestion and improving safety. Wang et al., (2015) developed a connected VSL control and vehicle acceleration control aiming to resolve moving jam. In this study the linklevel traffic controller regulated speeds through VSL systems to resolve stop-and-go waves, while the intelligent vehicles controlled accelerations through vehicle propulsion and brake systems to optimize their local situations. The simulation results showed that the connected VSL and the intelligent vehicles (equipped with car following control system) improved total time spent in the network and reduced fuel consumption rate compared to the uncontrolled scenario. 2.7 VSL and Driver Compliance/Enforcement The likely success of VSL systems are largely influenced by drivers compliance to the posted speed limit. In most jurisdictions, driver compliance with posted speed limits is highly influenced by the type and extent of speed limit enforcement (Povey et al., 2003; Benekohal et al., 2008). Therefore, many VSL systems, such as those implemented in the UK and the Netherlands, employ automated speed enforcement. Despite the fact that there is an increasing interest in VSL deployment on North American freeways, there are still barriers to automated speed enforcement (Hellinga et al., 2010). In this context, it becomes important to understand the influence of driver compliance on the effectiveness of VSL systems. 41

54 There are a number of studies that consider the impact of driver compliance rate to VSL. Park and Yadlapati (2003) examined the application of VSL in work zones in Virginia using microsimulation. They considered three driver compliance levels, namely 70%, 80% and 100%. However, their study did not state which compliance level would lead to the minimum acceptable performance. Lee and Abdel-Aty (2008) used a driver simulator to observe driver behavior on a freeway section equipped with a VSL system. The study showed that the presence and type of message displayed on the variable message signs (VMS) had a statistically significant impact on the level to which drivers complied with the downstream speed. Kwon et al. (2007) conducted a study on I-494 in Minnesota to assess driver compliance to VSL by defining two numerical expressions: 1. The difference between the vehicle speed and the posted speed that drivers were about to encounter, and 2. The change in the vehicle speed distribution before VSL to after VSL. The authors attempted to correlate these two numbers and found that the value of the correlation coefficient for different days ranged between 20% and 60%. They also found that the correlation was weaker as the difference between the actual traffic speed and the posted speed limit increased. This finding suggests that drivers were less likely to comply with VSL if the posted speed limit was significantly different from the speed they would otherwise choose. It is to be noted that the VSL was not enforced, rather advisory, in this case study. 42

55 Helinga et al. (2010) conducted a microsimulation study on the Queen Elizabeth Way freeway in Toronto, Canada, where four levels of compliance (low, moderate, high and very high) were defined. The results of the study indicated that the impacts of VSL, in terms of safety and travel time, were quite sensitive to the level of driver compliance. As the compliance to the speed limit increased, the safety benefits of VSL also increased. However, an increase in the travel time resulting from VSL was more pronounced with increased compliance with the posted speed limit. The authors explained that the increase in travel time depended on the parameter value for the chosen VSL strategy. Nevertheless, the study provided valuable insight on the impact of driver compliance on the operational and safety performance of VSL. The study also indicated that the selection of the VSL operating strategy could not be done independently of the decision regarding speed limit enforcement. 2.8 Summary In this chapter an overview of VSL control strategies, ranging from early rule-based approaches to the most advanced network-wide coordinated approach is provided along with their associated potential benefits and areas for improvement. The likely safety and environmental benefits of VSL strategies are also discussed with some further related aspects of VSL application, such as drivers' behaviour and compliance to VSL. The literature review suggested that, unlike rule-based VSL strategies, which have limited potential due to their reliance on simplistic localized control logic, network-wide coordinated proactive VSL control strategies have the inherent capability of acting proactively while 43

56 anticipating the complex behavior of traffic. However, the majority of the developed advanced proactive VSL strategies were based on the 2nd order macroscopic traffic flow model and utilized aggregate traffic speed and volume from point detection technology. Deployment of such technologies corresponds to high installation, maintenance costs, as well as high failure rates. In addition, macroscopic models used for VSL design deal with traffic flow in terms of aggregate variables (such as average speed, flow and density) and do not distinguish the behavior of individual drivers in a traffic stream. With the current advances in Connected Vehicles (CV) and Autonomous Vehicle (AV) initiatives, this thesis therefore, explores the scope of incorporating a 'Microscopic Approach' to the design of VSL control algorithms by focusing on individual driver's behaviors. In this microscopic approach, modelling driving behavior (e.g., acceleration, deceleration, lane change, compliance etc.) are important inputs to be considered for VSL application aimed at improving mobility, safety and sustainability of the network. The use of microscopic models also has great potential for achieving environmental benefit from VSL system implementation. Current aggregate emission/fuel consumption models do not include important parameters that can differentiate drivers' behavior such as the acceleration and deceleration maneuvers Dynamic or microscopic models, on the other hand, use second-bysecond microscopic data in terms of each individual vehicle's speed and acceleration and are more accurate than average-speed-based models. Moreover, none of the studies examined the impact of VSL on synchronizing driver behaviour that would result in a simultaneous improvements in mobility, safety and environment as a result of this synchronized behaviour in a multi-lane roadway. Therefore, there is a need for a framework able to continuously anticipate driver s decisions in response to VSL strategies and proactively optimize these strategies to meet 44

57 the above safety, mobility and environmental objectives. Chapter 3 presents a rigorous description of the methodology and framework to develop this novel anticipatory VSL approach. 45

58 CHAPTER 3: METHODOLOGY Introduction This chapter provides an overview of methodology for developing the novel proactive VSL control algorithm. First it describes the microscopic models used in this research including a traffic flow prediction model, lane changing model, surrogate safety model and a emission/fuel consumption model. Next it discusses about the implementation of the VSL algorithm in a microsimulation framework by developing a multi-criteria objective function. This chapter also describes the VSL trigger condition developed in this thesis and how real time driver's compliance was modeled to adjust the optimal VSL values. The last section provides an overview of the solution algorithm for the objective function. The final section concludes the chapter with the summary of the overall developed algorithm and methodology. 3 The content of this chapter has been taken from the paper: Khondaker, B. and Kattan, L., Variable Speed Limit: A Microscopic Analysis in a Connected Vehicle Environment, Transportation Research Part C: Emerging Technologies, Volume 58, pp , September

59 3.2 Overview of The Methodology In order to assess the sustainability impacts covering mobility, safety and environment, this thesis incorporated three distinct components into a single VISSIM microsimulation framework using microscopic data. These components were: (i) a microscopic traffic flow prediction model to minimize TTT (total travel time) of all vehicles in the network, (ii) a surrogate safety model TTC (time to collision) to capture the instantaneous safety between each individual pair of vehicles, and (iii) a microscopic emission and fuel consumption model 'VT-Micro model' (Rakha et al., 2004) to measure Emission (E)/Fuel Consumption(FC). Finally, a system-wide optimization using a multi-objective function was formulated to obtain the VSL values that: (i) minimized TTT, (ii) maximized safety as reflected in TTC, and (iii) minimized emission (E) and/or fuel consumption (FC). The optimization was conducted over a short-term prediction horizon of five minutes and repeated in a rolling horizon fashion. The details of the methodology has been described in a flow chart in Figure 3.1. In this research, it has been assumed that Road Side Equipment (RSE) collected data from vehicles and broadcasted this information via DSRC. Also, data used to design VSL were available at the microscopic level in a Connected Vehicle environment with the trajectory of the vehicles tractable. In other words, the input parameters involved the speed and position of each vehicle; consequently, depending on the predicted state of each vehicle, VSLs were adopted for each vehicle individually. 47

60 Figure 3.1: Flow Chart of the VSL Algorithm To develop a proactive VSL control strategy, Model Predictive Control (MPC) technique was used in this research (Maciejowski, 2002). In MPC approach, the future state is predicted so that traffic disturbances are anticipated before they even occur, and control strategies are injected in the system proactively. The MPC approach has four main components: (i) data input and traffic state estimation, (ii) traffic state prediction over a short time prediction horizon (Np), (iii) optimization using an objective function based on rolling horizon, and (iv) a control action that implements the first step of the optimization results. In a rolling horizon scheme, only the first optimized value is implemented. The horizon is then shifted one sample time (i.e., 1 minute) 48

61 with new information becoming available from the system and fed-back to the optimization function. The control time step used in this study was 1 minute, meaning that the VSL system was able to adjust the posted speed limit values every minute if required. Thus, the whole process was repeated continuously until the end of the simulation. To limit the computational complexity, a control horizon (Nc) was applied, after which the control variable did not change Microscopic Traffic Flow Model to Calculate Total Travel Time (TTT) A microscopic traffic flow prediction model was used in this study. The model was a general discretized longitudinal kinematic motion equation of vehicles. The general discretized longitudinal kinematic motion of the vehicles can be described by the following equations: ( + 1) = ( ) + ( ) (1) ( + 1) = ( ) + ( ) + ( ) (2) where ( ), ( ) and ( ) are the position, speed and acceleration of the i th vehicle in the network at time ; and, is the simulation time step size (s). In equations 1 and 2, the speed ( ) and position ( ) of any vehicle at current time instant (t) can be obtained from vehicle trajectory data. The acceleration term (a i ) is mainly a function of the corresponding VSL action and is described in the following paragraph. The driving process can be divided into two different regimes based on the corresponding behavior of drivers and traffic situation: free flowing and car following. The behavior of drivers as reflected by this acceleration term can take different forms, depending on the status of the episodes that drivers are in at a particular time instant. In order to reflect this behavior, the 49

62 Intelligent Driver Model (IDM) (Treiber et al., 2000) was adopted in this research. Compared to other car following models, IDM has only a few parameters making it easy to calibrate. In addition, while most of the car following models (e.g., GHR model, Gazis et al., 2000) describe only congested traffic state, IDM has the capability of describing both regimes free flow and congested state making it suitable for the adopted approach of this research. Moreover, in many of the stimulus-response based models, the acceleration of the vehicles is modeled by introducing a delay related to the reaction time. However, IDM model does not use the driver reaction time as a delay parameter for the determination of acceleration of a vehicle, which also makes it computationally suitable. In IDM, the acceleration can be defined by the following equation: =, 1, (, ) (3) where is the speed of the i th vehicle,, is the reference speed (variable speed limit) of the i th vehicle, is the actual gap between leading vehicle i-1 and following vehicle i (i.e., = ), is speed differential between leading vehicle i-1 and following vehicle i (i.e., = ),, is the maximum comfortable acceleration of the i th vehicle, is the free flow acceleration exponent, and (, ) is the minimum desired gap shown by the following equation: (, ) = + max + 2,,,0 (4) where is the mimimum inter-vehicular distance at standstill, T is the safe time headway and, is the maximum comfortable decceleration of the i th vehicle. 50

63 In equation 3, the acceleration is a superposition of two acceleration terms: free flow acceleration and car following acceleration. Under the free flow condition, when the actual gap of vehicles increases (i.e., >>0), the influence of the second term becomes negligible. Hence, the free flowing acceleration of the i th vehicle can be written as:, =, 1, (5) Equation 5 shows that, as the speed of vehicle i ( ) reaches the displayed speed limit (,), the acceleration approaches zero. However, when is greater or less than,, the acceleration (, ) becomes negative or positive. When the traffic situation becomes congested, actual speed, speed limit, and actual gap decrease, allowing the last term in equation 3 to become significant. Thus, the car-following acceleration of the i th vehicle can be written as:, =, 1 (, ) (6) Equation 6 shows that, when actual gap approaches the minimum desired gap (, ) in a congested situation, acceleration, decreases to zero. If becomes less than (, ), the acceleration becomes negative and the vehicle actually decelerates. In developing the VSL algorithm, it was necessary to define when drivers would switch from the free flowing state to the car following state. The following switching rule was used in this research based on minimum desired gap (, ) and actual gap between two consecutive vehicles: 51

64 =,, (, ),, (, ) < (7) Equation 7 shows that, when the actual gap between two consecutive vehicle is greater than the minimum desired gap, they are in a 'free flow state'. However, when the actual gap is less than the minimum desired gap, the vehicles are in a 'car following state'. Thus with the value of, equations 1 and 2 can be used to optimize TTT of all vehicles as shown by equation 8: ( ) = ( ) ( ) ( ) (8) where denotes the length of prediction horizon, and N is the total number of vehicles Microscopic Lane Changing Model MOBIL to Estimate/Predict the Trajectory of Individual Vehicle The microscopic traffic flow prediction model described above only considered longitudinal kinematic motion equation of vehicles with no consideration for lateral movement (i.e. lane changing maneuver). For a multi-lane roadway, it is necessary that the model reflects the lane changing behaviour of drivers over the prediction horizon. Hence, a microscopic lane changing prediction model is essential to estimate/predict the likely trajectory of individual vehicle for a given prediction horizon. For this purpose, the general deterministic lane changing model MOBIL (Minimizing Overall Breaking Induced by Lane Change) by Treiber and Kesting (2009) was used as described next. MOBIL model for microscopic car-following models describes the rational decision to change lanes andtherefore deals only with the operational decision process of drivers. When a lane 52

65 changing decision is considered, it is assumed that a driver makes a trade-off between the expected own advantage and the disadvantage imposed on other drivers (Kesting et al., 1999). In particular, the model includes the follower in the target lane in the decision process. Therefore, for a driver considering a lane change, the subjective utility of a change increases with the gap to the new leader in the target lane. However, if the speed of this leader is lower, it is favorable to stay in the present lane despite the smaller gap. A criterion for the utility including both situations is the difference in the accelerations after and before the lane change. In the MOBIL model, therefore, it is proposed that the utility function should consider the difference in vehicle accelerations (or decelerations) after a lane change, calculated with a microscopic longitudinal traffic model. The higher the acceleration in a given lane, the nearer it is to the ideal acceleration on an empty road and the more attractive it is to the driver. Therefore, the basic idea of the proposed lane-changing model is to formulate the anticipated advantages and disadvantages of a prospective lane change in terms of single-lane accelerations. MOBIL is a general deterministic lane changing model that derives lane changing rules for both discretionary and mandatory lane changes for a wide class of car-following models. The utility of a given lane and the risk associated with lane changes are determined in terms of longitudinal accelerations calculated with a microscopic car following model, which is IDM model in this case. This model is applicable for both symmetrical and asymmetrical lane changes. Lane changing decisions are based on two criteria; incentive criteria and the risk associated with a lane changing decision. Thus lane changes take place, if: 1. Incentive Criteria is satisfied: which means the potential new target lane is more attractive to derivers, and 53

66 2. Safety Criterion is satisfied: which means the change can be performed safely. Both of these criteria are based on the accelerations of vehicle in the old and the prospective new lanes, as calculated with the longitudinal IDM model. A specific lane change incident depends on the behavior of two consecutive following vehicles in the current lane and the target lane, respectively. This scenario can be described by Figure 3.2: Figure 3.2: A lane changing scenario, subject vehicle C considering lane change to the left (Treiber and Kesting, 2009) The following notations apply for Figure 3.2: Vehicle C: subject vehicle considering a lane change, Vehicle O : following vehicle in current lane, Vehicle n : following vehicle in the target lane, a c : acceleration of vehicle C in the actual lane, : acceleration of vehicle C in the target lane, : acceleration of the old follower, : acceleration of the new follower, 54

67 Safety criteria is satisfied if, after the lane change the deceleration imposed on the back vehicle ( ) of the target lane after a possible lane change does not exceed a specific threshold ( ). Thus: (9) Here, is calculated from the longitudinal model IDM and therefore, contains all the microscopic variables such as gap, speed, speed differential. Thus, if the follower is faster than the subject vehicle, larger gap is required between them and vice versa Incentive criterion is satisfied if, a lane change improves individual local traffic situation of a driver. Thus, the own advantage on the target lane (as measured by the increased acceleration or reduced braking deceleration) is compared against the disadvantage imposed to other drivers (measured by the decrease acceleration or increased braking deceleration). Since drivers are usually selfish, the disadvantages imposed on the other drivers are weighted by a politeness factor p whose values are typically less than 1. Thus the resulting incentive criterion is: + [ + ]> (10) Here, the first two terms denote the "own advantage" of a possible lane change of the subject vehicle. Also, p is the politeness factor which weights the total advantages (acceleration gain or less, if negative) of the two immediately affected neighbour. In summary the incentive criteria is satisfied if the own advantage ( i.e. acceleration gain) is higher than the weighted sum of the disadvantages (i.e. acceleration losses) of the old and new and old followers and the threshold. 55

68 The MOBIL lane changing model has some specific features which makes it different than the other lane changing models. This is denoted by the politeness factor p which can be interpreted as degree of altruism of drivers and can take different values. More specifically: p > 1 : represents a very altruistic behaviour. p in the range of [0, 0.5] : represents a realistic behaviour which means advantages of other drivers have a lower priority, but not neglected totally. p = 0 : represents a purely selfish behaviour, although even these selfish drivers do not ignore the safety criterion. p <0 : represents a malicious personality who accept own disadvantage in order to frustrate others. Even these malicious drivers do not ignore the safety criterion. There is also a very special case where p = 1 and =0, thus the incentive criteria is simplified as: + + > + + (11) This means lane changing takes place whenever the sum of the accelerations of all neighbour drivers increases after the lane change, or, in other words, the overall decelerations are minimized. The MOBIL model can also be used to model forced lane changes due to presence of on-ramp or off-ramp and even for lane closure due to incident. This is done by introducing a lane usage bias 56

69 bias in favour of the target lane. Thus for on-ramp traffic, bias is negative representing a bias to the left as shown by equation 12: + [ + ] bias > (12) Similarly, for a lane closure scenario, is positive for the vehicles in the left lane that is about to close, representing a bias towards the right as shown in equation 13: + [ + ]+ bias > (13) In this thesis, the asymmetric lane changing which is mostly common in European country is not considered and therefore, is not covered. The rational for using of MOBIL model in this research has several advantages such as : 1. First, compared with the other explicit lane-changing models, the assessment of the traffic situation is transferred to the acceleration function of the car-following model (IDM model in this case), which allows for a compact and general model formulation with only a small number of additional parameters. 2. Second, it is ensured that both longitudinal and lane-changing models are consistent with each other. For example, since the longitudinal model is collision-free, the combined models should be collision-free as well. 57

70 3. Third, any complexity of the longitudinal model such as anticipation is transferred automatically to the lane-changing model. 4. Finally, the braking deceleration imposed on the new follower in the target lane to avoid accidents is considered an obvious measure for safety. Thus, safety and motivational criteria can be formulated in a unified way in the MOBIL model Surrogate Safety Model to Calculate Time to Collision (TTC) In order to optimize safety, a surrogate safety measure TTC between each pair of vehicles has been adopted. TTC can be defined as the time it would take a following vehicle to collide with the leading vehicle if both vehicles movements remain unchanged. If proper precautions are taken within this time interval, collision can be avoided. TTC at a particular time instant between a pair of vehicles can be described by the following equation:, = ( ) ( ) ( ) ( ) (14) where t is the time interval, i is the leading and i+1 is the following vehicle. TTC, therefore, only depends on the same variables as IDM model, such as, instantaneous speed ( ) and position ( ), between two vehicles. These two variables, in turn, depend upon the instantaneous acceleration (a i ) of that pair of vehicles, where a i is a function of the variable speed limit. Since one of the main objectives of VSL control is increased safety by reducing speed differential 58

71 among vehicles (denominator in equation 9), the objective is the maximization of TTC by minimizing speed differential based on the position of each pair of vehicles. Bachmann et al. (2011), however, identified two cases where equation 14 may give erroneous results: i) when the leading (i) and following (i+1) vehicles are traveling at the same speed, and ii) when the leading (i) vehicle is travelling faster than the following (i+1) vehicle. In order to overcome this limitations, the revised definition in Bachmann et al. (2011) was adopted:, = ( ) 1( ) + 1( ) ( ), ( ) > ( ) ( ) ( ) (15) VT-Micro Model to Calculate Emission/Fuel Consumption In this research, VT-Micro model developed by Rakha et al. (2004) was adopted, since it has gained significant attention from several researchers for evaluation of the environmental impact of traffic management, operations, and ITS strategies. VT-Micro is a microscopic dynamic model that provides emissions and fuel consumption using second-by-second speed(vi) and acceleration (ai) of individual drivers. The model has the following form: log / = (, ) (16) where, / = fuel consumption (FC) or emission rates (E) (l/hr or mg/s) k = model regression coefficients = speed (m/s) = acceleration (m/s 2 ) 59

72 Thus, unlike planning level emission/fuel consumption models, such as EMFAC (Air Resources Board, 2011) and MOVES (US EPA, 2001) which use aggregate profiles of drivers, this model can accurately estimate the emission level and fuel consumption by taking into account each driver's start, stop, acceleration and deceleration behaviour. 3.3 Implementation of The VSL Algorithm In this research, it has been assumed that trajectories of all vehicles in the network are available, providing continuous information of each vehicle's speed ( ) and position ( ). Therefore, a multi-objective function was optimized to assess the sustainability benefit of the VSL algorithm. This is described in more detail in the following subsections Formulation of a Multi-Objective Function In this study, a multi-objective function was formulated with TTT as the network efficiency measure, TTC as the instantaneous safety measure and E and/or FC as the emission and/or fuel consumption measures. The variables used for all three measures were instantaneous speed (vi), acceleration (ai) and position (xi) of each vehicle. Hence, the MPC controller predicted the evaluation of traffic in the network over time and optimized the speed limit control in such a way that TTT and E/FC were minimized and TTC was maximized. However, only the first estimated control inputs were considered final and applied to the process. The system then received new information after 60 seconds; and, the process started all over again. The general form of the objective function is shown by the following equation: 60

73 = 1. ( ) ( ) + 2. / ( ) ( ) + 3. / ( ) / ( ) (17) Thus, TTT was calculated by summing up each vehicle s travel time over. Likewise, TTC and E/FC were calculated by summing up each vehicle s ratio of relative speed and relative position over and each vehicle's amount of emission produced/fuel consumption over respectively. Also, wi (i = 1,2,3) were the weights assigned, and ( ), ( ) and N E/FC(t) were the normalized values of the corresponding terms in the objective function (to make the units consistent). Two constraints were used for the above-mentioned objective function to ensure safety of drivers: 1. The difference between speed limits displayed on the same variable message sign in two consecutive time steps (i.e. 1 min) could not exceed 10 km/h:,( + 1),( ) 10 (18) 2. The difference between speed limits displayed in two consecutive variable message signs (i.e. 1 km spacing) at the same time step could not exceed 10 km/h:, ( )( ), ( )( ) 10 (19) These conditions protected drivers from experiencing sudden changes between speed limits that could be potentially dangerous, as it may confuse drivers and create shock waves. 61

74 Figure 3.3 shows the detailed flow chart describing the overall VSL activation and optimization process: Figure 3.3: Flow Chart of The VSL Optimization Process VSL Trigger Condition While designing a coordinated VSL system, it is important to ensure that the VSL system does not create any negative impact somewhere else in the network or induce an increase in travel time. Therefore, it is important to set trigger conditions that justify the initiation of VSL. In this study, a VSL trigger condition based on a sudden speed drop of a particular section with respect 62

75 to the successive upstream sections was used (Jo et al., 2012). Thus, if the average speed of a particular section dropped suddenly with respect to the two consecutive upstream sections, VSL was triggered, because a queue is formed with stations successively affected by the traffic jam from the bottleneck. For instance, beginning from the most downstream station in Figure 3.4, the speed at station 8 is lower than the other 2 upstream stations (4 and 6). Hence, station 8 can be identified as the back of queue that is forming at section 10 and propagating upstream to station 8. Figure 3.4: VSL trigger algorithm Two conditions, therefore, had to be satisfied in the development the VSL trigger algorithm: i) the average speed of the bottleneck station had to be low enough to justify it as a bottleneck section; and, ii) the lower speed should be sustained for at least one minute. The general form of the algorithm is as follows: If U i U i-1 and U i U i-2 and U i < (default speed limit - 10km/h) for 1 minute then S i is the bottleneck section. Hence, VSL should be triggered. 63

76 where U i represents the average speed of different sections, and S i represents section numbers. According to the above algorithm, whenever the first two conditions are satisfied and the speed of that particular section goes below 90 km/h (default is 100km/h) for 1 minute, the section is considered as an active bottleneck; and, VSL is triggered. Also, when the trigger condition is absent, VSL is deactivated automatically and the system gradually goes back to default speed limit values (i.e., 100km/h). More studies need to be done on the sensitivity of speed drop and its duration to represent VSL trigger condition Modeling Drivers' Compliance In this research, the compliance rate followed to the 'desired speed distribution' curve assigned to each vehicle class in VISSIM. In other words, a corresponding desired speed distribution curve, with which drivers were assumed to comply, was set up for each speed limit. It is important to note that the compliance rate was modelled in VISSIM as a function of the posted speed limit. Thus higher compliance rates were associated with higher posted speed limits and lower compliance rates were associated with lower posted speed limits (PTV Vision, 2011). With the presence of vehicle trajectory data in a Connected Vehicle environment, it is possible to adjust the selected VSL based on the observed real-time compliance rate. Knowing each vehicle's speed information in the previous time step, the average speed of a particular section can be fed-back to the current time step to adjust the calculated optimal speed limit values for that section. Thus: VSL (t) = (1+α) * V opt (t) (20) 64

77 α = V ( ) VSL ( ) VSL ( ) (21) where, V opt (t) = selected speed limit from the optimization model in the current time step (t), VSL (t) = displayed speed limit in the current time step (t), = real-time compliance rate of drivers, V ( ) = detected average speed of a particular section in the previous time step (t-1), VSL ( ) = displayed speed limit in the previous time step (t-1). The use of this real-time compliance enables the design of a more robust and efficient VSL control strategy. 3.4 Solution Algorithm For Optimization For systems like freeway traffic where a linear model is often difficult to identify, optimization based on a non-linear model is often the desired choice. The optimization function used in this research is non-smooth and non-linear and there might exist multiple optimal point, hence a global optimization method is required to perform the optimization process. Thus, to deal with this multiple optima caused by the non-smooth or discontinuous objective function, Genetic Algorithm (GA) was used. GAs have gained increasing attention in the last few years, especially in many control areas (Fleming and Purshouse, 2002). GA is a parallel stochastic optimization method that do not require any gradient information. This parallel characteristics enables GA to work with a set of population at each iteration, rather with a single solution. The above properties along with the 65

78 evolutionary operators and generating the next population, makes GA capable of avoiding getting trapped in local optima. Hence, GA is well suited for solving multi-objective optimization problems, even with conflicting objectives (de Fonseca, 1995). There exists two approaches to solve a multi-objective optimization problem using GA. The first approach solves the function as a set of Pareto Optimal solutions, also known as Pareto Front. rather than providing a single solution. This solution sets provide information about the trade-off between the design objectives and allows the decision maker to make an informed decision on which solution to choose. The second approach solves the objective function by combining all the objectives into a single function and then by weighting each of them appropriately. By changing weights systematically, it is possible to solve several sub-optimization problems obtaining optimal solutions in the objective space. All of the optimum solution points then represent the Pareto front (Kim and Weck, 2006). In this thesis, the second approach was chosen which means the optimization problem was formulated as a multi-objective function (Equation 17), with relative weights given to different terms of the objective function. Thus, we have used weighted sum approach of the multiobjective optimization, the goal of which is to seek the best solution that minimizes the objective function while satisfying constraints. In order to create this VSL control logic, VISSIM COM (Component Object Model) interface was used to write the user defined VSL logic using VBA. VISSIM COM enables to manipulate the attributes of most of the internal objects dynamically. In addition, MATLAB Global 66

79 Optimization Toolbox routine was interfaced with VISSIM to create an integrated and flawless data interchange between VISSIM and MATLAB to perform the optimization of the objective function. Hence, while simulation was still running in VISSIM, it facilitated the easy transfer of online data in MATLAB, performed the optimization and again returned the optimized speed control values back in VISSIM, based upon which the vehicles would flow. This integrated VISSIM COM/MATLAB environment used in this thesis for the design of the advanced traffic control measure is shown in Figure 3.5. Appendix A also provides the source codes written in VBA to execute the VSL commands. Figure 3.5: Workflow of the simulation environment 3.5 SUMMARY In order to assess the traffic impact considering mobility, safety and sustainability using data from CV, this research incorporated these three distinct components into a single VISSIM microsimulation framework These components were: (i) a microscopic traffic flow prediction model to minimize TTT (total travel time) of all vehicles in the network, (ii) a surrogate safety 67

80 model TTC (time to collision) to capture the instantaneous safety between each individual pair of vehicles, and (iii) a microscopic emission and fuel consumption model 'VT-Micro model' to measure Emission (E)/Fuel Consumption(FC). The approach also incorporated a lane changing model which provides a robust integrated speed limit selection and shockwave detection/prediction framework. A system-wide optimization using a multi-objective function was formulated to obtain the VSL values that: (i) minimized TTT, (ii) maximized safety as reflected in TTC, and (iii) minimized emission (E) and/or fuel consumption (FC). The optimization was conducted in a rolling horizon fashion over a short-term prediction horizon of five minutes using MPC technique. VSL trigger condition was based on a 'sudden speed drop' of a particular section with respect to the successive upstream sections. Real time driver's compliance was used to adjust the optimal speed limit values. For the optimization of the objective function, Genetic Algorithm (GA) was used because of its inherent capability of solving multi-criterion optimization problems. VISSIM COM (Component Object Model) interface was used to extend the capability of microsimulation by writing user-defined VSL logic. Finally, MATLAB Global Optimization Toolbox was interfaced with VISSIM to create an integrated and flawless data transfer between VISSIM and MATLAB and to perform the overall optimization process. 68

81 CHAPTER 4: CASE STUDY 1 - PROACTIVE VSL FRAMEWORK FOR A ONE LANE ROAD NETWORK Introduction This chapter demonstrates the application and performance of the developed VSL algorithm using individual trajectory data from CVs in a simulation environment. For this purpose a synthetic one lane road network has been considered in this chapter. In this research, it has been assumed that Road Side Equipment (RSE) collected data from vehicles and broadcasted this information via DSRC. Also, data used to design VSL are available at the microscopic level in a Connected Vehicle environment assuming the trajectory of the vehicles was tractable. In other words, the input parameters involves the speed and position of each vehicle; consequently, depending on the predicted state of each vehicle, VSLs are adopted for each vehicle individually. The remaining of the chapter is organized as follows: the first section described the set up of the test network where the algorithm was implemented. A detailed calibration process of the test network has been conducted in the second section. The third section describes the simulation results with sensitivity analysis. Finally, the last section summarizes the outcome of this chapter. 4 The content of this chapter has been taken from the paper: Khondaker, B. and Kattan, L., Variable Speed Limit: A Microscopic Analysis in a Connected Vehicle Environment, Transportation Research Part C: Emerging Technologies, Volume 58, pp , September

82 4.2 Description of the Test Network The developed approach was tested in a case study using the VISSIM microsimulation tool. In this research, a hypothetical single-lane 8 km roadway section was considered, as shown in Figure 4.1. The roadway was divided into 8 sections, with the length of each section as 1 km. The free flow speed was 100 km/h, and the demand was set at 2000 veh/h. In order to create an artificial bottleneck, an incident was scheduled to take place at the 6th section of the freeway 10 minutes after the beginning of the simulation. It was assumed that the collision resulted in the reduction of vehicular speed, as the vehicles involved in the incident pulled off the road. Thus, the speed limit was set to 30 km/h in that section for time period t from 600 s to 1800 s, i.e., it took 20 minutes to clear the incident. After 1800 s, the speed limit was again set to the default value. This scenario resulted in the formation of an active bottleneck and a queue upstream of the bottleneck. In order to mitigate the congestion and reduce the inflow to that bottleneck section, six dynamic speed limit control signs were placed in the middle of sections 1, 2, 3, 4, 5 and 7. Vehicles followed the 'desired speed distribution' curve assigned to them in VISSIM, unless they were hindered by other vehicles or objects (e.g., new speed limit). As soon as they encountered a new speed limit, vehicles adjusted their speed according to the new speed limit distribution and took some perception distance (which is a function of current speed and reaction time distribution) to adjust. The limitation of the rate of change of acceleration (jerk) in VISSIM also prevented any turbulence caused by sudden speed change. 70

83 Figure 4.1: Layout of the freeway In this case study, a prediction horizon (Np) of 5 minutes was chosen, which was approximately equal to the travel time of the network under normal traffic conditions. A control horizon (Nc) of 3 minutes was selected. It was assumed that the controller signal could change once per minute. The speed limit values were all discrete variables, i.e. VSL(t){ 50, 60, 70, 80, 90, 100} km/h with defined upper bound (100 km/h) and lower bound (50 km/h). Also a rounding algorithm was used in the optimization process so that the speed limit values are always rounded to the nearest 10th speed values. The normalized values of ( ), ( ) and ( ) were calculated by running the simulation for a speed limit of 90 km/h and thus collecting the corresponding values of ( ). Also, the values of the IDM parameters were chosen as,=1 m/s 2, ( ), ( ) and, = 3 m/s 2, = 1, = 2 m and T = 1.5 s. Also, the time when the vehicles enter a link in VISSIM network is defined by VISSIM stochastically using an average time headway (in sec)between two vehicles equal to 71

84 the inverse of the hourly volume. VISSIM assumes a Poisson arrival distribution; thus, average time headway is used as an average value of a negative interarrival exponential distribution. This is one of the limitation of VISSIM as Poisson arrival assumption can only hold under light traffic condition; however, when traffic flow becomes congested this assumption of Poisson distribution no longer hold, as arrival of vehicles is not independent anymore. 4.3 Model Calibration In model calibration procedure, the selection of the parameters defining the curve is an important part. In this research Newell's (1993) triangular fundamental diagram was adopted and calibrated using randomly sampled flow, density and speed data from simulation. The accident scenario created in this case resulted in this triangular fundamental diagram with both uncongested and congested branches. Following is a detailed description of the calibration process adopted in this research Freeway Representation and Data Acquisition The first step in the calibration process is the representation of the study network in successive cells. Each cells has to be homogenous, meaning that the number of lanes and other geometric features should be the same so that each cell can be represented by a single fundamental diagram. Consequently, the hypothetical 8 km freeway has been divided into eight sections with each section being 1 km in length. The free flow speed was 100 km/hr and the demand was set to 2000 veh/hr. The simulation was run for one hour and flow, speed and density data were 72

85 aggregated across the links over a 30 second interval period. Simulation was run with ten different random seeds and all the flow, density, speed data were averaged for the ten runs Estimation of the Parameters Capacity: In estimating the capacity of the freeway, the definition from Highway Capacity Manual (1) was adopted in this research. According to the Highway Capacity Manual, capacity is the maximum amount of flow that can reasonably be expected to traverse the cross-section of a road segment. Hence, capacity was estimated from the flow density diagram as 2435 veh/hr as the maximum value of flow across all sections of the freeway. Free-flow speed: This was estimated by performing a least-squares fit on the flow-density curve but only taking the values where the speed was above 90 km/hr since we were interested to estimate the free flow speed. Figure 4.2 shows the scatter plot for flow-density curve along with the estimated regression line for free flow speed. The estimated free flow speed was 95 km/hr according to the adopted procedure. 73

86 Flow vs Density Flow (veh/hr) Density (veh/km) Figure 4.2: Regression Line for Free Flow Speed Critical Density: Since the capacity and free flow speed was already known, the critical density can be determined using these two estimated values. This was done by horizontally projecting the maximum flow value to the free flow speed regression line to determine the tip of the flowdensity diagram. This tip of the diagram which was the intersection of the capacity and free flow line, determined the value of the critical density above which the flow became congested. the estimated value of critical density by this procedure was 26 veh/km and is shown in Figure

87 Figure 4.3: Estimation of Critical Density Jam Density: The jam density was determined by plotting a regression line for the congested side of the curve but allowing the line to pass through the tip of the flow-density diagram. The point where the regression line crossed zero flow was assigned as the jam density of the section. The estimated jam density was 122 veh/km and is shown in Figure 4.4. Figure 4.4: Estimation of Jam Density 75

88 Capacity Drop: Congestion may occur due to bottleneck formations that result from a lane drop, near on ramp with significant demand, a collision or other incidents. When analyzing data, it can be observed that flow in a bottleneck just before the onset of congestion is usually higher than the outflow of congestion at that particular bottleneck. This traffic flow phenomenon is known as capacity drop. The majority of past empirical studies confirm the existence of capacity drop phenomenon for highway bottlenecks. Thus it is important to determine the amount of capacity drop for the test network. In order to do it, a least square regression analysis was performed on the congested side of the flow-density diagram. Figure 4.5 shows this regression line and how it undercut the free flow line. The amount of undercut portion was the capacity drop and from the figure it is quite apparent that estimated capacity drop was 12%. Hence, considering a 12% capacity drop, the actual capacity of the study network was around 2100 veh/hr and the estimated jam density is 180 veh/km which corresponds to a maximum vehicular spacing of 5.5 m between passenger cars in total stopping condition 76

89 Flow (veh/hr) Flow vs Density Curve Capacity Drop Density (veh/km) Figure 4.5: Estimation of Capacity Drop Table 4.1 shows the estimated values of the network parameters. Since all of the values of the parameters reproduced realistic results, the default values of the driver behavior parameters of VISSIM were adopted. Table 4.1:Parameter Estimates for the Study Network Parameter Method Used to Estimate Value Capacity Highway Capacity Manual [10] 2400 veh/h (without capacity drop) Free Flow Speed Least-Squares fit 95 km/h Critical Density Horizontal projection on the maximum flow 26 veh/km Jam Density Plotting regression line for the congested side of the curve and allowing the line to pass 122 veh/km Capacity Drop through the tip of the flow-density diagram Least square regression analysis on the congested side of the flow-density diagram 77 12% (considering 12% capacity drop, the maximum flow is 2100 veh/h and jam density is 180 veh/km)

90 4.4 Simulation Results Using the calibrated network, simulation was run with ten different random seeds for 1 hour with 5 minutes as a warm-up period which was disregarded in the analysis. Hypothesis testing was conducted to examine the difference in the mean and variance between the 2 populations that corresponded to 10 and 20 simulation runs respectively. The results showed that 10 simulation runs were statistically sufficient for the case study (i.e., no statistical difference between the variance and mean of the two population. The 'desired speed decision' attribute in VISSIM was used to model VSL via VISSIM-COM. In order to analyze the simulation results and compare the performances of the network under uncontrolled and controlled scenarios, Average Travel Time (ATT) and Average Fuel Consumption (AFC) were used, as described in equations 1 and 2. It is to be noted that only the fuel consumption part of VT-Micro model has been considered in this paper. = (1) = (2) where, N denotes the number of vehicles that have entered the network in the simulation time period. TTC as the safety indicator was calculated as an output using VISSIM-COM at each time step. Since the average value of TTC does not provide much insight about the possible safety condition, a surrogate safety measure (SSM) was used to assess the safety condition by comparing the calculated TTC and the threshold TTC as shown in equation 3: 78

91 Surrogate Safety Measure =. (3) In this research, the threshold value of TTC was set to 1.5 sec as suggested by Sayed et. al., (1994), Hayward (1972) and Van der Horst (1991). In addition, the Surrogate Safety Assessment Model (SSAM) developed by FHWA also uses a TTC of 1.5 sec to estimate the surrogate measures of safety corresponding to each vehicle-to-vehicle interaction and determine whether or not each interaction satisfies the criteria to be identified as an official conflict (FHWA, 2008). However, the threshold TTC value depends on driver behaviour since different drivers have different response times and they might also undertake different measures depending upon the vehicle s performance, prevailing traffic conditions, visibility, etc. Therefore, the use of the 1.5 sec threshold TTC value needs further investigation. Finally, four scenarios were investigated by varying the weights assigned to TTT, TTC and FC, as shown in Table

92 Table 4.2:Scenario Description Scenario Number Scenario Description Weights W1 W2 W3 Uncontrolled No VSL Control Scenario 1 (S1) Only TTT is optimized Scenario 2 (S2) Only TTC is optimized Scenario 3 (S3) Only FC is optimized Scenario 4 (S4) TTT, TTC and FC are optimized Case of 100% Market Penetration Rate Table 4.3 shows the results of the simulation runs for the above mentioned scenarios assuming 100% penetration rate of vehicle probes (i.e. CV) with 80% passenger cars and 20% heavy vehicles. The results of the analysis showed that, compared to the uncontrolled case, there was considerable improvement in all the Measures of Effectiveness (MOEs) for the controlled scenario. TTT was reduced 20.5% for S1 and around 19% for S2, S3 and S4. It is quite apparent from the results that reducing the speed variation in S2, decreasing the sudden acceleration/deceleration in S3 and taking into account the optimization of all three MOEs in S4 helped create smoother flows, which also contributed to the improved travel time in S2, S3 and S4. 80

93 Table 4.3:Simulation Results for Different Scenarios Scenario Description ATT (Avg Travel Time ) veh-h Collision Probability AFC (Avg Fuel Consumption) (l/hr) Average Delay/veh (S) Total No. of Stops Flow veh/h Speed km/h Density veh/km Uncontrolled SD of speed km/h Scenario 1 (% Change compared to Uncontrolled) Scenario 2 (% Change compared to Uncontrolled) Scenario 3 (% Change compared to Uncontrolled) Scenario 4 (% Change compared to Uncontrolled) (-20.5%) (-19.7%) (-18.7%) (-18.1%) (-9.8%) (-11%) (-6%) 0.23 (-7.6%) (-14.8%) (-14.8%) (-16.1%) (-5.5%) 120 (-38%) 121 (-37%) 129 (-33%) 125 (-35%) 1975 (-57%) 2408 (-47%) 2710 (-40%) 2389 (-47%) 1936 (+5%) 1939 (+4.8%) 1930 (+4.8%) 1935 (+4.7%) 71.5 (+10%) 72 (+11%) 70 (+8%) 71 (+9%) (-15.5%) (-15%) (-15%) (-14%) 21 (-25%) 21 (-25%) 21 (-25%) 21 (-25%) The largest improvement in collision probability (11%) occurred in S2, and the largest improvement in AFC (16%) occurred in S3. There were also significant improvements in the average delay per vehicle, total number of stops, flow, speed, density and standard deviation (SD) of speed for all scenarios. The improvement in the total number of stops for all scenarios implies that the proposed VSL algorithm was able to smooth traffic flow by reducing the number of vehicle stops, which in turn had a positive impact on the environment in terms of reducing fuel consumption. However, more experiments need to be conducted on other networks of realistic sizes to confirm if the results can be generalized. 81

94 In summary, the results of Table 4.3 imply that, by assigning different weights, it is possible to achieve the maximum benefit according to the desired policy while resulting in simultaneous improvements in the other two measures. In other words, our findings reveal that S1 which optimized for mobility, resulted in improvements in terms of safety and sustainability. Similarly, S2 which optimized for safety alone, lead to improved mobility and environment impact. Even when optimizing only for sustainability (S3), the results showed benefits in terms of mobility and safety; however, the safety benefits were not as pronounced as other scenarios. The simultaneous improvements in all measures obtained in all examined scenarios can be explained by the fact that all scenarios in one way or another, attempted to suppress shockwaves, which resulted in travel time improvements, increased safety through reduction of speed variation and sudden changes in acceleration/deceleration, which in turn lessened fuel consumption and emissions. It is important to note that the emission reduction in S4 was not as substantial as those of the other three scenarios. One possible explanation could be the weights assigned to the various components. By changing weights systematically, it is possible to solve several sub-optimization problems obtaining optimal solutions in the objective space. All of the optimal solution points then represent the Pareto front. Hence, future work on the sensitivity analysis of the weights needs to be conducted. In addition, more work is required to examine the impact of different network topographies, congestion levels, O-D patterns, etc. Figures 4.6(a) and 4.6(b) show the traffic flow/throughput in various sections of the study area for the uncontrolled case and VSL implementation in the S4 scenario. Figure 4.6 (a) shows that, when the incident occurred (i.e., at 600 s), it resulted in a drop in flow close to section 6. 82

95 However, Figure 4.6 (b) shows that, even before traffic breakdown occurred and VSL being proactively activated, the traffic inflow entering the jammed section was delayed on purpose to maintain stable flow condition. Thus, the VSL system was able to stabilize and smooth traffic flow on the whole freeway by eliminating sudden acceleration/deceleration of drivers (stop and go), which reduced travel time. Figure 4.7 provides further explanation through the change in the shape of the flow-density diagram when VSL was activated. A lower VSL value would result in shifting the critical density to the right, thereby delaying the occurrence of traffic breakdown. By shifting the traffic state from the congested region (i.e., stop and go condition) to the uncongested region, a larger number of vehicles could pass at higher speed through the vicinity of the bottleneck area, which in turn resulted in reduction in travel time compared to the uncontrolled case. Figures 4.6 (c) and 4.6 (d) show the speed distributions in various sections of the network in the S4 and uncontrolled scenarios respectively. The figures illustrate that a lower speed was sustained almost until the end of the simulation period in the uncontrolled case, whereas the lower speed began to pick up about halfway through the simulation time in the controlled case (S4), as a result of bottleneck elimination and the corresponding stop and go conditions. The computation time for the 1 hour simulation was around 5-8 min in a 3.6 GHz Intel Xeon PC, which is at least eight times faster than real time. 83

96 (a) (b) (c) (d) Figure 4.6: Traffic flow (a, b) and speed (c, d) distribution under VSL control (S4) (right) and uncontrolled scenario (left). 84

97 Figure 4.7: Flow-Density curve for VSL and No-VSL cases Figure 4.8 shows the changes in VSL values among the six variable message signs throughout the duration of the simulation for scenario 1 only. The Figure shows that VSL was mostly activated during the incident period and deactivated again as soon as the shockwave disappeared. Figure 4.8: VSL Rates with Simulation Time (For scenario 1 only) 85

98 4.4.2 Case of 50% Market Penetration Rate With CV/AV technology still moving towards deployment, there will be a transition period until a 100% market penetration rate is achieved. Therefore, further analysis was conducted assuming a lower % penetration of CV. For the microscopic traffic state prediction step, the trajectory data from every vehicle is required, since the variables needed for the analysis are mostly related to vehicle-to-vehicle interaction (e.g., spacing, speed differential, acceleration/deceleration). Hence, it is necessary to estimate the trajectory of each unequipped vehicle on the roadway from the available CVs. In this context, the principle of microscopic estimation of freeway vehicle positions from the behavior of CVs developed by Goodall et al. (2014) was adopted. The algorithm estimated the locations and trajectory of unequipped vehicles travelling between each two consecutive CVs by examining their behaviour. This was achieved by comparing the acceleration/deceleration behavior of each two pairs of CVs with the expected acceleration/deceleration. The reader may refer to Goodall et al. (2014) for more details of this approach. In this part of the analysis, a market penetration rate of 50% for equipped vehicles (all passenger cars) was assumed. Again, the simulation was run with ten different random seeds for 1 hour with 5 minutes as a warm-up period which was disregarded in the analysis. Table 4.4 summarizes the results of the simulation runs for all four scenarios (i.e. for different weights in the objective function). 86

99 Table 4.4:Simulation Results for 50% CV Penetration Rate Scenario Description ATT (Avg Travel Time ) veh-h Collision Probability AFC (Avg Fuel Consumption) (l/hr) Uncontrolled case VSL Case Scenario 1 (% change) Scenario 2 (% change) Scenario 3 (% change) (-17%) (-16%) 0.24 (-15%) 0.17 (+7.5%) (-2.5%) 0.16 (+1.3%) (-7%) (-6.5%) 0.23 (-10%) Scenario 4 (% change) (-17.5%) (-4.5%) (-11%) As shown in Table 4.4, at 50% penetration rate the approach outperformed the uncontrolled scenario consistently in terms of improved mobility and reduction in fuel consumption. However, mixed results were obtained in terms of safety. Thus, S1 which optimized for mobility alone, resulted in reduction in both travel time and fuel consumption but at the expense of significantly higher safety risk. However, S2, which optimized for safety alone, led to simultaneous improvements in all three measures. While this finding was consistent with the earlier findings for the case of 100% penetration rate, the improvements were not as pronounced ( i.e. 16%, 2.5%, 6.5% as compared to 20%, 11% and 15% respectively). For S3, which optimized for AFC only, resulted in reductions in both travel time and AFC, but again at the expense of increasing collision probability. On the other hand, S4, which optimized all of the 87

100 three components, provided the largest benefit in terms of mobility, safety and sustainability. Thus, unless, safety term is included in the objective function, increased collision risk would result. This might be explained by the fact, that the safety measure is very sensitive to the information on the relative vehicle positions/speed, which was unknown and estimated for 50% of the vehicles in the case of 50% penetration rate of CV s. In summary, the results suggested that formulating the problem as a multi-criteria optimization was needed to realize optimum benefits in terms of mobility, safety and sustainability when the trajectory of only 50% of the vehicles was available. However, with 100% penetration rate, optimizing for safety alone was enough to achieve simultaneous and optimum improvements in all measures, implying that the multi-objective optimization was not necessary. 4.5 SUMMARY In this chapter, a one-lane simulated road network was used to demonstrate the feasibility of the developed VSL approach using data from CVs. Based on the simulation results, the VSL system was shown to result in significantly improved performances in terms of mobility, safety and sustainability. A sensitivity analysis was conducted to compare the performance of the developed approach for different weights in the objective function and for two different percentages of CV. With a hypothetical freeway modeled in VISSIM microsimulation, the developed approach outperformed the uncontrolled scenario, resulting in TTT reductions of around 20%, safety improvements of 6-11%,and overall fuel consumption reductions of 5-16% with 100% CV penetration. Our findings revealed that the scenario which optimized for safety alone, resulted in 88

101 more optimum improvements as compared to the multi-criteria optimization. Thus, one can argue that in case of 100% penetration rates of CVs, optimizing for safety alone is enough to achieve simultaneous and optimum improvements in all measures. However, mixed results were obtained in case of lower % penetration rate which showed higher collision risk when optimizing for only mobility or fuel consumption. This indicated that with such % penetration rate, multicriteria optimization was crucial to realize optimum and balanced benefits for the examined measures. 89

102 CHAPTER 5: CASE STUDY 2 - VARIABLE SPEED LIMIT WITH ANTICIPATORY LANE CHANGING DECISIONS IN A TWO-LANE NETWORK Introduction This chapter extends the concept of the previous chapter by incorporating driver behaviour based on trajectory data from a two-lane freeway segment. In particular, the chapter examines how the speed limit controls can be co-ordinated and optimized to reduce frequent lane changing and overall braking, thus to achieve greater traffic throughput, safety and sustainability by synchronizing driver behaviour. VSL systems have the potential to change lane distribution, thereby synchronize driver behaviour, discourage lane changing behaviour and stabilize traffic flow (Knoop et al., 2010). Although secure lane changing is crucial for safe driving, maintaining desired speeds and reducing frequent lane changes are important aspects of driving comfort. These factors influence not only the individual driver behaviour, but also have significant impact on the stability, capacity and breakdown of traffic flow. Therefore, an effective VSL control strategy requires a cumulative optimal action plan for all vehicles in the network. In this chapter, a lane changing interaction extension of the previously developed VSL system has been proposed by using MOBIL lane changing model (Treiber and Kesting, 2009). The core of the approach of this chapter is the incorporation of lane changing model which provides a robust integrated speed limit selection and shockwave detection/prediction framework. 5 The content of this chapter has been taken from the paper: Khondaker, B. and Kattan, L., Variable Speed Limit Strategies With Anticipatory Lane changing Decision, submitted to Transportation Research Part C: Emerging Technologies, March

103 5.2 Driver Behaviour with Anticipatory lane Changing Decisions Lane changing and acceleration/deceleration behaviours are the primary driver s decision variables on a freeway and they have a significant effect on traffic control strategies such as VSL. According to previous studies, lane changing, in particular, has a considerable impact on traffic flow characteristics and freeway safety. In heavy traffic, lane changing is a key trigger to traffic breakdown, capacity drop, and traffic oscillations (Laval and Daganzo, 2006; Jin, 2010; Oh and Yeo, 2015 and Knoop et al., 2010). When traffic is close to capacity, a lane changing maneuver affects at least three vehicles: the lane changer, the follower in the target lane and the follower in the current lane. Then this impact propagates downstream and creates a domino effect on other vehicles (Zheng et al., 2011). These traffic perturbations result in higher acceleration/deceleration which burns 20-30% more fuel and CO2 emission (Khan et al., 2014). Additionally, lane changing maneuver is confirmed to have an adverse impact on freeway safety (Pande and Abdul-Aty, 2006; Zheng et al.,2010 and Zheng, 2014). While the impact of acceleration and deceleration behaviours have received some attention; none of the published studies appears to account for the effect of lane changing behaviour in developing and evaluating freeway control strategies. In fact, traffic control and driver s behaviour mutually impact each other. For instance, lane changing behaviour is mainly triggered by speed differences between adjacent lanes, and drivers desire for travelling faster. The occurrence of a frequent lane changing maneuvers might lead to shockwave formation which would activate freeway control schemes such as VSL. On the other hand, the presence of freeway management schemes such as VSL systems harmonize the travel speed by reducing 91

104 speed differences among vehicles travelling in the same lane and/or adjacent lanes, which discourages frequent lane changing behaviour. This interaction between driver s behaviour and control strategies suggest the need of an integrated framework where both anticipated driver behaviour and control strategies are modelled as mutually influencing each other to seamlessly optimize the efficiency of freeway facilities. Therefore, this chapter provides a detailed case study on driver's anticipatory behaviour resulting from the extended VSL algorithm. More details of the models and the anticipatory behaviour of drivers are presented in the subsequent sections. 5.3 Numerical Experiments The proposed VSL approach using IDM and MOBIL model was tested in a numerical experiment using the same road network as described in chapter 4 but with two lanes. Hence, as shown in Figure 5.1, a hypothetical two-lane 8 km freeway segment with 8 sections each being 1 km was considered. For this network also, the flow follows a triangular FD calibrated with a free flow speed of 100 km/h, jam density of 120 veh/km, capacity of 2400 veh/hr, critical density of 24 veh/km and a capacity drop of 10%. The same incident scenario was replicated for this network by placing six dynamic speed limit control signs in the middle of sections 1, 2, 3, 4, 5 and 7 to manage the freeway traffic in the presence of active bottleneck resulting from the speed reduction. 92

105 Figure 5.1: Layout of the two-lane freeway In this case study, the values of the MOBIL parameters (Treiber and Kesting, 2009) were used as follows; = 4 / 2, h = 0.2 / 2, bias = 0.3 /. Furthermore, a pure selfish behaviour of drivers were chosen as reflected in =0. Also, the numerical example examines the microscopic driver behaviour analysis for a base case scenario, where, only the first objective of the multi-criteria objective function in equation 1 was considered. = 1. ( ) ( ) + 2. ( ) ( ) + 3. / ( ) / ( ) (1) Thus, the VSL focused on only minimizing total travel time (TTT). In the base case scenario, traffic demand was loaded at a rate of 2000 veh/hr. In addition, a 100% penetration rate of CV was considered with all vehicles as passenger cars. 5.4 Results on Impact of Driver's Behaviour in the Base Case Scenario In order to evaluate the performance of the proposed algorithm on synchronizing driver behaviour, the following performance measures has been used in this chapter, which are: 93

106 1. Lane changing rate (LCR) as shown in equation 2 = (2) Where, = Number of lane changes by vehicle i and = the time interval (1 min in this case) 2. Frequency of acceleration and deceleration of drivers Figure 5.2 illustrates the results of Lane Changing Rate (LCR) for the uncontrolled and VSL controlled scenarios. With congestion building up as a result of bottleneck formation, the uncontrolled case exhibits higher LCR as compared to the VSL controlled case. The difference in the LCR between the uncontrolled and VSL control case is mostly prominent during the incident period (i.e. 600 sec to 1800 sec). The average LCR in the uncontrolled case is 120 LCR/min as compared to 105 LCR/min for the VSL controlled case. A t-test analysis also suggests that this differences in the mean LCR is significant at a 95% confidence level. Thus, the VSL system retards the vehicle to join the queue at a lower speed with lesser speed variances, which in turn synchronizes drivers' behaviour by reducing frequent lane changes. Whereas, in the uncontrolled case the high speed variances encourage drivers to switch lanes frequently, resulting in a higher LCR. 94

107 Figure 5.2: Lane Changing Rate With Time for Uncontrolled and VSL-Control Scenario In order to assess the above lane changing behaviour of drivers, the speed profiles of both lanes have also been estimated and compared in Figure 5.3. The Figure 5.3 (a) reveals that in the No- VSL case, there is a large difference in the average speed profiles which is expected to trigger more lane changing behavior; whereas in VSL control case (Figure 5.3 b) there is less incentive to the drivers for changing lanes as speed in both lanes are almost same. 95

108 Speed profile (No VSL case ) Speed (km/hr) Lane 1 Lane Distance (m) (a) Speed profile ( VSL case ) 100 Speed (km/hr) lane 1 lane Distance 4000 (m) (b) Figure 5.3: Speed Profile in Both Lanes for Uncontrolled and VSL-Control Scenario 96

109 In addition to disrupting traffic flow negatively in terms of safety and efficiency, frequent lane changing rate also creates discomfort to the drivers. Furthermore, at high traffic density, frequent lane changes might result in higher acceleration/deceleration rate. This is because the following vehicle needs to adjust its speed and spacing with respect to the lead vehicle. This sudden deceleration behaviour results in increased fuel consumption and CO2 emission. Therefore, it is expected that comparison of the acceleration/deceleration rates of uncontrolled and VSL controlled scenario will also provide a measure of the effectiveness of the system. Figure 5.4 shows the frequency distribution of the acceleration/deceleration rates for both uncontrolled and VSL controlled case. The figure illustrates that the VSL control scenario results in higher frequency of acceleration and deceleration rates in the lower range (i.e m/sec2 to 0.5 m/sec2) compared to the uncontrolled scenario. Whereas, lower frequency of higher acceleration and deceleration rates are prevalent in the VSL case compared to the uncontrolled case. Thus, the higher frequency of large accelerations and decelerations in the uncontrolled case indicates more frequent hard braking or speeding up, which is associated with higher emission and fuel consumption. On the other hand, the higher frequency of lower accelerations and deceleration rates that are close to zero in the VSL case indicates a smoother traffic flow with fewer stop and go, and also corresponds to lower emission and fuel consumption. In summary, the results imply that the VSL system is able to slow down vehicles before they approach the bottleneck, which creates a smoother acceleration/deceleration profile and, thus, suppress shockwave. Whereas, in the uncontrolled case, while travelling at higher speed, vehicles encountered a dense platoon which induces hard breaking and creates a domino effect of 97

110 more hard breaking which propagates further downstream. This behaviour can further be interpreted as a bi-product of lane changing behaviour of drivers, which implies that frequent lane changing creates non-smooth acceleration and deceleration profile, all these creates higher probability of collision and higher emission/fuel consumption Frequency distribution of acceleration/decceleration % of frequency no vsl VSL -2.5 and below -1.5 to to to to 1.5 acceleration/decceleration interval (m/sec2) 1.5 to and above Figure 5.4: Frequency Distribution of the Acceleration/Deceleration Rate To identify driver behavior when comparing the VSL control and uncontrolled case, a time-space diagram showing the vehicle trajectories has also been investigated. Figure 5.5(a) and 5.5(b) shows the trajectory diagram for a sets of vehicles for both the VSL controlled and uncontrolled case. The figure reveals that the pattern of the trajectories are different where the uncontrolled case resulted in a trajectory where frequent stop and go condition is visible (fig 5.5a) compared to the VSL controlled case (fig 5.5b). The trajectories also show the increased travel time for the uncontrolled case due to this stop and go behaviour compared to the VSL counterpart. Thus, the 98

111 VSL system was able to create a smoother acceleration and deceleration pattern by eliminating stop and go behaviour as well as frequent lane changes, which also reduces travel time, emission and fuel consumption. (a) (b) 99

112 Figure 5.5: Time-Space Diagram For the Uncontrolled (a) and VSL Control (b) Case Figure 5.6 provides the speed contour plots for the VSL and No-VSL case with vehicle trajectories. As it can be seen from the contour plot in Figure 5.6(a), the very first point of shockwave appears in proximity of bottleneck section ( i.e. section 6 at 6000 m) due to the speed reduction from free flow to 50 km/hr at that particular instant ( i.e. 600 sec). The shockwave was persistent until the incident was cleared and speed was raised again to the default value triggering a capacity drop. This shockwave, however, did not spill back and propagate upstream, because traffic was still able to flow with a reduced speed. Around after 30 min, since the incident was cleared, the speed began to pick up and shockwave disappeared, thus restoring free flow condition. On the other hand, the improvement due to VSL control is clearly visible in Figure 5.6 (b) where it shows that the shockwave is almost completely avoided. Thus, the use of VSL control was sufficient to completely avoid any congestion, causing a significant reduction in travel time. 100

113 (a) (b) Figure 5.6: Speed Contour Plot For the Uncontrolled Case (a) and VSL Control Case (b) 101