Citation |

- Permanent Link:
- https://ufdc.ufl.edu/UFE0049251/00001
## Material Information- Title:
- Intersection Control Optimization and Simulation for Automated Vehicles at Isolated Intersections
- Creator:
- Li, Zhuofei
- Place of Publication:
- [Gainesville, Fla.]
Florida - Publisher:
- University of Florida
- Publication Date:
- 2015
- Language:
- english
- Physical Description:
- 1 online resource (156 p.)
## Thesis/Dissertation Information- Degree:
- Doctorate ( Ph.D.)
- Degree Grantor:
- University of Florida
- Degree Disciplines:
- Civil Engineering
Civil and Coastal Engineering - Committee Chair:
- ELEFTERIADOU,AGELIKI
- Committee Co-Chair:
- WASHBURN,SCOTT STUART
- Committee Members:
- YIN,YAFENG
RANKA,SANJAY CRANE,CARL D,III - Graduation Date:
- 8/8/2015
## Subjects- Subjects / Keywords:
- Acceleration ( jstor )
Algorithms ( jstor ) Intelligent vehicles ( jstor ) Intersections ( jstor ) Motor vehicle traffic ( jstor ) Signals ( jstor ) Speed ( jstor ) Trajectories ( jstor ) Trajectory optimization ( jstor ) Vehicles ( jstor ) Civil and Coastal Engineering -- Dissertations, Academic -- UF automated -- intersection -- optimization - Genre:
- bibliography ( marcgt )
theses ( marcgt ) government publication (state, provincial, terriorial, dependent) ( marcgt ) born-digital ( sobekcm ) Electronic Thesis or Dissertation Civil Engineering thesis, Ph.D.
## Notes- Abstract:
- Intersection control is an important component of the transportation system and can significantly contribute to vehicular delay along urban streets. The current emphasis on the development of automated (i.e., driverless and with the ability to communicate with the infrastructure) vehicles brings at the forefront several questions related to the functionality and optimization of intersection control in order to take advantage of these advanced vehicle capabilities. The objective of this research is to develop and simulate an intersection control algorithm that allows for the system performance and the trajectory of each single vehicle to be jointly optimized under an automated vehicle environment. First, a signal control optimization algorithm was developed assuming a simple intersection with two through movements. An optimization horizon scheme was developed to implement the algorithm and to continually process newly arriving vehicles. The algorithm was coded in MATLAB and results were compared against traditional actuated signal control for a variety of demand scenarios. It was concluded that that the proposed signal control optimization algorithm could reduce the intersection average travel time delay by 16.2% to 36.9% and increase throughput by 2.7% to 20.2%, depending on the demand scenario. Next, the proposed optimization algorithm was expanded for a four-approach intersection with the consideration of turning movements and a full set of possible phases. Implementing the proposed algorithm, the intersection controller makes decisions on the vehicle passing sequence using a genetic algorithm based optimization method, and at the same time it calculates the optimum vehicle trajectories. The optimization process repeats over a time horizon to process continually arriving vehicles. The algorithm was coded in Java and was compared against the conventional actuated signal control. The results showed that the proposed algorithm is able to reduce the intersection average travel time delay (by 16.3% to 56.0%) and increase the throughput (by 3.5% to 27.3%) under various demand scenarios. Compared to the actuated control method, the proposed algorithm is less sensitive to the balances in demand. An increase in the percentage of turning traffic increases ATTD slightly. Also, the proposed algorithm provides greater benefits for longer communication ranges under relatively congested conditions. ( en )
- General Note:
- In the series University of Florida Digital Collections.
- General Note:
- Includes vita.
- Bibliography:
- Includes bibliographical references.
- Source of Description:
- Description based on online resource; title from PDF title page.
- Source of Description:
- This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
- Thesis:
- Thesis (Ph.D.)--University of Florida, 2015.
- Local:
- Adviser: ELEFTERIADOU,AGELIKI.
- Local:
- Co-adviser: WASHBURN,SCOTT STUART.
- Electronic Access:
- RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2016-08-31
- Statement of Responsibility:
- by Zhuofei Li.
## Record Information- Source Institution:
- UFRGP
- Rights Management:
- Applicable rights reserved.
- Embargo Date:
- 8/31/2016
- Classification:
- LD1780 2015 ( lcc )
## UFDC Membership |

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PAGE 1 1 INTERSECTION CONTROL OPTIMIZATION AND SIMULATION FOR AUTO MATED VEHICLES AT ISOLATED INTERSECTIONS By ZHUOFEI LI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQ UIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2015 PAGE 2 2 Â© 2015 Zhuofei Li PAGE 3 3 To my parents PAGE 4 4 ACKNOWLEDGMENTS I would have never been able to complete this dissertation without the support of my committee members, friends and my family. First, I would like to express my sincere appreciation to my dissertation committee. I would like to thank my adviser Dr. Lily Elefteriadou for her inspiring guidance , continuous encouragement , and genuine con cern in my academic and personal development . S he has always been a role model for me . I would like to thank Dr. Yafeng Yin and Dr. Scott Washburn, who are outstanding professional researchers, for the ir insightful suggestions and inspirations, which were of great value to my research . I would also like to thank Dr. Sanjay Ranka and Dr. Carl Crane for serving as the external members of my committee and providing me with valuable comments and suggestions from various perspectives . I am also grateful to my f riends, especially Xi Zhao and Qingnan Liu, who share d my joys and worries, and accompanied me during my growth over all these years. N o matter how far apart we live, w e will always be connected heart to heart. A s pecial thanks goes to my parents and my bo yfriend Yiqiang for their unconditional love and support through this whole process . Without their support and faith in me, I could not have done this . PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATION S ................................ ................................ ........................... 10 ABSTRACT ................................ ................................ ................................ ................... 12 CHAPTE R 1 INTRODUCTION ................................ ................................ ................................ .... 14 1.1 Background ................................ ................................ ................................ ....... 14 1.2 Dissertation Objectives ................................ ................................ ..................... 17 1.3 Dissertation Outline ................................ ................................ ........................... 18 2 LITERATURE REVIEW ................................ ................................ .......................... 1 9 2.1 Intersection Control Methods ................................ ................................ ............ 19 2.2 Existing Signal Control Strategies ................................ ................................ ..... 21 2.2.1 Conventional Signal Timing Methods ................................ ...................... 21 2.2.2 Traffic Responsive Control ................................ ................................ ...... 22 2.2.3 Adaptive Signal Control ................................ ................................ ........... 23 2.3 Advanced Automated Vehicle Technolog y ................................ ....................... 29 2.3.1 Development of The Autonomous Vehicle ................................ .............. 29 2.3.2 Connectivity of Automated Vehicles and Vehicular Communication Systems ................................ ................................ ................................ ........ 30 2.4 Intersection Control Algorithms Using Wireless Communication ...................... 33 2.4.1 Intersection Control Algorithm Employing Vehicle t o Infrastructure Communication Technology ................................ ................................ .......... 33 2.4.2 Vehicle Warning or Control Algorithms Using Infrastructure to Vehicle Communication Data ................................ ................................ ..................... 38 2.4.3 Non Signalized Intersection Control in A Vehicle Infrastructure Cooperation Environment ................................ ................................ .............. 41 2.5 Summary of the Literature Review ................................ ................................ .... 42 3 SIGNAL CONTROL OPTIM IZATION FOR A SIMPLE TWO APPROACH INTERSECTION ................................ ................................ ................................ ..... 45 3.1 Methodology Framework ................................ ................................ .................. 45 3.1 .1 Trajectory Adjustment Logic ................................ ................................ .... 47 3.1.2 Feasible Signal Plan Enumeration ................................ .......................... 47 PAGE 6 6 3.2 Trajectory Optimization Algorithm ................................ ................................ ..... 49 3.2.1 Step 1: Determine The Trajectory of The First Vehicle. ........................... 51 3.2.2 Step 2: Calculate The Trajectories of The Following Vehicles. ................ 61 3.2.3 Step 3: Check Whether The Vehicle Can Depart The Intersection before The End of Green. ................................ ................................ .............. 67 3.3 Optimization Horizon Scheme ................................ ................................ .......... 67 3.4 Experimental Evaluation ................................ ................................ ................... 69 4 INTERSECTION CONTROL OPTIMIZATION FOR A G ENERAL TWELVE MOVEMENT INTERSECTIO N ................................ ................................ ............... 92 4.1 Methodology Framework ................................ ................................ .................. 92 4.2 Optimization Algorithm ................................ ................................ ...................... 94 4.2.1 Trajectory Opti mization Algorithm ................................ ........................... 95 4.2.2 Genetic Algorithm Based Control Optimization ................................ ..... 119 4.3 Simulation ................................ ................................ ................................ ....... 123 4.4 Sensitivity Analysis ................................ ................................ ......................... 125 5 CONCLUSIONS AND RECO MMENDATIONS ................................ ..................... 147 5.1 Signal Control Optimizati on for A Two Approach Intersection ........................ 147 5.2 Intersection Control Optimization for A General Four Approach Intersection . 148 5.3 Re commendations for Future Research ................................ ......................... 149 LIST OF REFERENCES ................................ ................................ ............................. 151 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 156 PAGE 7 7 LIST OF TABLES Table page 3 1 Input variables for Case 2 subcases ................................ ................................ ... 74 3 2 Input variables for Case 3 subcases ................................ ................................ ... 74 3 3 Trajectory Calculation input variables for the following vehicles ......................... 75 3 4 Required input parameters ................................ ................................ ................. 77 4 1 Threshold vehicle arrival times for Case T1 ................................ ..................... 130 4 2 Threshold vehicle arrival times for Case T2 ................................ ..................... 131 PAGE 8 8 LIST OF FIGURES Figure p age 3 1 Sketch of the two approach Intersection and its communication range .............. 78 3 2 Vehicle trajectory adjustment behav io r at a signalized intersection .................... 78 3 3 Optimized vehicle trajectories ................................ ................................ ............. 79 3 4 Vehicle trajectories with different number of com p onents ................................ .. 79 3 5 Different departing scenarios based on the trajectory of the first vehicle ............ 81 3 6 Three component vehicle trajecto r y ................................ ................................ ... 82 3 7 Adjusted trajectory for the first vehicle in Case 1 ................................ ................ 82 3 8 Adjusted trajectories for vehicle s of Case 2 ................................ ........................ 83 3 9 Adjusted trajectori es for vehicles of Case 3 ................................ ........................ 84 3 10 The special case of Case 3 a and 3 b ................................ ................................ 85 3 11 Adjusted trajectories for vehicles of C ase 4 ................................ ........................ 86 3 12 Hypothetical departure curve ................................ ................................ .............. 86 3 13 Adjusted tra jectories fo r the following vehicles ................................ ................... 87 3 14 Layout of the optimization horizon scheme ................................ ........................ 88 3 15 Flow chart of the optimization pr ocess ................................ ............................... 89 3 16 Comparison of the actuated signal control and the proposed signal optimization algorithm under various demand levels ................................ .......... 90 3 17 Comparison of the actuated signal control and the proposed signal optimization algorithm under different communication range/link length ............ 91 4 1 Sketch of the intersection and its Co mmunication Range ................................ 132 4 2 Layout of the optimization process ................................ ................................ ... 132 4 3 Hypothetical saturation flow departure curve and shifted hy pothetical satur ation flow departure curve ................................ ................................ ........ 133 4 4 Flow chart of the trajectory calculation process ................................ ................ 134 PAGE 9 9 4 5 Trajectory and spati al path of turning vehicles ................................ .................. 134 4 6 Hypothetical saturation flow departure curves and hypothetical saturation flow deceleration c urves for turning vehicles ................................ .................... 135 4 7 Illustration of the subcase regions for Case T1 ................................ ................ 136 4 8 Illustration of the subcase regions for Case T2 ................................ ................ 137 4 9 Illustration of the subcase regions for Case TF1 ................................ .............. 138 4 10 Illustration of the subcase regions for Case TF2 ................................ .............. 139 4 11 Genetic Algorithm flowchart ................................ ................................ .............. 140 4 12 Flow chart of the optimization process ................................ ............................. 141 4 13 Comparison of the actuated signal c ontrol and the proposed signal optimization algorithm under balanced demand scenarios ............................... 142 4 14 Comparison of the actuated signal control and the proposed signal optimization algorithm under un balanced demand scenarios ........................... 143 4 15 Comparison of the actuated signal control and the proposed signal optimization algorithm under different turning percentag e scenarios ................ 144 4 16 Comparison of the average travel time delay between the two control algorithms under different communication range/link length ............................. 145 4 17 Compar ison of the throughput between the two control algorithms under different communication range/link length ................................ ........................ 146 PAGE 10 10 LIST OF ABBREVIATIONS ACC Adaptive Cruise C ontrol ACS Lite Adaptive Control Software Lite AIM Autonomous Inte rsection M anagement ASC Adaptive Signal Control ATTD Average Travel Time D elay AWEGS Advance Warning of End of Green Systems BSM Basic Safety Message CVIC Cooperative Vehicle Intersection Control DSRC Dedicated Short Range C ommunications FCC Federa l Communications Commission GLE Green Light E xtension G A Genetic Algorithm OBE On Board Equipment O PAC Optimized Policies for Adaptive Control PMSA Predictive Microscopic Simulation Algorithm RLPE R ed Light P reemption RHODES Real Time Hierarchical Optimized Distributed Effective System RSE Road Side Equipment SAE Society of Automotive Engineers SCATS Sydney Co ordinated Adaptive Traffic System SCOOT Split Cycle Offset Optimisation Technique SLINK Single Link Clustering A lgorithm TOD Time of Da y PAGE 11 11 V2 I Vehicle to I nfrastructure V2V Vehicl e to V ehicle VCA V ehicle C lustering A lgorithm VICAC Vehicle to Infrastructure Communication based Adaptive C ontrol VII Vehicle Infrastructure Integration WiMAX Worldwide Interoperability for Microwave Access PAGE 12 12 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy INTERSECTION CONTROL OPTIMIZATION AND SIMUL ATION FOR AUTOMATED VEHICLES AT ISOLATED INTERSECTIONS By Zhuofei Li August 2015 Chair: Lily Elefteriadou Major: Civil Engineering Intersection control is an important component o f the transportation system and can significantly contribute to vehicular delay along urban streets. The current emphasis on the development of auto mated (i.e., driverless and with the ability to communicate with the infrastructure) vehicles brings at the forefront several questions related to the functionality and optimization of intersection control in order to take advantage of these advanced vehicle capabilities. The objective of this research is to develop and simulate an intersection control algorithm that allows for the system performance and the trajectory of each single vehicle to be jointly optimized under an automated vehicle environment . First, a signal control optimization algorithm was developed assuming a simple intersection with two through movements . An optimization horizon scheme was developed to implement the algorithm and to continually process newly arriving vehicles. The algorithm was coded in MATLAB and results were compared against traditional actuated signal control for a variety of demand scenarios. It was concluded that that the proposed signal control optimization algorithm could reduce the intersection PAGE 13 13 average travel time delay by 16.2% to 36.9% and increase throughput by 2.7% to 20.2%, depending on the demand scenario. Next, the proposed optimization algorithm was expand ed for a four approach interse ction with the c onsideration of turning movements and a full set of possible phases . Implementing the proposed algorithm, the intersection controller makes decisions on the vehicle passing sequence using a genetic algorithm based optimization method, and a t the same time it calculates the optimum vehicle trajectories. The optimization process repeat s over a time horizon to process continually arriving vehicles. The algorithm was coded in Java and was compared against the conventional actuated signal control . The results showed that the proposed algorithm is able to reduce the intersection average travel time delay (by 16.3% to 56.0 % ) and increase the throughput (by 3.5% to 27.3%) under various demand scenarios. Compared to the actuated control method, the pr oposed algorithm is less sens itive to the balances in demand . A n increase in the percentage of turning traffic increases ATTD slightly. Also, the proposed algorithm provides greater benefits for longer communication ranges under relative ly congested condit ions . PAGE 14 14 CHAPTER 1 INTRODUCTION 1.1 Background Automated vehicles are those that use various sensors and connectivity to gather information and autonomously perform driving functions. The National Highway Traffic Safety Administration (NHTSA) defined vehic le automation into five levels, ranging from vehicles that do not have any automated control functions (level 0) through fully automated vehicles (level 4) (NHTSA , 2013) . Fully automated vehicles are able to perform all drivi ng functions and monitor roadway conditions for an entire trip. They are different from autonomous vehicles which sense the environment, navigate and perform driving functions with no assistance from other vehicles or the infrastructure, or connected vehic les which are connected with the surrounding vehicles and roadside infrastructure but still need a driver to control the steering, acceleration, and braking. The combination of t heir autonomous and communication functions allow s the automated vehicle to op erate more efficiently and safely. Automated vehicle technology has advanced significantly in the past few years. In June 2011, Nevada passed a law that authorized the use of automated cars on public roads. So far four U.S. states (Nevada, Flo rida, Califo rnia, and Michigan), along with Washington D.C. , have legalized the operation of automated vehicles. The availability and potential wider use of automated vehicles poses the question: How can we use this technology to improve traffic operations in our tran sportation systems? Intersection control is an important component of the transportation system and it has a significant impact on transportation system efficiency. Based on the control method, intersections can be classified into : 1) uncontrolled interse ction s, which PAGE 15 15 operates based on the basic rules of the road ; 2) yield and stop control led intersections which explicitly assign the right of way to road users through the used of stop or yield signs ; and 3) signalized intersection s . Among the three types o f intersection control method, the uncontrolled and yield or stop controlled methods are usually used for intersections with relative low volume . For high volume intersections where the less restrictive form of control is not able to effective in assuring safety and efficiency , installation of traffic signal s need to be considered. If properly installed and designed, traffic signals are able to increase the intersection capacity, improve safety and allow orderly movement through a complex situation (Roess, Prassas, & McShane, 2004) . Therefore, compared to other control types, signalized intersection plays a very important role in improving transportation system performance and mitigating congestions , and improvement in traffic sig nal timing has the potential to significantly benefit the transportation system. For signalized intersections, throughput and delay depend on signal control, which is determined as a function of flow. Pre timed control uses historical flow information, whi le actuated control uses actual approach demand on a cycle by cycle basis. The development of adaptive signal control (ASC) improves the conventional actuated signal control to a certain extent by adjusting the signal timing to accommodate time varying tra ffic patterns . In the ASC system, vehicular traffic is detected by strategically placed sensors to predict when and where the traffic will be, and the signal controller utilizes these predict ions to compute optimal signal timings and simultaneously imp leme nt the m in real time. However, the effectiveness of ASC largely depends on the prediction of vehicle arrivals. S everal field implementation results PAGE 16 16 indicate that the benefits of ASC are still debatable (Shoup, 1998; Girianna & Benekohal, 2002 ) . The limit ation s in getting accurate real time demand information cau ses difficulties in optimizing signal timing s . As a result, the developed signal timing plan may not be adequate to meet the fluctuations . This ineffective response to the fluctuating demand is on e source of the delay f or currently used signal control methods (i.e. pre timed signal control, actuated signal control, and ASC) . The automated vehicles are able to provide full information regarding the vehicle arrivals to the controller. Then, the contro ller will be able to prod uce a more efficient timing plan or vehicle passing plan (if traffic signals are not used in the intersection system) to guide vehicles through the intersection . Another source of delay is due to driver reaction related delays. Th e use of automated vehicle technology also has the potential to reduce this type of delay through the use of their communication capability as well as the potential to fully control vehicle trajectories. I f the optimized vehicle trajectories, which are cal culated based on the signal timing information or the vehicle passing plan , are transmitted to approaching vehicles in advance , the intersection capacity would be better utilized. For example, these optimal trajectories may direct vehicles to accelerate ( up to a point) to fill up the gaps and save time for the following vehicles . T here have been some studies that developed algorithms to improve intersection control employing the communication capability and the automated function s of the automated vehicles . However, most of the previous research either use d more detailed and accurate data obtained from the approaching vehicles to PAGE 17 17 improve the intersection control algorithm, or optimize d vehicle trajectories based on the signal timing information or vehicle p assing plane provided in advance. In both cases , only data obtained through one way communication ( either from the vehicle to the controller or from the controller to the approaching vehicles ) are used in the optimization . In order to fully utilize the adv anced technology of the automated vehicle system and ma ximize the intersection efficiency , an intersection control algorithm that allows to jointly optimiz e the system performance and the trajectory of each single vehicle , is proposed and developed in this dissertation. 1.2 Dissertation Objectives The objective of this research is to develop an intersection control algorithm that allows for the system performance and the trajectory of each single vehicle to be jointly optimized under an automated vehicle environment . It is assumed that this automated vehicle environment enables bidirectional communication between vehicles and the intersection controller. Thus, the control algorithm is optimized based on more detailed and accurate information (such as speed , location, etc.) obtained from all automated trajectories are optimized based on the decisions from the controller ( signal timing or vehicle passing sequence ) , and these a re transmitted to the automated vehicles. In order to evaluate the proposed algorithm under various scenarios, simulation tool s that are capable of modeling the proposed optimization systems are also developed. The following tasks are performed to accompl ish the above objective s . 1. Dev elop a control optimization algorithm for an intersection that consists of two single lane through only approaches under a 100% automated vehicle environment . PAGE 18 18 2. Code a simulator i mplement ing the algorithm proposed in Task 1 , and compare the results against traditional actuated signal control to assess its effectiveness. 3. Expand the proposed optimization algorithm in Task 1 so that it can be implemented for a general four approach intersection with the consideration of turning veh icles and all possible phase combinations . 4. Code an intersection simulator implementing the optimization algorithm developed in Task 3 and compare the proposed algorithm to traditional actuated signal control. 1.3 Dissertation Outline The remainder of thi s dissertation is organized as follows. Chapter 2 provides an overview of the literature on the existing intersection control methods especially the signal control strategies , the Automated Vehicle technology, and previous research that developed intersect i on control algorithms employing automated vehicle functionalities . Chapter 3 discusse s the development of a signal control optimization algorithm for a very simple intersection that consists of two one way streets with through traffic only, under an autom ated vehicle environment. A MATLAB simulation and analysis of the proposed algorithm are also presented in this Chapter. An extended optimization algorithm for a standard four approach intersection which considers turning movements is presented in Chapter 4, along with the development of a Java based simulation and evaluation of the proposed algorithm . Finally, the o verall conclusions and recommendations for future work are provided in Chapter 5 . PAGE 19 19 CHAPTER 2 LITERATURE REVIEW This chapter first provides a b rief summary of the exi sting intersection control methods with the emphasis on the existing signal control strategies . Following that, it describes the advanced automated vehicle technology , along with a discussion of the vehicular communication system . Fi nally , a review of the existing intersection control algorithms implementing wireless vehicle to infrastructure communication is presented. 2.1 Intersection Control Method s Intersection is an integral component of the transportation system. A typical four approach intersection has twelve vehicular movements which create many potential crossing and merge conflicts. The objective of intersection control is to control and manage these conflicts in a way that provides safe and efficient movement through the in tersection for vehicles and other road users. The existing intersection control strategies can be classified into three different levels (Roess, Prassas, & McShane, 2004) : Level 1: basic rules of the road (uncontrolled interse ctions) Level 2: yield or stop control Level 3: traffic signalization The un controlled intersection does not have signing or traffic signals installed. It operates under the basic rules of the road, such as vehicles on the left must yield to vehicles on th e right and the through vehicles have the right of way over turning vehicles. The uncontrolled intersections are common in rural areas and residential neighborhoods, where both the traffic volume and speed are low and no or little collision history has bee n observed in history . PAGE 20 20 If the sight distance of the intersection is not sufficient or the in tensity of the traffic demand and the complexity of the intersection indicate an un safe operation under no control, a higher level of control, the yield or stop co ntrol, need to be considered. The three basic control strategies of Level 2 control are yield control, two way stop control, and multi way stop control. Yield sign is placed on certain approaches, generally not on the major street , to an intersection. Veh icles controlled by the yield sign have to slow down and yield to the traffic that is given the right of way. Vehicles need stop only when necessary to avoid interference with the major street traffic. Tow way stop control is the most common form of the le vel 2 control. T he stop signs should normally be posted on the minor street to stop the traffic before they entering the major roadway . It is used when application of less restrictive control or the basic rules of the road cannot provide safe and efficient operations of the intersection. Under the multi way stop control, traffic from all intersection approaches are required to stop before entering the intersection. Intersections with multi way stop control are generally implemented as a safety measure and a re often used on low speed, low volume facilities with approximately equal volumes on the intersecting roadways . Traffic signalization is the ultimate form of intersection control. It alternately assign s right of way to specific movements to reduce the nu mber of conflicting movements. If properly installed and designed, traffic signals are able to increase the intersection capacity, improve safety and allow orderly movement through a complex situation efficiently. For intersections where the less restricti ve control method cannot accommodate the traffic demand and t he complexity of the intersection safely and PAGE 21 21 effectively , installation of traffic signals need to be considered. Compared to the other form of control, traffic signalization is usually implemente d for more congested intersection . Therefore, it plays a very important role in improving transportation system performance and mitigating congestions . 2.2 Existing Signal Control Strategies 2.2.1 Conventional S ign al Timing M ethods The conventional signal timing methods include two primary types of signal timing algorithms that are currently widely implemented in the field : pre timed and traffic actuated. P re timed signal control has fixed interva l durations and cycle length that are predetermined. During t he signal control process, the intervals rotate follow ing a fixed sequence and timings . P re timed signal s can be optimized by adjusting their control parameters (cycle length and time split) off line base on the predicted dema nd. Most of the modern day sig nal timing for a pre timed control is based on the theoretical work conducted by Webster (1958) . Well designed pre timed traffic signal s are able to provide a fairly efficient operation for intersections with tight spaci ng , such as intersections at central business districts or diamond interchan ges (MoDOT, 2013) . However, these cannot deal with unplanned fluctuations in traffic flows , and thus actuated controllers are preferred at most intersec tions . In contrast to pre timed control, intervals for actuated control are called and extended in response to the presence of detected traffic . Therefore, it provides greater efficiency compared to pre timed signals by servicing traffic as required. D epe nding on the number of traffic movements that are monitored by detect ors , a ctuated control algorithms are divided into fully actuated and semi actuated . B oth types can reduce PAGE 22 22 delay and number of stops by being responsive to changes in demand and traffic pa ttern s , but their efficiency also largely depend s on the selection of the appropriate control parameters. There are a number of programs used for actuated signal timing optimization. Transyt 7F , Synchro , and PASSER II are some of the most widely used optim ization tools. As traffic patterns change over days and weeks, both the pre timed and actuated signals usually operate different timing plans at different times of the day and days of the w eek. This operation is conducted based on the predetermined time o f day and day of week schedule , and is referred to as the Time of Day (TOD) signal control (Koonce , et al., 2008) . Most of the US traffic systems implement the TOD signal timing, and most of these systems use three to five wee kday timing plans and up to six plans for other special cases such as weekends, holidays, incidents, etc . (Gordon, 2010) . However, the TOD signal control method only works well for consistent and predictable traffic conditio ns. For unusual situations (e.g. special events, incident s , construction, extreme weather), the timing plan selected based on the time of day schedule may not be the most appropriate for the current traffic condition. 2.2.2 Traffic Responsive Control Traf fic responsive control method s are b ased on traffic detector data and they automatically select a plan from the timing plan library that is best suited to the current traffic condition s (Koonce , et al., 2008) . There are gener ally two categories of timing plan selection strategies that are currently used by the traffic responsive signal control systems in the US. Signature matching strategy . Using t his strategy for each specific timi ng plan stor ed in the lib rary. For a specific timing plan, each PAGE 23 23 detector has a signature. Its value is usually a combination of volume and occupancy , and is often referred to as the expression Volume (V) + Factor (k) x Occupancy (O) (Koonce , et al., 2008) . During the operation, data from multiple detectors are obtained and matched to the library of signature sets. If the signal timing plan that best matches the detected data is not the one that is currently in use , a transition will be mad e to the signal timing plan with the closest match. In order to avoid unnecessary back and forth transition s between timing plans that are close to the selection threshold, this strategy also develops a hysteresis algorithm that smooth the response s to cha nges in traffic conditions (Gordon & Tighe, 2005) . Parameter selection strategy . This strategy assigns specific detectors to select particular signal control parameters. A detector may be assigned to one or more parameters. Selection of cycle, split and offset is based on the respective detector data (Gordon, 2010) . 2.2.3 Adaptive Signal Control Adaptive Signal Control ( ASC) is a signal control technology that automatically adjust s signal para meters in response to real time traffic conditions. In a n ASC system, vehicle data are detected through strategically placed sensors at an upstream and/or downstream point. Then, a particular algorithm is used to predict the traffic condition at the downst ream intersection and adjust the signal timing parameters . Despite the different algorithms for traffic prediction and signal timing optimization, all ASC systems follow a similar process : 1) Collect and process data through a detection system to identify traffic conditions ; 2) Evaluate alternative signal timing plans using a traffic model ; 3) Identify the best signal timing strategy based on a performance metric and implement it in the signal controller . The above three steps are repeated every few PAGE 24 24 minutes to keep traffic flowing smoothly. As t he ASC technology is designed to adjust the signal timing in reaction to actual conditions , it is expected to reduce queue length, traffic delay and travel times . The remainder of this section describes several ASC al gorithms that have been deployed in the U.S . Sydney Co ordinated Adaptive Traffic System (SCATS) . SCATS is the first real world application of the adaptive traffic system. It was first implemented in Australia , in the 1970s (Lowr ie, 1982) . SCATS adaptive control strategy is conducted a t two levels, Strategic C ontro l by the regional computer and Tactical C ontrol by the local control at each intersection, to determine the three princip al signal timing parameters ( cycle length, pha se split and offset ) . Strategic Control is the top level of control that determines the optimum cycle length, split and offset for a group of signals (which are know as subsystems) to suit the average traffic condition of the subsystem . Intersections in a subsystem are always coordinated and one of them is defined as the critical intersection . Cycle length and phase split of the critical intersection is determined based on the principle that the most congested lane has a degree of saturation, which is defin ed as the ratio of the effectively used green time to the total available green time, around 0.9. The non critical intersections share a common cycle length, interrelated split and offset with the critical intersection. Under the control of the regional co mputer, Tactical Control is operated by the local controller for determining split and offset that meet the cyclic variation in demand at each intersect ion. The combination of the Strategic Control and Tactical Control enables the system to handle both the gradua l systemic changes and the rapid cyclic variations in traffic demand. SCATS also combines adaptive signal control with other conventional control strategies , including PAGE 25 25 isolated signal operation , time based coordination, and flashing yellow operation , to meet various operational needs . Split Cycle Offset Optimisation Technique (SCOOT) . Since its inception by the UK Transport Research Laboratory in 1981, SCOOT has become the most widely used adaptive traffic control system with over 200 world wide impl ementations (Jhaveri, Perrin, & Martin, 2003) (Zhao & Tian, 2012) . The SCOOT system divides a network into intersections. All intersections inside the same reg ion are coordinated. The operation of SCOOT significantly relies on its detection system. Both stop line detectors and advance detectors , which are typically placed 150 1 000 feet upstream of the stop line , are used in the SCOOT system (Koonce , et al., 2008) . The advance detectors provide a count of approaching vehicles. Based on those data, the SCOOT model predicts the progression of traffic from the detector to the stop line. The stop line detectors collect the ing information and transfer the rofiles (Transport Research Laboratory, UK, 2013) . All th is information collected by the detection system is then used by SCOOT i n three optimizers: split optimizer, offset o ptimizer, and cycle time o ptimizer (Zhao & Tian, 2012) . The cycle time optimizer continuously adapt s the cycle time of each region to ensure the most congested intersection in the sy stem is operating at 90% saturation. The split optimizer incrementally changes the pre determined green time of every phase and to determine whether the phase should be extended, shortened or remain the same. The o ffset optimizer evaluates the scheduled a nd the possible changed offsets based on information stored in cyclic flow profiles , and implement s the one with the best predicted PAGE 26 26 performance measures. With the three optimizers, SCOOT can adjust signal timing pla ns in response to the real time traffic fluctuations and follow trends over time to maintain constant co ordination of the signal network (Transport Research Laboratory, UK, 2013) . Real Time Hierarchical Optimized Distributed Effective System (RHODES). RHODES was developed by a research team at the University of Arizona in 1990 (Mirchandani & Head, 2001) . As a real time traffic adaptive control system , it collects traffic data from various types of detectors, predicts future traffic streams, and calculates the optimum signal timing plan based on the se predictions. The control and prediction problem is decomposed into three hierarchical levels in the R HODES system. The highest level of R HODES, which i s referred to as the network loading level , predicts the general travel demand characteristics over longer periods of time ( typically one hour ) and estimates the traffic load on each particular link . Based on the load estimates, the middle level control, w hich is the network control level , establish es coordination constraints for each intersection and allocates the approximate green times for different movements. At the lowest level, the intersection control level , phase sequence and durations are determine d based on observed and predicted arrivals of individual vehicles, as well as coordination and operation constraints . The development team pointed out three features of RHODES that makes it a viable and effective control system ( Mirchandani & Head, 2001) : 1) it allows implementation of the most recent technology in the control system to advance the data transferring, processing and control strategy implementing process ; 2) it considers the stochastic variations in traffic PAGE 27 27 flow ; and 3) it explicitly predicts individual vehicle arrivals, platoon arrivals and traffic flow rates in response to this variation. Optimized Policies for Adaptive Control (OPAC). Sponsored by the U.S. Department of Transportation , OPAC was originally develo ped at the University of Ma ssachusetts, Lowell in the early 80s (Liao, 1998) . OPAC is a real time demand responsive algorithm that utilizes d ynamic programing techniques to optimize signal timing plans and minimize the tot al in tersection delay and stops . Using OPAC , a sequence of switching decisions is made in a control period at fixed time intervals to determine whe ther the current phase should be terminated or extended. Dynamic programming method is used for the optimization, and a rolling horizon technique is applied to dynamically revis e the decisions based on real time arrival information collected by the upstream detectors . Although originally designed for signal control of isolated intersections, OPAC can also serve as a b uilding block for coordinated network signal optimization in the Virtual Fixed Cycle network version (VFC OPAC) (Gartner, Pooran, & Andrews, 2001) . VFC OPAC consists of a three layer control architecture : the Local Control Laye r (Layer 1) for determining phase durations subject to the cycle length constraint from Layer 3 , the Coordination Layer ( Layer 2 ) for optimizing the offsets at eac h intersection (once per cycle) , and the Synchronization Layer (Layer 3) for calculating the network wide virtual fixed cycle . Adaptive Control Software Lite (ACS Lite) . In 2001, FHWA initiated the development of ACS Lite, a reduced scale version of ACS, to reduce the high cost of deployment and maintenance of the regular adaptive systems (Shelby, Bullock, Gettman, Ghaman, Sabra, & Soyke, 2008) . ACS Lite is designed to consolidate the PAGE 28 28 adaptive processing into the closed loop systems, and provide cycle by cycle adjustments to the signal timing parameters (cycle, spli t and offset) in response to changing traffic conditions. The control algorithms of ACS Lite include a Run Time Refiner, Transition Manager and Time of Day Tuner. Based on the principle that the recent past predicts the near future , t he Run Time Refiner u ses the most recent data to evaluate alternative timing plans. C ycle, splits, and offsets are adjusted in small, incremental steps to balance the degree of utilization across all phases and capture the maximum progressed traffic flow in the green band. The adjusted timing plan is downloaded to the local controller every 5 15 minutes. When transitioning between one plan and another, t he Transition M anager choses the best transition method to minimize the time spent out of coordination . The Time of Day Tuner periodically updates the time of day signal timing plans and uses the updated signal timing plans as the baseline for its adaptive operation. Compared to other ASC algorithms, ACS Lite is slower in responding to rapid changes in traffic flows, however, it significantly reduces the costs for implementing the ASC technology (Shelby, Bullock, Gettman, Ghaman, Sabra, & Soyke, 2008) (Koonce , et al., 2008) . According t o Zhao and Tian (2012) , t he ASC technology is expected to improve the intersection traffic conditions as it is designed to adjust the signal timing in response to the real time condition . However, previous field tests and evaluation studies showed mixed res ults. A lot of studies indicated improvements over the traditional signal control s ystems (Peters, Monsere, Li, Mahmud, & Boice, 2008) (Samadi , Rad , Kazemi , & Jafarian, 2012) (Hutton, Bokenkroger, & Meyer, 2010) (Andrews, Elahi, & Clark, 1997) . However, there are also studies which showed no improvements (Petrella, Bricka, PAGE 29 29 Hunter, & Lappin, 2005) (Girianna & Benekohal, 2002) (Shoup, 1998) . Petrella et al. (2005) c oncluded from their study that if an optimized signal timing plan has already been deployed , the ASC systems c annot further improve the system performance . They also indicate that the effectiveness of ASC heavily rel ies on tr affic and network conditions. 2.3 Advanced Automated Vehicle Technology 2.3.1 Development of The Autonomous Vehicle Autonomous vehicles are those that are capable of driving without human intervention. They are also known as self driving car s. The se vehicles detect the operational environment via a variety of sensors such as GPS, lidar , radar and computer vision . The detected information is th en compared to a preloaded map to identify obstacles and find the appropriate navigation paths (Wikipedia, 2014) (Pawsey & Nath, 2013) . The earliest quasi autonomous demonstration system dates back to the 1920s when Houdina Radio Control demonstrated a radio controlled drive r less car in New York City (Wikipedia, 2014) . The vehicle was controlled through radio signals sent by a car that followed it. The radio impulses wer e received by the transmitting antennae on the tonneau of the vehicle and were transmitted to a circuit breaker to direct the movements of the vehicle. The important milestone in the development of the autonomous vehicle was the Mercedes Benz robotic van d esigned by Ernst Dickmanns and his team at Bundeswehr University Munich in the 1980s (Forrest & Konca, 2007) . The prototype achieved 39 miles per hour on the roads without traffic. Since then, the development of autonomous veh icle has advance d significantly both in technology and legislation . Numerous major companies and research PAGE 30 30 organization s are involved in autonomous vehicle related projects . Many major automotive manufact urers, including Mercedes Benz, General Motors, Ford, Volkswagen, Audi, Nissan, Toyota, BMW and Volvo, are developing and testing prototype autonomous vehicles. In June 2011, Nevada passed a law that authorized the use of autonomous cars on public roads. As of the end of 2013, four U.S. states (Nevada, Flori da, California, and Michigan) have legalized the operation of autonomous vehicles. 2.3.2 Connectivity of Automated Vehicle s and Vehicular Communication S ystem s The auto nomous driving capabilities of autonomous vehicles have the potential to benefit the tr ansportation system in the form of reducing crashes that are cause by driver error, reducing the space required for safety gaps, and relieving the constraints state (i.e., it does not matter if the driver is under age, over age , disabled , or di stracted) . However, the self driving capability cannot bring further improvements in terms of improving system operation, mitigating congestions, and reducing environmental impacts as long as the vehicles operate all by themselves (Parent, 2013) . With the development of the vehicular communication technology , vehicles are able to exchange information with the surrounding vehicles and the roadside infrastructures. By taking advantage of this communication technology, the automat ed vehicle combines the communication functionality with its autonomous capability. B esides perform driving functions autonomously, automated vehicles also enables information exchange relevant to driving safety and transportation efficiency with other veh icles and roadside infrastructures (Walsh, 2014) . Through the communication, automated vehicles can be much more efficient in avoiding accidents and traffic congestions . F or example , they can notify surrounding vehicles before making a lane PAGE 31 31 change so other drivers can make safer decisions. Automated vehicles can also cooperate with the infrastructure to improve traffic condition by implementing variable speed limits or advanced intersection management. All t he information exchan ges are accomplished through the vehicular communication system . Vehicular communication system is a peer to peer network that uses vehicles and roadside units as the communicating nodes . Through v ehicle to vehicle (V2V) and vehicle to infrastructure (V2I) communication , which are accomplished by on board sensor s , processing, and wireless communication modules available on the vehicles and roadside units , applications can be enabled to enhance transportation safety and efficiency ( Papadimitratos, et al., 2008) . The ability to exchange information through the V2V and V2I communication is a foundation for the vehicular communication system. There are several different communications platforms that support information exchange betwe en vehicle and infrastructure, including Dedicated short range communications (DSRC) Wi Fi Worldwide Interoperability for Microwave Access (WiMAX) Cellular Bluetooth 3G/4G However, the non DSRC communications have 1.5 to 5 second latencies, which would del ay data transmission. T he latency of DSRC is only 0 .002 seconds (Smith, Venkatanarayana, Park, Goodall, Datesh, & Skerrit, 2011) . Besides, DSRC has many other advantages: it is very robust in the face of radio interference; i t works with high vehicle speeds (up to 120 mph); and its performance is immune to extreme weather PAGE 32 32 conditions (RITA, 2011) (Smith, Venkatanarayana, Park, Goodall, Datesh, & Skerrit, 2011) . DSRC is a short to medium range communications service that is specifically designed to support cooperative, safety critical applications in a vehicular communication system by per mitting high data transmission . In Report and Order FCC 03 324, the Federal Communi cations Commission (FCC) allocated 75 MHz of spectrum in the 5.9 GHz band for DSRC (RITA, 2014) . The spectrum was allocated for safety purpose s . However, it is flexible enough to support mobility and environmental applications . The types of safety and mobility information that could be sent and receive d with DSRC in a vehicular communication system are specified by the Society of Automotive Engineers (SAE) J2735 DSRC Message Set Dictionary . The standard defines three levels of information carried by the DSRC : data elements , data fields, and message sets. Data elements are grouped into different data fields, which are further grouped into message sets (SAE, 2009) . The intersection signal control opera tion studied in this dissertation primarily rel ies on the Basic Safety Message (BSM) Part I, which contains core data elements, including vehicle position, heading, speed, acceleration, steering wheel angle, and vehicle size . The specific data elements con tain ed in the BSM Part I are listed below. MsgCount TemporaryID DSecond Position ( Local 3D ) The data elements are: Latitude , Longitude , Elevation , Positional Accuracy Motion The data elements are: Transmission a nd Speed; Heading ; Steering Wheel Angle ; Acceleration Set 4 Way (3 axes of acceleration plus yaw rate ) PAGE 33 33 Control Brake System Status V ehicle Basic Vehicle Size The BSM Part 1 m e ssage could be transmitted approximately 10 times per second over DSRC (McGurrin, 2012 ) . By receiving these messages from approaching vehicles, the intersection controller could gain a more comprehensive understanding of the incoming traffic and would be able to optimize the signal timing based on th is information , as discussed later in this d issertation . 2.4 Intersection Control Algorithm s Using Wireless Communication Most of the existing literature related to employing communication technology to improve intersection control can be summarized into two categories. The first category uses data obtained from approaching vehicles to improve the intersection control algorithm , whil e the second provides signal timing information to the drivers so that they can optimize their trip perspective . The re are also a few studies that have investigated vehicle trajectory adjustment and vehicle passing time optimi zation, and developed intersection control algorithms without using the conventional stop and go style traffic signal s in a vehicle infrastructure cooperation environment. Each of the above mentioned categories is discussed in the following subsections. 2.4.1 Intersection Control Algorithm Employing Vehicle to Infrastructure Communication Technology Gradinescu et al. (2007) prop osed an adaptive signal control algorithm based on short range wireless communication between vehicles and fixed controller nodes installed at the intersections. Based on the volume and demand information received from the approaching traffi c within the communication range, t he intersection controller PAGE 34 34 calculates the timing plan once every cycle for the cycle that follows the current one. Cycle length is first calculated using , and green splits are then determined to maintain equal degrees of saturation on each link. The calculated signal timing plan is further adjusted to meet the maximum cycle and pedestrian minimum green. An integrated simulation tool was developed and two intersections in Bucharest were coded into the simu lator. By comparing the proposed algorithm to the existing, pre timed signal control method in the simulation environment, the researchers concluded that the proposed system significantly reduced the intersection average delay, fuel consumption and polluta nt emissions during rush hours. Based on the communication technology between traffic signals and the approaching vehicles, Yan et al. (2008) proposed a n algorithm to control traffic signal s at an isolated intersection that consists of two single lane approaches. During the control process, traffic lights of each direction detect the movements of incoming vehicles in its road. The detected information, including vehicle intentions, speeds, positions and priorities are t hen used in a vehicles passing sequence problem to find the signal timing that minimizes the total travel time of the intersection . The Branch and Bound method was adopted for solving the problem and the depth first search method was chosen to find the opt imum solution. Analysis of the computational times in various scenarios showed that the proposed algorithm is practical for implementing in the field. They then conducted a follow up study (Yan, Dridi, & Moudni , 2009) and exp a nded the algorithm to analyze a four way intersection with shared right turn lanes and exclusive left turn lanes. A forward dynamic programming algorithm was proposed to solve the intersection evacuation problem. PAGE 35 35 Berg (2010) proposed improvements to the conventional red light preemption (RLPE) and green light extension (GLE) algorithm based on instantaneous traffic data obtained through short range wireless transmitters in cars and elements of the road infrastructure . The proposed algorithm was demonstrated for a fully actuated intersection, which was controlled based on instantaneous location coordinates and velocity vectors transmitted from approach ing vehicles. They described the architecture of the software in bot h RSE (Road Side Equipment) and OBE (On Board Equipment) domains for implementation of the RLPE and GLE functionality , and implemented the algorithm in a control environment at DEN S O's Vista, California facility. Performance improvements were observed at t he tested intersection compared to the existing signal control scheme . Smith et al. (2011) developed three signal control algorithms ( o versaturated conditions algorithm , v ehicle clustering algorithm and p redictive micro scopic simulation algorithm ) based on the conventional control strategies to address spill back during oversaturated conditions, prevent the breakup of vehicle platoons on the major street, and reduce the predicted future vehicle delays using the real time DSRC data . The o versaturated conditions algorithm was developed to modify the offset and splits at the upstream intersection, so the affected approach is either delayed or cut short, as dictated by the real time queue length on the downstream link. A dditi onal time available from the affected approach is allocated to the oppos ing approach. The V ehicle C lustering A lgorithm (VCA) was designed primarily for a high speed major corridor crossing low speed, low volume side streets . It uses a novel gap out a pproac h, ensures that leftover queues on roads with green indications are cleared, and prevents the PAGE 36 36 breakup of vehicle platoons using the single link clustering algorithm (SLINK) . The Predictive Microscopi c Simulation Algorithm (PMSA) was developed based on the rolling horizon traffic control scheme . Using the location and speed data obtained from DSRC equipped vehicles, microscopic simulation models are developed to continuously minimize the predict ed future vehicle delays over the rolling horizon . The three pro posed algorithm s all take advantage of the advanced V2V and V2I communication technologies , they are either impossible or cost prohibitive with the conventional detector data alone. The algorithms were evaluated using the VISSIM microscopic traffic simulat ion software . The results showed that when a ssuming 100% market penetration , significant reductions were observed for all algorithms, up to 28% in certain oversaturated scenarios, 6% in VCA, and 8% in PMSA. At 20% market penetration, the oversaturated cond itions algorithm generated 8% improvements in delay, while at 25% market penetration the VCA and PMSA benefits were either insignificant or non existent. By taking advantage of the vehicle tracking capability of the IntelliDrive SM system, Yi (2011) developed a dilemma zone protection method for high speed intersections. The proposed system continuously tracks the position and speed of the approaching vehicles through DSRC. Based on the information, the system determines whether a vehicle needs dilemma zone protection, and dynamically calculates the passage time. The proposed method was compared with the conventional fixed point detection scheme. Equations were developed for calculating the probability of failure of dile mma zone protection, and a quantitative analysis was conducted to evaluate the effectiveness of different control strategies. The results showed that for high speed PAGE 37 37 intersections, the size and passing time of the dilemma zone are sensitive to the variation s in field conditions, and the proposed algorithm operates more safely and more effectively as it can better capture this variation. He et al. (2011) developed a signal control optimization algorithm using a unified pla toon based mathematical formulation (PAMSCOD) under a vehicle to infrastructure communications environment. During the proposed optimization process, existing queues and significant platoons from each intersection approach are first identified using a prop osed headway based platoon recognition algorithm using real time information from probe vehicles. Based on the identified platoon data, the current traffic signal status, and requests from vehicles with higher priorities (such as transit buses and emergenc y vehicles ), a mixed integer linear program (MILP) formulated with the consideration of shockwaves and physical queues is solved to determin e future optimum signal timing plans. Arterial coordination was also considered in PAMSCOD using a platoon based dyn amic coordination strategy . Different from the conventional coordinated signals, which are managed through the determination of o ffsets, splits, and a global cycle length, the proposed algorithm calculates the optimal parameters of the coordinated signal t iming plan s in the MILP problem using real time platoon information. S imulation experiments were conducted using VISSIM under different saturation levels, including both non saturated and oversaturated scenarios. Both automobiles and buses were considered in the traffic stream. Compared to the conventional coordinated actuated signal control, PAMSCOD significantly reduce delays in all the tested scenarios for both travel modes. PAGE 38 38 Yan et al. (2013) studied a vehicle passing sequence problem under the framework of AIM. In their study, autonomous vehicles were grouped into small units and each unit was considered as and independent individual. The system controller gathers arrival information of all the units and finds the mos t efficient passing sequence that can minimize the overall evacuation time using the proposed GA. Comparison with the pre timed signal control and the adaptive signal control showed that the proposed algorithm efficiently improved the intersection performa nce. However, the system controller only makes decisions on vehicle passing sequence using the given arrival information but does not consider adjusting vehicle trajectories to further improve the intersection performance. 2.4.2 Vehicle Warning or Control Algorithms Using Infrastructure to Vehicle Communication Data Mandava et al. (2009) introduced an arter ial velocity planning algorithm which dynamically provides speed advice to vehicles approaching a signalized interse ction to reduce the number of stops, improve fuel efficiency and reduce emissions . In the proposed system, signal timing information is trans mitted to equipped vehicles when they are approaching an intersection equipped with DSRC technology . After receivin g the signal timing information, the vehicle acceleration/deceleration rate is determined by solving an optimization problem with the objective to minimize the acceleration/deceleration rates and increase the possibility of encountering a green light. The c orresponding speed profile is then back calculated and provided to the driver. The proposed algorithm was implemented for a 10 intersection corridor in a stochastic simulation environment. It was found that the velocity planning algorithm could reduce ene rgy consumption and emissions by 12 14%. PAGE 39 39 Sunkari and Balk e (2011) described a proof of concept of the development of an Advance Warning of End of Green Systems (AWEGS) under the Connected Vehicle environment to improve i ntersection safety and reduce lost time. Based on the constant m e ssage exchanging between vehicles and signal controllers, the OBE installed in each vehicle identifies the scenario it may encounter and determines whether or not to display its based on the corresponding c riteria . Activation of the warning message provides the drivers with enough time to respond to the termination of the current green phase. Different form the conventional AWEGS application , in the proposed syste m t he advance warning massage is displayed in side the vehicle instead of on the road side . Also, t he message is vehicle specific and only displayed for those that absolutely need it . The proposed AWEGS are expected to improve intersection safety and elimina te deficiencies of the conventional AWEGS. Rakha et al. (2012) developed a fuel optimal vehicle trajectory adjustment algorithm at signalized intersections using vehicle to infrastructure communication. In the proposed system, trajectory optimization is conducted in two steps after the vehicle enters the DSRC communication range around an intersection . First, a proposed arrival time at the intersection is computed based on existing queue length, lead vehicle information, and signal timing information. Then, a fuel optimal speed profile is calculated using a vehicle acceleration model, roadway characteristics, a microscopic fuel consumption model, and the proposed time computed in step one. S imulations in MATLAB were condu cted for various scenarios to evaluate the proposed eco vehicle speed control application . Simulation results showed that the proposed algorithm has PAGE 40 40 the potential to reduce fuel consumption by preventing sudden stop and sh a rp a cceleration /deceleration . Cai et al. (2012) proposed an adaptive traffic signal control method, which is denoted as the vehicle to infrastructure communication based adaptive control (VICAC) , using real time DSRC data . Based on a vehicle travel tim e estimation model, the proposed VICAC selects the optimum timing plan using an approximate dynamic programming method with the objective to minimize travel time throughout the controlled network . As an additional feature of the VICAC method, a speed adjus tment algorithm was developed to reduce unnecessary stops, improve fuel efficiency and reduce emission s . Using the algorithm, t he VICAC controller selects the leading vehicle of a platoon , calculates the adjusted speed and sends the message back to the sel ected vehicles through Infrastructure to Vehicle (I2V) communication. Although signal optimization and vehicle trajectory adjustment are both considered in the VICAC system , they are not optimized at the same time. The optimized signal timing is used as in put information in the calculation of the adjusted speed. Therefore, speed adjustment in the proposed system is just an additional performance improvement function supplementary to the adaptive signal control . It does not take a role in the signal control optimization. Some a utomobile companies also have developed vehicle to traffic signal communication systems to assist vehicles to take advantage of the green wave . Two such examples are the Audi Travolution project and the BMW Traffic Light Assistant proj ect. In 2006, the a utomobile company Audi launched the T ravolution project aims to provide the drivers with more efficient, safer and greener driving experiences at PAGE 41 41 signalized intersections by taking advantage of the vehicle to infrastructure communication technology (Audi, 2010) . The project uses wireless LAN and UMTS links that allows vehicles to communicate with traffic lights. Traffic signals in the system continuously transmit a package of timing information to the appr oachi ng vehicle. Based on this information, the on board computer can calculate an optimal speed using which the vehicle is able to go through the intersection without having a stop. The calculated optimal d by the adaptive cruise control (ACC) system, which can automatically alter without human intervention. For vehicles that are stopping at the light, the system can provide them the amount of remaining red time. A similar sys tem was developed by the BMW Traffic Light Assistant project, which uses advance information of traffic signal phasing for determining the optimum speed to enable the drivers to take advantage of the green wave (BMW, 2012) . The system can also warn the drivers if they are about to run a red light. 2.4.3 Non Signalized Intersection Control in A Vehicle Infrastructure Cooperation E nvironment There are a few papers that have studied vehicle trajectory adjustment and ve hicle passin g time optimization for developing an intersection control algorithm without using the conventional stop and go style traffic signal s. Dresne and Stone (2004) developed an auto mated intersection management (AIM) system u tilizing a cell based intersection reservation system. The system identifies clear paths that can direct the vehicles through the intersection by processing the time space reservation requests sent from vehicles. Follow on research was conducted to accomm odate high priority vehicles (Dresner & Stone, 2006) and traditional human driven vehicles (Dresner & PAGE 42 42 Stone, 2007) and to maximize the vehicle arrival speed in order to minimize the time spend in side the intersection (Au & Stone, 2010) . The proposed system provides feasible paths for vehicles to go through the intersection without conflict and the calculated trajectory for a particular vehicle is the optimum for itsel f. However, the proposed system cannot optimize the system performance with the consideration of all the vehicles. For example, i f the reservation request sent by a vehicle is denied because of an existing conflicting request, the vehicle has to slow down and make another reservation later. The front vehicle cannot speed up to create a gap for the vehicle to fill in. Another similar study was conducted by Rakha et al. (2012) , to develop a Cooperative Vehicle Intersection Control (CVIC) system based on bidirectional communications between vehicles and an intersection controller. Vehicle trajectories are adjusted and their passing time is determined based on solving a non linear constrained optimization problem. As a result, vehicles are able to safely cross the intersection through sufficient gaps in the opposing approach. This algorithm was reported to largely reduce the total stopped delay compared to an actuated control. However, the objective function of the optimization problem is minimizing conflicts between vehicle trajectories of opposing approaches. Only feasible, not the optimum, solutions can be found for the vehicles to find sufficient gap. Therefore, the adjusted trajectories are not necessary to be the ones that can minimize the intersection delay. 2.5 Summary of the Literature Review Automated vehicles are those that use a variety of sensing techniques and connectivity with surrounding vehicles and roadside infrastructures to gather information and autonomously perform driving functions. They are different from autonomous PAGE 43 43 vehicles which sense the environment, navigate and perform driving functions all by the vehicle themselves, or connected vehicles which are connected with the surrounding vehicles and roadside i nfrastructure but still need the drivers to control the steering, acceleration, and braking. A utomated vehicle s integrate the communication functionality with their autonomous capability and enable information exchange relevant to driving safety and transp ortation efficiency through the V2V and V2I communication technology. Among the various communication platforms that support information exchange between vehicle and infrastructure, DSRC is the only short range wireless alternative that provides designated licensed bandwidth, fast speed, low latency, high reliability, security and privacy. Also, the safety and mobility information that can be sent and received with DSRC are specified by the SAE J2735 DSRC Message Set Dictionary. Auto mated vehicle technology has advanced significantly in the past few years both in technology and legislation . The current emphasis on the development of auto mated (i.e., driverless and with the ability to communicate with the infrastructure) vehicles allows for the possibility of develop ing a new intersection control algorithm that can simultaneously optimize the vehicle trajectories and optimize decisions of the intersection controller (i.e. traffic signal changing decisions or vehicle passing sequence) to improve the intersectio n efficiency . T he intersection control algorithms developed so far either use data obtained from approaching vehicles to improve the control algorithm , or optimize the trajectory for each single vehicle based on the signal timing information provided in advance . Both of these approaches rely on one way communication, either from the controller to the vehicle or PAGE 44 44 from the vehicle to the controller . There are also a few papers that have studied vehicle trajectory adjustment an d vehicle passing time optimization. They developed non signalized intersection control algorithms in a vehicle infrastructure cooperation environment. However, the proposed algorithms cannot optimize the system performance to its maximum efficiency. PAGE 45 45 CH APTER 3 S IGNAL CONTROL OPTIMIZATION FOR A SIMPLE TWO APPROACH INTERSECTION This c hapter introduces the proposed methodology that can cooperatively optimize the vehicle trajectories and the signal timing for a simple two approach intersection . The first sec tion provides an overview of the methodology fram ework for a two approach intersection . The secon d section details the trajectory optimization algorithm , and the third explains the optimization horizon algorithm implementation. The fourth section outlines the simulation effort along with a comparison of the proposed algorithm performance against conventional actuated control. 3.1 Methodology Framework The methodology assume s there is an intersection optimization controller designed to gather individual veh icular information and to calculate optimum signal timings. The resulting optimum signal timing plan is implemented, while at the same time the intersection controller calculates the optimal trajectories for all vehicles within tion range and transmits these back to the vehicles. The communication between the intersection controller and the vehicles is assumed to follow V2I communication protocols . A suitable wireless communication that can provide high accuracy and low latency is required. Therefore, in this study , the proposed algorithm was developed based on the DSRC communication technology. The optimization is conducted inside the assumed communication range as shown in Figure 3 1. The magnitude of this range depends on the efficient communication distance between vehicles and the infrastructure. Using the DSRC communication technology, the maximum communication rage is 1000 meters (3281 PAGE 46 46 feet) (Guo & Balon, 2006) . Therefore, the communication rang e is assumed to be 3000 feet from the center of the intersection. Since the analysis intersection during this initial stage has only two single lane approaches, the methodology considers only two signal phases, and no turning movements or lane changes. Al so, communication and computation performance are assumed to be completed instantaneously, resulting in no time delays for the computing process and information transmission. All the vehicles are assumed to be passenger cars. With the above assumptions th e optimization process is as follows: 1. At the beginning of the optimization, identify the vehicles inside the communication range and gather the required input information for the intersection controller; 2. Based on the length of the optimization period, mini mum green time and maximum green time for each approach, enumerate all the feasible timing plans and compute the optimum vehicle trajectories and associated minimum average travel time delay (ATTD) of each timing plan; 3. Identify the minimum among the minim um ATTDs; the associated signal timing plan is the optimum signal timing plan and the adjusted vehicle trajectories are the optimum vehicle trajectories; 4. Transmit the optimization results to the signal controller and the vehicles respectively, and implemen t the optimized signal timing and vehicle trajectories for the designated optimization period; 5. Repeat step 1 through step 4 to conduct the optimization over the time horizon for continuously entering vehicles. As discussed earlier, it is assumed that ther e are no delays in the first three steps and in the information transmission of the fourth step. Thus the optimized vehicle trajectory and signal timing can be determined and implemented at the beginning of every optimization period. Note that this assumpt ion was made for simplifying the optimization process. However, the proposed optimization algorithm is capable of PAGE 47 47 considering the additional time required for data transmission and computation to better reflect field conditions. The difference is that vehi cle trajectories during this additional time period need to be estimated. The remainder of this section provides additional information on the vehicle trajectory adjustment logic as well as the feasible signal timing enumeration. 3.1.1 Trajectory Adjustmen t Logic The time space diagrams in Figure 3 2 illustrate two basic vehicle trajectory adjustments. In Figure 3 2A , travelling at its original speed, the subject vehicle would have to stop at the intersection and wait for the next green signal as shown by t he dashed curve. But if the signal timing information is available in advance, we can calculate the speed at which the vehicle could drive through the intersection without having to stop. In this way, stopped delay as well as startup delay (accelerating fr om a complete stop) can be reduced. The horizontal distance between the dashed curve and the solid curve is the travel time saved by this trajectory adjustment. Likewise in Figure 3 2B , a vehicle may be directed to accelerate (without exceeding the speed limit) in order to clear the intersection earlier. These two trajectory adjustment behaviors can not vehicles to leave the intersection earlier. 3.1.2 Feasible Si gnal Plan Enumeration Since only two phases are considered in this research and the resulting number of scenarios is limited, simple enumeration is implemented for selecting the optimu m signal timing plan. (The next chapter discusses the e xpansion of this method to multilane approaches and consider s a more rigorous optimization approach. ) PAGE 48 48 First, based on the length of the optimization period, minimum green time and maximum green time for each arterial approach, we calculate the minimum and the maximum total number of phases that could be scheduled for the optimization time period usin g the following two equations: ( 3 1) ( 3 2) where N max = maximum total number of phases N min = minimum total number of phases g min,1 = mini mum green time of approach 1 (the approach that is first given green during the optimization time period), sec g min,2 = minimum green time of approach 2, sec g max,1 = maximum green time of approach 1, sec g max,2 = maximum green time of approach 2, sec t opt = length of the optimization period , sec = round down to the largest integer that does not exceed x = round up to the smallest integer that is not less than x Second, for e ach specific number of phases , enumerate all the feasible phase splits that solve Equation 3 3 with the minimum green and the maximum green constraints: ( 3 3) PAGE 49 49 Where t opt = length of the optimization period , sec g 1,i = duration of the i th green phase of approach 1, sec g 2,j = duration of the j th green phase of approach 2, sec N = total number of phases n 1 = numb er of green phases for approach 1 n 2 = number of green phases for approach 2 Those combinations of the number of phases and the phase durations are all the feasible signal timing plans. This process was coded in the MATLAB simulation using looping sta tements. 3.2 Trajectory Optimization Algorithm The key issue of the optimization process is the algorithm of finding the optimum vehicle trajectories that can minimize the ATTD for a given signal timing plan. A trajectory optimization algorithm was develop ed considering the maximum discharge rates from each intersection approach. Using this algorithm, vehicles are required to accelerate to the maximum allowed speed before they reach the intersection and leave the intersection at the saturation flow rate. In other words, as shown in Figure 3 3 all the trajectories are required to meet and coincide with the hypothetical maximum speed trajectory (the dashed line) before they arrive at the intersection in order to utilize the green time to its maximum efficiency . However, some of the vehicles are not able to accelerate to the maximum speed before they reach the intersection (the first vehicle in Figure 3 3) or at the hypothetical time (the last vehicle in Figure 3 3). In those cases, PAGE 50 50 the vehicles are required to accelerate to the maximum speed at their earliest possible time. Each optimized trajectory must have at least two components . This is because a single component trajectory (Figure 3 4A ) with a constant acceleration rate can be controlled either by the f inal speed or by the travel time, but not both. In order to schedule the vehicle arrivals at saturation time headway and to have them accelerate to the maximum speed when they reach the intersection, both parameters must be controlled. However, u sing only two component trajectories (Figure 3 4B ) does not offer as much flexibility, and vehicles cannot easily be scheduled to reach the intersection at maximum speed. If the vehicle cannot be scheduled to reach the intersection with the maximum speed, it has to accelerate to the maximum speed in the downstream link, which also results in a three component trajectory. As shown in Figure 3 4C, t he three component trajectory provides considerable flexibility for controlling vehicle arrival time and arrival speed. H owever, since all the vehicles accelerate to the maximum speed at the time when they arrive at the intersection, using this type of trajectory there is not as much flexibility for controlling the time headway between two consecutive vehicles during the acc eleration/deceleration. Therefore, the vehicles are allowed to accelerate to the maximum speed before they arrive at the intersection, resulting in at most a four component trajectory. As shown in Figure 3 4D , the first and third components have constant a cceleration, while the second and the fourth have constant speed. The speed of the fourth component is always the maximum speed. Generally, the optimized vehicle trajectories obtained in this research consist of four PAGE 51 51 components; however, some vehicles may only have three or two or even one component if the time duration of one or some of the components is 0. Based on the definition for the four component trajectory, a trajectory optimization algorithm was developed to minimize the vehicle travel time and to maximize the green time utilization. For a given signal timing plan with multiple green phases, the green intervals are considered in chronological sequence during the trajectory optimization process, one in each iteration. In every iteration, all the ve hicles that have not left the intersection will be considered for traveling through the intersection during the current green interval. The initial location and speed of the vehicles are used as input at the beginning of every iteration. The following step s are followed in every iteration: 3.2.1 Step 1 : Determine The Trajectory of The First V ehicle. Ideally, the first vehicle reaches the intersection at the beginning of the green using the maximum speed and all the following vehicles discharge keeping a sat uration time headway, as depicted in Figure 5 a. However, sometimes the first vehicle is not able to accelerate to the maximum speed when the green starts and generates a lost time, as depicted in Figure 5 b. Therefore, the trajectory of the first vehicle determines the maximum capacity of the green interval and the hypothetical arrival time scheduled for the following vehicles. So the first step in the trajectory adjustment algorithm is to determine the trajectory of the first vehicle. At the beginning of the optimization, the vehicle is either stopped at the intersection or is a certain dista nce away from the intersection. For vehicles that are stopping at the intersection, in order to save time for the following vehicles, they are required to accelerate t o the maximum speed at the ir earliest feasible time using the PAGE 52 52 maximum acceleration rate . For vehicles that are a certain distance away from the intersection , we assume their trajectories are three component trajectories (the first and last component of the trajectory has constant acceleration, while the middle one has co nstant speed) as shown in Figure 3 6 . The reason for not using the four component trajectory is that there is no need to consider the time headway for the first vehicle and the three compone arrival time and speed. Based on vehicle kinematics , t he following equations can be used for calculating a three component trajectory: ( 3 4 ) In the above equations, t he input variables are: T = time duration from the beginning of the optimization to the time when the green interval starts, sec D = the initial distance of the vehicle to the intersection, ft v 0 = the initial speed of the vehicle, ft/sec v 3 = fina l speed when the vehicle reach the intersection, ft/sec a 1 = deceleration rate (negative) for the first component of the trajectory, ft/sec 2 a 3 = acceleration rate (positive) for the third component of the trajectory, ft/sec 2 The output variables tha t define the trajectories are: PAGE 53 53 v 2 = speed for the constant speed component of the vehicle trajectory, ft/sec t 1 = time duration of the first trajectory component, sec t 2 = time duration of the second trajectory component, sec t 3 = time duration of t he third trajectory component, sec d 1 = distance the vehicle passed in the first trajectory component, ft d 2 = distance the vehicle passed in the second trajectory component, ft d 3 = distance the vehicle passed in the third trajectory component, ft A mong the input parameters listed above , T , D , and v 0 are given at the beginning of the optimization. v 3 , a 1 , and a 3 have to be determined on a case by case basis. For through vehicles studied in this chapter , we assume their approaching speeds do not exce ed the predetermined maximum allowed speed. As a result, the last non constant speed trajectory component is always an acceleration component ( a 3 >0) in order to maximize the vehicle arrival speed at the intersection. initial arrival time (arrival time using its initial speed v 0 ) and the start time of the green phase, the first component of the vehicle trajectory may be an acceleration component, a deceleration component, or the vehicle trajectory only has one acceleration component . Based on the above discussion, the trajectory of the first vehicle can be categorized in one of the following four cases. Case 1: The vehicle is stopped at the intersection at the beginning of the optimization. Case 2: At the beginning of the optimizati on, the vehicle is a certain distance away from the intersection, and using the initial speed the vehicle will arrive the intersection before the green starts. Case 3: At the beginning of the optimization, the vehicle is a certain dista nce away from the in tersection. U sing the initial speed the vehicle will arrive the PAGE 54 54 inte rsection after the green starts, and i f the vehicle accelerates to the maximum speed at the beginning using the maximum acceleration rate, it will arrive at the intersection before the gre en starts. Case 4: At the beginning of the optimization, the vehicle is a certain distance away from the intersection. If the vehicle accelerates to the maximum speed at the beginning of the optimization using the maximum acceleration rate, it will still a rrive at the intersection after the green starts. The trajectory optimization method for each of the cases will be discussed below in more detail. Case 1 . In this case, the vehicle is initially stopping at the intersection. In order to fully utilize the g reen time, it is required to accelerate to the maximum speed usin g the maximum acceleration rate at the beginning of the green to save time for the following vehicles. Adjusted trajectory for the first vehicle in this case is as illustrated in Figure 3 7 . The hypothetical arrival times (those that ensure the maxim um utilization of the green time , and the associated hypothetical arrival speed is v max ) for the following vehicles are: ( 3 5 ) where T arrival,i = hypothetical arrival time of the i th vehicle, sec g start = start time of the green interval, sec v max = maximum allowed speed for all vehicles, ft/sec a acc,max = maximum acceleration rate for all vehicles, ft/sec 2 h sat = saturation time headway, sec Case 2. At the beginning of the optimization, the vehicle of this case is a certain distance away from the intersection, and using the initial speed the vehicle will arrive the intersection before the green starts. Therefore, ideally the vehicle in this case should PAGE 55 55 first decelerate and then accelerate to the maximum speed before arriving at the intersection . Since the vehicle in this case must first decel erate and then accelerate to the maximum speed, based on the available distance for the acceleration and deceleration this case is further divided into four subcases in order to determine the specific values for v 3 , a 1 , and a 3 . Case 2 a : ; Case 2 b : ; Case 2 c : ; Case 2 d : . Where a acc,design = design ed acceleration rate. It is a predetermined value that is less than the maximum acceleration rate and is used in the algorithm to smooth the trajectory and avoid rapid acceleration, ft/sec 2 a acc,max = maximum acceleration rate for all vehicles , ft/sec 2 a dec,max = maximum deceleration rate for all vehicles , ft/sec 2 All the other variables are as previously defined. For all these four subcases, vehicles can always arrive at the int ersection at the time when the green interval starts, and the objective of the trajectory adjustment is to maximize the vehicle arrival speed (up to the maximum allowed speed) and direct the vehicle to depart the intersection smoothly. Among those four cas es, t he values of D in Case 2 a and Case 2 b are both long enough for vehicles to accelerate to v max before PAGE 56 56 they arrive at the intersection. However, Case 2 a has a longer D that allows vehicle to use smaller acceleration and deceleration rate. Vehicles o f Case 2 c also have both the deceleration and ac celeration process, but they are not able to accelerate to v max before arrive at the intersection. Therefore, a dec,max and a acc,max are implemented to maximize the vehicle arrival speed. The values of D in Ca se 2 d is too short that vehicles only have the deceleration component before they arrive at the intersection. In this research we assume the vehicles always have enough distance to stop if they need to do so. But the initial distance to the intersection s top bar in this case is less than the distance required for a full stop. I t is implies that the green interval will start bef speed decelerate s to 0. Therefore, the vehicle in this case first decelerates to reach the intersection at the b eginning of the green interval, and then accelerate s to v max using the maximum acceleration rate after departing the intersection. Figure 3 8 shows the adjusted trajectories for these four subcases. The input variables , v 3 , a 1 , and a 3 , for each of the sub cases of Equation 3 4 are listed in Table 3 1. a dec,design is defined as the design de celeration rate. It is a predetermined value that is less than the maximum de celeration rate and is used to smooth the trajectory . All the other variables are as previous ly defined. Plugging those values of the input variables back into Equation 3 4 , the vehicle trajectories of these four subcases can be so lved by the following equations: PAGE 57 57 ( 3 6 ) lated by the following equation: ( 3 7 ) Case 3. At the beginning of the op timization, the vehicle of this case is a certain distance away from the intersection, and using the initial speed the vehicle will arrive the intersection after the green starts. If the vehicle accelerates to the maximum speed at the beginning using the m aximum acceleration rate, it will arrive at the intersection before the green starts. Therefore, using a general three component trajectory, the vehicles in this case have two acceleration components, which means the vehicle first accelerate s to a certain speed and keep this speed for a while, and then accelerate s again to reach the maximum speed. S ome vehicles are possible to have only two or even one component if the time duration of one or some of the components is 0 . Calculation of the trajectories in this case is similar to the discussion for Case 2. The trajectories can also be calculated using Equation 3 4 , except in this case the value of a 1 is positive as the first component is an accelerating component. In order to determine the input variables v 3 , a 1 , and a 3 , Case 3 is further divided into three subcases based on the length of the initial distance between the vehicle and the intersection. Case 3 a : ; PAGE 58 58 Case 3 b : ; Case 3 c : . All the variables are as previously defined Vehicles of those subcases can also arrive at the intersection at the time when the green interval starts, thus the objective of the trajectory adjustment is to maximize t he vehicle arrival speed (up to the maximum allowed speed) and direct the vehicle to depart the intersection smoothly. The values of D in Case 3 a and Case 3 b are long enough for vehicles to accelerate to v max before they arrive at the intersection. The difference is compared to Case 3 a, the distance in Case 3 b is shorter and vehicles have to use a acc,max in order to reach v max before their arrival. But in Case 3 a, smaller acceleration can be implemented to smooth the trajectory. The values of D in Cas e 2 c is too short that vehicles only have one acceleration component before they arrive at the intersection. They will accelerate to v max using a acc,max after departing the intersection. Figure 3 9 shows the adjusted trajectories for the three subcases of Case 3. Besides the subcases discussed above, there is a special case for both Case 2 a and Case 2 b. As illustrated by Figure 3 10A, assume the acceleration component is a portion of the departing trajectory with a acceleration rate a acc (a acc ,design fo r Case 2 a and a acc ,max for Case 2 b). F or a normal case in Case 2 a or Case 2 b, the arrival time using the initial speed t 0 , is greater than the tangent line arrival time t tan . Therefore, the vehicle trajectory can be ca lculated by solving Equation 3 4 . However, there are also cases, the initial speed arrival time t 0 of which is smaller than t tan , a s shown in Figure 3 10 B. For such cases, Equation 3 4 has no solution assuming a positive value for the PAGE 59 59 acceleration rate a 1 of the first acceleration/deceler ation component. Therefore, a negative value should be used for a 1 and t hese cases should be considered using the method proposed for Case 2. They may be categorized into Case 2 a, Case 2 b or Case on. Based on the above discussions, t he input variables for each of the subcases (not including the special cases discussed above) of Case 3 are listed in Table 3 2. All the variables are as previously defined. Vehicle trajectories of these three subcases can be calculated by plugging the values of the input variables listed in Table 3 2 back into Equation 3 4 . The solutions are: ( 3 8 ) ( 3 9 ) Not e that, for this case it is possible that a 1 and a 3 have the same value . In that case, the second equation in Equation 3 8 for calculating v 2 will be used. Case 4: At the beginning of the optimization, the vehicle of this case is a certain distance away f rom the intersection. If the vehicle accelerates to the maximum speed at the beginning of the optimization using the maximum acceleration rate, it will still arrive at the intersection after the green starts. PAGE 60 60 In this case, the vehicles are not able to rea ch the intersection at the time when the green starts. T herefore, they are required to accelerate to the maximum speed at their earliest time to save time for the following vehicles. Two subcases of this case are: Case 4 a : ; Case 4 b : . Figure 3 11 shows the adjusted traject ories for vehicles of this case. The vehicle trajectories for these two sub case s can be represented also by the equations for a general three component traject ory. The mathematical expression for the adjusted trajectories of Case 4 a is: (3 10 ) The adjusted trajector ies of Case 4 b is: (3 11 ) The hypothetical arrival time for the following vehicles is: PAGE 61 61 ( 3 12 ) All the variables are the same as previously defined. 3.2.2 Step 2: Calculate The Trajectories of The Following V ehicles. After determining the trajectory of the first vehicle, trajectories of the following vehicles are calculated one by one. As shown in Figure 3 4D , four component trajectories are assumed for the following vehicles. The first and third components have constant acceleration, while the second and the fourth one ha ve constant speed. T he speed of the fourth component is always the maximum speed. The following equations can be used for the trajectory calculation. ( 3 13 ) In the above equations, the input variables are: T = time dura tion from the beginning of the optimization to the time when the green interval starts, sec D = the initial distance of the vehicle to the intersection, ft v 0 = the initial speed of the vehicle, ft/sec v 4 = final speed when the vehicle reach the inte rsection, ft/sec PAGE 62 62 a 1 = acceleration/deceleration rate for the first component of the trajectory, ft/sec 2 a 3 = acceleration/deceleration rate for the third component of the trajectory, ft/sec 2 t 4 = time duration of the fourth trajectory component, sec d 4 = distance the vehicle passed in the fourth trajectory component, ft The output variables that define the trajectories are: v 2 = speed for the constant speed component of the vehicle trajectory, ft/sec t 1 = time duration of the first trajectory c omponent, sec t 2 = time duration of the second trajectory component, sec t 3 = time duration of the third trajectory component, sec d 1 = distance the vehicle passed in the first trajectory component, ft d 2 = distance the vehicle passed in the second trajectory component, ft d 3 = distance the vehicle passed in the third trajectory component, ft Among the input parameters, D , and v 0 are given at the beginning of the optimization; v 4 equals the maximum speed ; T , a 1 , a 3 , t 4 , and d 4 have to be determine d based on the trajectory of the previous vehicle. Note that the trajectory cases of the first vehicle discussed in the previous step all have an acceleration component before they reach the maximum speed (the orange curve in Figure 3 8 through Figure 3 1 1 ). Assuming the acceleration component of the first vehicle is part of a departure curve, where the vehicle starts from full stop and a ccelerates to the maximum speed, there is a set of saturation departure curves that maximize the green time utilization for the following vehicles that depart the intersection. PAGE 63 63 Since four component trajectories are assumed for the following vehicles studied in this step, the ideal situation is that the third and forth component of the vehicle trajectories can meet and coinc ide with the hypothetical saturation departure curves, such as the first four vehicle trajectories depicted in Figure 3 12. However, some of the vehicles , such as the fifth vehicle in Figure 3 12, are not able to meet the hypothetical departure curve even using the maximum acceleration rate at the beginning. In this case, the most time saving maneuver for the vehicle is to accelerate to the maximum speed at its earliest possible time . Based on the initial speed and distance at the beginning of the optimiza tion period, following vehicles are divided into three categories to calculate the input variables in Equation 3 13 . Case F 1: Using the initial speed the vehicle will arrive the inte rsection ( t 0 ) before or at the tangent line arrival time t tan . Case F 2 : Using the initial speed the vehicle will arrive the inte rsection ( t 0 ) after the tangent line arrival time t tan , and i f the vehicle accelerates to the maximum speed at the beginning using the maximum acceleration rate, it will arrive the intersection befo re the hypothetical departure curve . Case F 3: Using the initial speed the vehicle will arrive the inte rsection after the tangent line arrival time t tan , and i f the vehicle accelerates to the maximum speed at the beginning using the maximum acceleration r ate, it will arrive the intersection after the hypothetical departure curve. The adjusted trajectories of the above cases are presented in Figure 3 13. The trajectory optimization method for each of the cases will be discussed below in more detail. Case F 1 . Using the initial speed , the vehicle of this case will arrive the intersection ( t 0 ) before or at the tangent line arrival time t tan . Therefore, the vehicle in this case should first decelerate and then accelerate to the maximum speed before arriving PAGE 64 64 at the intersection . The third and forth co mponent of the trajectory coincide with the hypothetical departure curve. Assume the vehicle is the i th vehicle that is considered to depart during the current green interval. Input variables T i , a 3 ,i , d 4 ,i , t 4 , i , a nd a 1,i , are determined by the following equations. (3 14 ) (3 15 ) (3 16 ) (3 17 ) (3 18 ) Where d depart,i : distance of the hypothetical departure curve to the intersection for the i th vehicle, ft T depart,i : arrival time of the hypothetical departure curve for the i th vehicle, sec a depart,i : accele ration rate of the hypothetical departure curve for the i th vehicle , sec Other variables are the same as previously defined. After determining the input variables, vehicle trajectory can be calculated by plugging those values into Equation 3 13 . The re sulting trajectory can be expressed by the following equations. PAGE 65 65 ( 3 19 ) Equation 3 19 can be calculated by the following equation. ( 3 20 ) Case F 2 . Using the initial speed the vehicle of this case will arrive the inte rsection ( t 0 ) after the tangent line arrival time t tan , and i f the vehi cle accelerates to the maximum speed at the beginning using the maximum acceleration rate, it will arrive the intersection before the hypothetical departure curve. Therefore, the vehicle in this case the vehicles in this case have two acceleration componen ts, and it first accelerate s to a certain speed and keep this speed for a while, and then accelerate s again to reach the maximum speed. The third and forth component of the trajectory coincide with the hypothetical departure curve. Input variables T i , a 3 , i , d 4 ,i , a nd t 4 ,i , can also be calculate d using Equation 3 14 through Equation 3 17 as those variables are all determined by the hypothetical departure curve. The input variable a 1,i , can be determined by the following equations. ( 3 21 ) V ehicle trajectory can be calculated by plugging those values into Equation 3 13 . The solutions are: PAGE 66 66 ( 3 22 ) lated by the following equation. ( 3 23 ) Case F 3 . In this case, if the vehicle accelerates to the maximum speed at the beginning using the maximum acceleration rate, it will still arrive the intersection after the hypothetical departure curve. Therefore, the vehicles are not able to meet the hypothetical departure curve , and they are required to accelerate to the maximum speed at their earliest time to save time for the following vehicles. The vehicle trajectories for this case can also be represented by the equations for a general four compo nent trajectory. The mathematical expression for the adjusted trajectories of Case F 3 is: (3 24 ) From on the discussions above, it can be noted that calculations of the input variables T i , a 3 ,i , d 4 ,i , t 4 ,i , a nd a 1, i , are all based on the hypothetical departure curves, which can be defined by three characteristic parameters d depart,i , a depart,i , and T depart,i . PAGE 67 67 Since the determination of the hypothetical departure curves depends on the trajectory of the previous vehi cle, equations for calculating the values of those three characteristic parameters are developed based on the trajectory cases of the previous vehicle. The equations are listed in Table 3 3. 3.2.3 Step 3 : Check Whether The Vehicle Can Depart The I nters ecti on before The End of G reen. The algorithm checks whether the vehicle can depart the intersection before the end of green; if not the vehicle is assigned to the next iteration. The first vehicle that cannot depart the intersection before the current green w ill be the first vehicle to depart during the next green interval. 3.3 Optimization Horizon Scheme A n optimization horizon scheme was developed to conduct the optimization over the time horizon for continuously entering vehicles. Using this scheme, the ove rall planning horizon ( t planning ) is divided into overlapping stages. These stages overlap at fixed intervals, the length of which is referred to as the optimization period ( t o pt ). The stage length ( t stage ) is the time period over which vehicle trajectorie s are projected and the optimum signal timing is calculated (Figure 3 14 .) Optimization is conducted at the beginning of every stage using the available information (initial speed and location) of all the vehicles inside the communication range. The optim ization yields the optimum vehicle trajectories and the optimum signal timing plan over the time period t stage . For Stage 1, the optimization is conducted over the entire time period for all the vehicles inside the communication range at T 1, start . Therefo re, t opt in Equation 3 1 through 3 3 equals t stage for this stage. In order to avoid frequent changes in vehicle trajectories, starting from Stage 2, signal timing is only optimized for the tail period ( t o pt ) that does PAGE 68 68 not o verlap with the previous stage . Signal timing in the remaining time of the stage ( t stage t o pt ) remains as previously calculated. In this way, vehicles that could pass the intersection during the previous stages can keep their scheduled trajectories. Only trajectories of the residual v ehicles from the previous stage (vehicles represented by the thicker lines in Figure 3 14 ) and the newly arriving vehicles (vehicles that enter the communication range before the next stage starts) are optimized in the new stage. The reason for having the overlap between stages is to avoid having vehicles too close to the intersection at the start of the new stage. That would result in relatively low flexibility for modifying their trajectories. In the optimization horizon scheme discussed above, the stage length t stage is a very important quantity. If it is too long, all the vehicles will pass the intersection before the stage ends and the remaining time is wasted. If it is too short, vehicles that are far away from the intersection cannot arrive at the sto p bar even at the end of the stage, and only the vehicles that are close to the intersection can be scheduled. However, the trajectory. The ideal situation is the l ast vehicle passes the intersection just before the stage ends. Based on this, the following is developed for estimating t stage . ( 3 2 5 ) D 1 : = demand of approach 1, veh/sec D 2 : = demand of approach 2, veh/sec v avg,1 : a = a verage travelling speed of the vehicles from approach 1 , ft/sec v avg,2 : = average travelling speed of the vehicles from approach 2, ft/sec PAGE 69 69 v max : = maximum feasible travelling speed of all the vehicles, ft/sec d inf : = distance between the boundary of the communication range and the intersection, ft h s at : = saturation time headway, sec Another important parameter of the optimization horizon scheme is the length of the optimization period t opt . T he closer the vehicle to the intersection, the more difficult it is to adjust its trajectory. Thus the firs t newly arrived vehicle should be at such a distance that it can be scheduled to pass the intersection at the beginning of the new signal timing period to avoid any lost time. This idea can be expre ssed by the following equation: ( 3 2 6 ) All the variables are as previously defined. Solving the above equation for t o pt : ( 3 2 7 ) t o pt should be estimated for both approaches, and the smaller one should be implemented for the optimization system. The resul ting value should also be adjusted to ensure that t stage is an exact multiple of t o pt . 3.4 Experimental Evaluation The proposed algorithm was coded in MATLAB. The flow chart in Figure 3 15 summarizes the steps of the simulation process used for evaluating the optimization a lgorithms described previously. The simulation tests were run for 15 minutes with a warm up period of 1 minute to initialize the input data for the optimization of the first stage. At the beginning of the PAGE 70 70 simulation, the system randomly generates the arrival times and speeds for all the vehicles that enter the communication range during the overall planning horizon ( t planning =15 minutes). When conducting optimization for a specific stage, only residual vehicles left from the previous stag e and the vehicle arrivals since the previous stage beginning are considered, along with their associated arrival times and speeds are used as input. Vehicle arrival was assumed as a Poisson process (i.e., interarrival times follow the exponential distri bution), with the average time headway as the rate parameter of the distribution. The average travelling speed was assumed as the mean of the distribution ( ), and standard deviation ( ) was assumed as 1. Based on these assumptions, vehicle arrival times and initial speeds were generated using the random number generator in MATLAB. Several parameters must be determined before the implementation. Such parameters include the ma ximum travelling speed, the maximum acceleration and deceleration rates, the saturation headway, the maxim um and minimum green times, the optimization period, and the stage length. The values of these parameters for this study are provided in Table 3 4. Th e value of the optimization period t o pt and the stage length t stage were determined for each of the tested scenarios using Equation 3 2 5 and Equation 3 2 7 . Two of the most important outputs of the proposed algorithm are the optimized signal timing and the optimized vehicle trajectories. In this MATLAB simulation, the optimized signal timing plan is summarized by a two row matrix for each approach. The PAGE 71 71 first row lists the start time of each green phase and the second row presents the associated phase duratio n. The optimized trajectory for each vehicle is presented using a four row matrix. The four elements of each column represent the time, and the associated location, speed and acceleration rate at each acceleration changing point of the optimized trajectory . Based on the information provided by this matrix, vehicle trajectories can be plotted. In addition, the departure time, final speed, and the travel time delay of each vehicle, throughput of each approach and the intersection ATTD are calculated and prese nted as outputs at the end of the simulation. Computational cost was also calculated for each optimization stage. It shows that getting the optimum solution for a regular stage takes less than 1 second (the average of 50 runs is 0.8783 second). Therefore, it is reasonable to assume the computation performance is instantaneous. Various s cenarios were tested using the MATLAB simulation. The same set of scenarios and intersection configuration was also simulated for an actuated signalized intersection using CO RSIM TM . Two performance measures, intersection ATTD and average throughput, were compared. For each scenario tested in both MATLAB and CORSIM TM 10 runs were conducted with different random number seeds to obtain statistically valid results. F igure 3 16 pr esents the comparison between the actuated control and the proposed algorithm under different demand levels (averages of 10 runs). Figure 3 16A and Figure 3 16B shows the comparison results when balanced demands were assigned to the two approaches. In thos e two figures, both the ATTD and the throughput are improved after implementing the proposed optimization algorithm and PAGE 72 72 the improvement is more significant for scenarios with higher demand. When the demand is not more than 1000 vphpl, implementation of the proposed optimization algorithm reduces the ATTD by 16.2% to 27.6%, and increases the throughput by 2.7% to 5.5%, depending on the demand scenario. When the demand increases to 1200 vphpl, improvement in ATTD and throughput is as high as 36.9% and 20.2% r espectively. Note that under the actuated signal control, throughput for the 1000 and 1200 vphpl scenarios is similar, implying that the demand of 1000 vphpl is near/at capacity for the approach. For the proposed algorithm, the throughput increases signifi cantly. Therefore, it can be concluded that the proposed optimization algorithm increases the capacity of the intersection approach. Figure 3 16C and Figure 3 16D presents how the balances in demand impact the performance of the proposed algorithm. For all the tested scenarios, the total demand of the two approaches is 2000 vphpl, but different levels of demands were assigned to each approach in different scenarios. The two figures show that for all the tested scenarios, both the ATTD and the throughput are improved after implementing the proposed algorithm, and the improvement decreases (the improvement decreases from 26.7% to 13.5% in ATTD and decreases from 13.4% to 2.1% in throughput) as the demand difference between the two approaches increases. This is because in order to accommodate the unbalanced demand, limited green time is assigned to the side streets. As a result, the green intervals for the side street are short and far apart. Although the proposed algorithm can reduce time lost by better utilizi ng the green time, some vehicles still need to wait for a long time before being discharged, resulting in high delays for the side street traffic. PAGE 73 73 Figure 3 17 presents comparisons of the ATTD between the two control algorithms for different communication r ange/link length. For the proposed algorithm, the communication range changes for different test scenarios . In order to ensure the delay times were calculated inside the area with the same size, the link length of the actuated test scenarios were changed a ccordingly. Figure 3 17A presents the comparison for a demand of 800 vphpl for both approaches, and Figure 3 17B provides results for a demand of 1100 vphpl for both approaches. Both figures show that the proposed algorithm significantly reduces the averag e delay time when the communication range is more than 2000 feet, and the amount of improvements are similar for different scenarios (30.1% to 31.9% for the 800 vphpl demand scenarios and 33.9% to 36.3% for the 1100 vphpl demand scenarios). However, when t he communication range is shorter than 2000 feet, the improvements decrease as the distance decreases (from 30.1% to 3.3% for the 800 vphpl demand scenarios, and from 33.9% to 14.7% for the 1100 vphpl demand scenarios). This is because the closer the vehic le to the intersection, the more difficult to adjust its trajectory. The extent of the communication range limits the trajectory optimization ability of the proposed algorithm. Note that although the threshold for the most efficient communication range is 2000 feet for both demand levels, this value might be different for other scenarios with different settings (demand, maximum speed, optimization stage length, etc). Comparison between Figure 3 17A and Figure 3 17B also shows that the proposed algorithm wor ks better for the more congested scenarios. Throughputs were also compared for the same set of scenarios but there is no clear trend. PAGE 74 74 Table 3 1 . Input variables for Case 2 subcases . Subcases Input Variables Hypothetical Time for Followi ng Vehicles Case 2 a Case 2 b Case 2 c Case 2 d Table 3 2 . Input variables for Case 3 subcases . Subcases Input Variables Hypothetical Time for Following Vehicles Case 3 a Case 3 b Case 3 c PAGE 75 75 Table 3 3 . Trajectory Calculation input variables for the following v ehicles . Trajectory Cases of the Previous Vehicle d depart,i a depart,i T dep art,i Case 1 Case 2 a Case 2 b Case 2 c Case 2 d Case 3 a Case 3 b PAGE 76 76 Table 3 3. Continued Trajectory Cases of the Previous Vehicle d depart,i a depart,i T depart,i Case 3 c Case 4 a Case 4 b Case F 1 and Case F 2 Case F 3 PAGE 77 77 Table 3 4 . Required input p arameters . Parameters Values Assumed in This Study Maximum Travelling Speed (mph) 35 Maximum Acceleration Rate (ft/s 2 ) 4.5 Design Acceleration Rate (ft/s 2 ) 2.5 Maximum Deceleration Rate (ft/s 2 ) 11.0 Design Deceleration Rate (ft/s 2 ) 6.0 Saturation Time Headway (sec) 2.0 Minimum Green (sec) 6 Maximum Green (sec) 25 PAGE 78 78 Figure 3 1 . Sket ch of the two approach Intersection and its communication r ange . A B Figure 3 2 . Vehicle trajectory adjustment behavior at a signalized i ntersection . A) Scenario of deceleration, B) scenario of acceleration. PAGE 79 79 Figur e 3 3 . Optimized vehicle t rajectories . A Figure 3 4 . Vehicle trajectories with different number of c omponents . A) One component trajectory, B) two component trajectory, C) three component trajectory, D) four component trajectory. PAGE 80 80 B C D Figure 3 4 . Continued PAGE 81 81 A B Figure 3 5 . Different departing scenarios based on the trajectory of the first v ehicle . A) Ideal scenario, B) time lost scenario. PAGE 82 82 Figure 3 6 . Three component vehicle traject or y. Figure 3 7 . Adjusted trajectory for the first v ehicle in Case 1 . PAGE 83 83 A B C D Figure 3 8 . Adjusted trajectories for v ehicles of Case 2 . A) Case 2 a, B) Case 2 b, C) Case 2 c, D) Case 2 d. PAGE 84 84 A B C Figure 3 9 . Adjusted trajectories for v ehicles of Case 3 . A) Case 3 a, B) Case 3 b, C) Case 3 c . PAGE 85 85 A B Figure 3 10 . The special case of Case 3 a and 3 b. A) A normal case of Case 3 a and 3 b, C) A special case of Case 3 a and 3 b . PAGE 86 86 A B Figure 3 11 . Adjusted trajectories for v ehicles of Case 4 . A) Case 4 a, B) Case 4 b. Figure 3 12 . Hypothetical departure curve . PAGE 87 87 A B C Figure 3 13 . Adjusted trajectories for the following v ehicles . A) Case F 1, B) Case F 2, C) Case F 3. PAGE 88 88 Figure 3 14 . Layout of the optimization horizon s cheme . PAGE 89 89 Figure 3 15 . Flow chart of the optimization p rocess . PAGE 90 90 A B C Figure 3 16 . Comparison of the actuated signal control and the proposed signal optimization a lgorithm u nder various demand l evels . A) Comparison of ATTD (balanced d emand) , B) Comparison of throughput (balanced d emand) , C) Comparison of ATTD (unbalanced d emand) , D ) Comparison of throughput (unbal anced d emand) . 0 50 100 150 200 200 400 600 800 1000 1200 ATTD (sec) Demand (vphpl) Actuated Control Proposed Algorithm 0 200 400 600 800 1000 1200 200 400 600 800 1000 1200 Throughput (vehicles) Demand (vphpl) Actuated Control Proposed Algorithm 0 20 40 60 80 100 120 140 ATTD (sec) Demand (vphpl) Actuated Control Proposed Algorithm PAGE 91 91 D Figure 3 16. Continued A B Figure 3 17 . Comparison of the actuated signal control and the proposed signal optimization a lgorithm u nder different communication range/link l ength . A) Scenarios with the d emand of 800 vphpl , B) Scenarios with the d emand of 1100 vphpl . 0 500 1000 1500 2000 2500 Throughput (vehicles) Demand (vphpl) Actuated Control Proposed Algorithm 0 5 10 15 20 25 30 35 40 500 1000 1500 2000 2500 3000 ATTD (sec) Communication Range/Link Length (ft) Actuated Control Proposed Algorithm 0 20 40 60 80 100 120 500 1000 1500 2000 2500 3000 ATTD (sec) Communication Range/Link Length (ft) Actuated Control Proposed Algorithm PAGE 92 92 CHAPTER 4 INTERSECTION CONTROL OPTIMIZATION FOR A GENERAL Twelve movement INTERSECTION This c hapter expands the optimization algorithm developed in the previous chapter for general four leg , twelve movement intersections with the consideration of turning vehicles . First, an overview of the methodology framework is presented in the first section . Then, t he secon d section details the optimization algorithm, including the trajectory op timization algorithm and the implementation of the Genetic Algorithm ( GA ) for solving the optimization problem. The proposed algorithm was coded in Java. The third section outlines the simulation effort, and the last section discusses the sensitivity analy sis and compares the performance of the proposed algorithm to conventional actuated control. 4.1 Methodology Framework T he optimization algorithm proposed in the previous chapter was developed for a signalized intersection system. Trajectory optimization a lgorithm was developed based on signal timing plan and the resulting optimized signal timing was transmitted to the roadside traffic signals. However, it can be note that the control algorithm is designed for a 100% automated vehicle environment, and the v ehicles do not need the signal indications to decide when to stop or go. Instead, they are able to receive the optimized trajectories from the intersection controller through the wireless communication technology, and the optimized trajectories will guide the vehicles to go through the intersection. Therefore, the conventional signal phasing and green splits are not used for the intersection control system proposed in this chapter . I nstead, an intersection controller is designed to allow conflicting traffic to proceed by allotting the right of way to each single vehicle , rather than to a certain movement, over time and space. As a PAGE 93 93 result, the original signal timing optimization problem is converted to a vehicle passing sequence problem, which determines the optimum vehicle passing sequence that can minimize the average intersection delay. In this way, the vehicle trajectories can be scheduled with more flexibility and the intersection can be more efficiently used without the consideration of minimum green and maximum green constraints. Figure 4 1 shows the configuration of the intersection used in this study. We assume the studied intersection is a four leg intersection with three lanes on each approach, one for each turning movement. We also assume there is a n intersection optimization controller that is designed to gather vehicle information, make decisions on vehicle passing sequence and calculate optimal vehicle trajectories. The communication between the intersection controller and the vehicles is assumed to be enabled by DSRC communication technology. Based on the 1000 meters (3281 feet) maximum communication rage of DSRC , the communication range of the intersection control system is assumed to be 3000 feet from the center of the intersection. It is also assumed that the exclusive left and right turning lanes are long enough that they allow turning vehicles to enter their objective lanes before entering the Communication Range so that lane changes are not considered in the proposed algorithm. The numbers with arrows in Figure 4 1 indicate the number of different movements. At the beginning of the optimization, the intersection controller identifies the vehicles inside the communication range and gathers the information that is required for the optimizatio n. Then, the controller runs the optimization algorithm and solves the vehicle passing sequence problem. At the same time, vehicle trajectories are calculated PAGE 94 94 by implementing the trajectory optimization algorithm. After getting the optimization result, the calculated vehicle trajectories are transmitted to vehicles directing them through the intersection. After the last vehicle in this group leaves the intersection, the first optimization stage ends. Then, a new optimization stage starts and the above proce ss is repeated for vehicles that entered the communication range during this second time period. This iterative process is repeated until all the vehicles that have entered the communication range during the entire optimization period are processed. Figure 4 2 shows this optimization process graphically. Since the number of vehicles that are being processed during each optimization stage is different and the departing time of the last vehicle is uncertain, the duration is different for each optimization sta ge. For simplicity, it is also assumed that the information transmission and the computing process (Step 1 through Step 3 in Figure 4 2) can be completed with no measurable processing delay. With the assumptions discussed above, the optimization algorithm being used in each optimization stage is discussed in the following section in more detail. 4.2 Optimization Algorithm As discussed earlier , t he control algorithm is designed for a 100% automated vehicle environment, and the vehicles do not need signal ind ications to decide whether to proceed or stop. Instead, they receive the optimized trajectories from the intersection controller through the wireless communication technology, and the optimized trajectories guide the vehicles through the intersection. The refore, traditional phasing is not considered, and movements through the intersection are allowed in a much more flexible way in order to minimize delay. PAGE 95 95 In order to develop the optimization algorithm for this type of control system the following two task s need to be completed: 1) develop a trajectory optimization algorithm that can optimize vehicle trajectories based on the vehicle passing sequence; and 2) select an optimization method and implement it to solve the vehicle passing sequence problem. To co mpete those two tasks, a traject ory optimization algorithm, which can optimize the vehicle trajectory only based on the trajectory of its previous vehicle and the exiting time of the last vehicle that has departed the intersection from a conflicting approa ch , was first developed . Based on the proposed trajectory optimization algorithm a vehicle passing sequence problem was formulated with the objective of finding a vehicle passing sequence that can minimize the average intersection delay. GA was adopted to solve this optimization problem. The following two sub sections present the two algorithms in more detail. The following notations are used: i : the i th vehicle that will be scheduled to pass the intersection, i , N is the total number of vehicles inside the communication range. j : the j th vehicle from a particular movement k : the k th movement, k C ( k ) : the set of movements that conflict with movement k 4.2.1 T ra jectory Opt imization Algorithm For the intersection control system proposed in this chapter , there are two rules that must be followed by all the vehicles inside the system to avoid conflicts. First, no PAGE 96 96 lane changes are allowed, thus vehicles on the same lane cross t he intersection First In First Out (FIFO). Second, vehicles from conflicting movements cannot be located inside the intersection at the same time. On the basis of these two rules, the trajectory optimization algorithm is developed to optimize the vehicle trajectories such that vehicles can leave the intersection at their earliest possible time and the average intersection delay can be minimized. 4.2.1.1 Trajectory Optimization Algorithm for Through Vehicles Define the trajectory component as a portion of vehicle trajectory with a constant acceleration rate. Then, the number of trajectory components for a vehicle is the number of times its acceleration rate changes during the trip. For example, if the acceleration rate does not change during the entire trip , the vehicle trajectory is a single component trajectory. Vehicle trajectories with different number of components were compared and speed. Similarly to the traj ectory optimization algorithm developed in Chapter 3, the four component trajectory is used for all vehicles that are not the first vehicle of a particular movement and the three component trajectory is used for all the first vehicles since there is no nee d to consider the time headway for them. Since vehicles must accelerate to reach the maximum speed before departing the intersection, the third trajectory component is always an acceleration component and the speed of the fourth component is always the ma ximum speed. A ssume that the third and the fourth component are part of a hypothetical departure curve, which starts from a full stop and accelerates to the maximum speed. The hypothetical departure PAGE 97 97 curve that can reach the intersection at the earliest fea sible time is defined as the hypothetical saturation flow departure curve, as the dashed curve in Figure 4 3A . The time difference between the hypothetical saturation flow departure curve and the fourth component of the previous vehicle trajectory is the s aturation time headway. Therefore, the hypothetical saturation flow departure curve can be determined based on the third and the fourth component of the previous vehicle trajectory. The hypothetical saturation flow departure curve can be defined by three parameters, which are the hypothetical departure distance d hypo depart , hypothetical saturation flow departure time T hypo,depart and the hypothetical acceleration rate a hypo,depart , as shown in Figure 4 3A . Those three parameters can be calculated using th e following equation. ( 4 1) ( 4 2) ( 4 3) where j i : the sequence number for the i th vehic le d stop : the vehicle length, ft v max, k : the maximum speed of movement k , ft/sec a 3, j : the acceleration rate for the third trajectory component of the j th vehicle from a particular movement, ft/sec 2 h sat : the saturation time headway, sec All the other variables are as previously defined. PAGE 98 98 The objective of the trajectory optimization algorithm is to adjust the vehicle trajectory such that it can meet and coincide with the hypothetical saturation flow departure curve. In this way, all the vehicles try to leave the intersection at their earliest possible time and save time for the following vehicles in order to maximize the utilization of the approach and minimize delay. Also, the vehicle trajectory cannot go above the hypothetical saturatio n flow departure curve to ensure a safe headway with the vehicle in front. The utilization of the hypothetical saturation flow departure curve helps optimize vehicle trajectories and at the same time gua rantees the FIFO rule. To address the second rule, th e parameter T enter , which is the earliest feasible time that the vehicle can enter the intersection, is defined. The value of T enter can be calculated as the intersection exiting time for the last vehicle that has left the intersection from a conflicting m ovement, such that when the vehicle enters the intersection, vehicles from the conflicting movements all have cleared the intersection. T enter can be calculated using the following equation: ( 4 4) where k i : the movement t from which the i th vehicle approaches the intersection T enter, i : the earliest time that the i th vehicle can enter the intersection, sec T exi t ( k , i ) : the intersection exiting time of the last vehicle from movement k before the i th vehicle enters the intersection, sec All the other variables are as previously defined. PAGE 99 99 After determining the hypothetical saturation departure curve, the earlie st entering time T enter is also calculated. If the arrival time at the intersection for the hypothetical saturation departure curve T arrival, hypo is earlier than T enter , the hypothetical saturation departure curve is shifted to ensure a vehicle arrival ti me at T enter , as shown in Figure 4 3B . The shifted hypothetical saturation departure curve is then used for the trajectory calculation. For the shifted hypothetical saturation departure curve, the values of d hypo,depart and a hypo,depart are the same as tho se in the original hypothetical saturation flow departure curve. But the T hypo,depart will be delayed such that the vehicle will not arrive at the intersection before T enter . The value of the new T hypo,depart can be calculated using the following equation. ( 4 5) All the variables in the above equation are as previously defined. After determining the hypothetical saturation flow departure curve, vehicle trajectory calcu speed and location. The categorization of the trajectory optimization cases and the is can be found in the previous chapte r . The only change need to be made is that during the trajectory calculation process , the variable ( hypothetical intersection arrival time ) used in Chapter 3 should be calculated using the method discussed in this chapter. In summary, tr ajectory optimization for through vehicles is conducted follo wing the steps shown in Figure 4 4 . If the vehicle is the first vehicle of a specific movement that passes the intersection during the current optimization stage, T enter is first calculated as th e earliest time that the vehicle can enter the intersection. Then, the vehicle PAGE 100 100 trajectory calculation case will be identified based on T enter and location. Trajectory optimization cases for the first vehicles are also identi fied in the previous chapter. the specific trajectory calculation case accordingly. T enter is used as T arrival, hypo in those equations. If the vehicle is not the first vehicle of that m ovement, the hypothetical saturation flow departure curve of this vehicle should first be determined. Then, T enter is calculated and compared with the intersection arrival time for the hypothetical saturation departure curve T arrival, hypo to determine whe ther it must be shifted. Based on the initial speed and distance of the vehicle, its trajectory optimization case will be identified and its trajectory will be calculated. 4.2.1.2 Trajectory Optimization Algorithm for Turning Vehicles While through vehic les can accelerate to the maximum allowed speed before reaching the intersection in order to maximize the green time utilization, turning vehicles need to enter the intersection at a lower desired entering speed v in (Point A in Fi gure 4 5 ). After entering the intersection, the vehicle continues decelerating while making the turn until it reaches a minimum speed. According to previous research (Fitzpatrick & Schneider, 2005) , the midpoint of the tu rning curve (Point B in Figure 4 5 ) appears to be the location where the speed is the slowest. Then, the vehicle accelerates again and leaves the intersection (Point C in Figure 4 5 ) with speed v out . At some point in the downstream link (Point D in Figure 4 5 ), the vehicle accelerates to its desired speed. The entering speed v in , exiting speed v out and midpoint speed v mid all depend on the PAGE 101 101 conditions along the entering approach and the intersection geometry (free flow speed, radius of the curve, lane width, etc.) Despite the difference in vehicles' trajectories when crossing vs. turning at the intersection, the essential idea of optimizing trajectories for turning vehicles is still to maximize efficiency and intersection utilization. Similar to the algorithm proposed for through vehicles, three component trajectories are implemented for first vehicles and four component trajectories are implemented for the following vehicles. All the turning vehicles are required to reach the same desired entering speed v in (all the vehicles studied in this research are assumed to be passenger cars) and enter the intersection at the earliest feasible entering time. For vehicles that are able to reach v in at the stop bar, a predetermined turning trajectory can be implemented. Other vehicles are required to tr averse the intersection at their earliest possible time. For through vehicles, we assume their approaching speeds do not exceed the maximum allowed speed. As a result, the last non constant speed trajectory component before they arrive at the intersection is always an acceleration component. Therefore, the hypothetical saturation departure curves are introduced for the trajectory calculation. However, for turning vehicles, their travelling speeds may be higher than the desired entering speed v in , and in tha t case the vehicles need to decelerate before making a turn. Therefore, the third trajectory component for turning vehicles could either be an acceleration component or a deceleration component. Accordingly, the hypothetical saturation flow curve, which is used for the trajectory optimization, could either be a hypothetical saturation flow departure curve or a hypothetical saturation flow deceleration curve. During the trajectory optimization process, the type of the PAGE 102 102 hypothetical curve should be determined by the trajectory of the previous vehicle. Figure 4 6 shows the two scenarios under which these two types of hypothetical curves are used. The hypothetical saturation flow departure curve for turning vehicles is similar to that for the through vehicles. It is used when the last non constant speed component of the previous turning vehicle is an acceleration component. It can be calculated using Equation 4 1 through Equation 4 3, but replacing v max with v in in Equation 4 2. The hypothetical saturation deceler ation curve starts from the maximum speed v max and decelerates to the desired intersection entering speed v in . It is used when the last non constant speed component of the previous vehicle is a deceleration component, and it keeps a saturation time headway with the hypothetical saturation deceleration curve of the previous vehicle, as shown in Figure 4 6B . The three parameters that define the hypothetical saturation flow deceleration curves are the hypothetical saturation deceleration distance d hypo,dec , hy pothetical saturation flow deceleration time T hypo,dec and the hypothetical deceleration rate a hypo,dec . The three parameters can be calculated using the following equations: ( 4 6) ( 4 7) ( 4 8) All the varia bles are as previously defined. If the shifted hypothetical saturation flow deceleration curve is used, the values of d hypo,dec and a hypo,dec are the same as in the original saturation flow deceleration curve. The value of the new T hypo,dec can be calculat ed using the following equation: PAGE 103 103 ( 4 9) Based on the definitions of the hypothetical saturation flow curves, the trajectory for turning vehicles can be optimized following the steps in Figure 4 4 . If the vehicle is the first vehicle for a certain movement during the current optimization stage, its trajectory can be calculated based on the earliest vehicle entering time T enter and its trajectory optimization case, which can be identified based on th and initial distance to the intersection. If the vehicle is not the first vehicle, its hypothetical saturation flow trajectory curve first needs to be determined. The trajectory of the vehicle is then calculated based on the hypot hetical saturation trajectory curve and its trajectory optimization case. The trajectory optimization cases for turning vehicles, including the criterion f or selecting the suitable case and the shape of the vehicle trajectory (vehicle's maneuvers during th e entire trip, starting from the time it enters the communication range until it finishes the turning and accelerates back to the maximum speed) associated with each case, are discussed in the following paragraphs . Trajectory Optimization Cases for The F irst Vehicle Similar to the algorithm proposed for through vehicles, three component trajectories are assumed for the first vehicle. The first and last component of the trajectory has constant acceleration, while the middle one has constant speed. Based on the kinematic equations, the following equations are developed for calculating a general three component trajectory. PAGE 104 104 ( 4 10 ) I n the above equations, the input variables are: T arrical,hypo = the intersection arrival time of the hypothetical saturation flow curve or the shifted hypothetical saturation flow curve , sec T start = the start time of the optimization stage, sec D = the initial d istance of the vehicle to the intersection, ft v 0 = the initial speed of the vehicle, ft/sec v 3 = final speed when the vehicle reach the intersection, ft/sec a 1 = deceleration rate (negative) for the first component of the trajectory, ft/sec 2 a 3 = acceleration rate (positive) for the third component of the trajectory, ft/sec 2 The output variables that define the trajectories are: v 2 = speed for the constant speed component of the vehicle trajectory, ft/sec t 1 = time duration of the first trajec tory component, sec t 2 = time duration of the second trajectory component, sec t 3 = time duration of the third trajectory component, sec d 1 = distance the vehicle passed in the first trajectory component, ft d 2 = distance the vehicle passed in the s econd trajectory component, ft PAGE 105 105 d 3 = distance the vehicle passed in the third trajectory component, ft Among the above input parameters, T start , D , and v 0 are given at th e beginning of the optimization, v 3 and T arrival, hypo can be calculated after getti ng the hypothetical saturation flow curve using Equation 4 1 through Equation 4 9. Therefore, it is the other two parameters, a 1 , and a 3 two variables vary as the initial status of the vehicles and T arrival, h ypo changes, thus need to be determined on a case by case basis. In order to simplify the trajectory calculation, it is assumed that there are only two predefined feasible values a acc,max and a dec,max to choose from. The ideal value for v 3 is v in . However, for some of the cases, there is not enough distance for the vehicle to accelerate to v in , resulting in an entering speed that is lower than v in . For safety concerns, it is assumed that vehicles are always able to decelerate to a speed that is no higher th an v in before its arrival at the intersection. T he trajectory of the first vehicle is first categorized into four cases based on its initial distance to the intersection at the beginning of the optimization stage . For each case, the feasible types of the v ehicle trajectory are analyzed. Vehicle trajectories are further categorized into different subcases based on their intersection arrival time, and e ach subcase contains only one trajectory type. The value of the input variables ( a 1 , and a 3 ), and the thresh old intersection arrival times for each subcase are identified. For a subject turning vehicle, given the actual start time of the optimization ( T start ), hypothetical intersection arrival time ( T arrival,hypo ), inter section ( D ) , we can identify which subcase the vehicle belongs to and what are the values for the input variables for calculating its trajectory. In order to differentiate the PAGE 106 106 turning vehicle trajectory cases from the through vehicle cases, capital letter T is used in the case number. Case T 1 enough for it to complete any acceleration or deceleration maneuver and reach their desired speed when arriving at the intersection. The vehicle the following constraint: ( 4 11 ) Subcase regions, and the corresponding threshold trajectory and arr ival times are shown in Figure 4 7A . In Case T 1A, the initial speed v 0 is lower than the desired entering speed v in while in Case T 1B v 0 is greater than v in . The subcases in Case 1 are: Case T 1A a/Case T 1B a : Case T 1A b/Case T 1B b : Case T 1A c/Case T 1B c : Case T 1A d/Case T 1B d : As previously defined, is the hypothetical intersection arrival time and is also the earliest time that the vehicle ca n enter the intersection . T 1 , T 2 and T 3 in the above criterion are the threshold values that used to identify the trajectory calculation subcase in Case T 1 (including both Case T 1A and Case T 1B). Their values are summarized in Table 4 1. Among all the traj ectories in this case, the trajectory 1 has the earliest arrival time. If T arrival,hypo locates before T 1 on the time axis (Case T 1A a and Case T 1B a), the vehicle is required to use Trajectory 1 to reach the intersection at its earliest feasible time. Mor e specifically, the vehicle needs to first accelerate to the maximum speed v max PAGE 107 107 using the maximum acceleration rate a acc,max and travel with that speed for a certain time, then decelerate to v in (desired entering speed) using the maximum deceleration rate a dec,max before arriving at the intersection. For T arrival,hypo between T 1 and T 2 (Case T 1A b and Case T 1B b), the shape of the vehicle trajectory is similar to Trajectory 1. The only difference is that the vehicle does not need to reach the maximum speed v max . Instead, it accelerates to a speed v constant less than v max , and uses v constant for the constant speed portion of the trajectory. Then, the vehicle decelerates to v in before arriving at the stop bar. As T arrival,hypo moves to the right, it will get to a point T 2 and the vehicle trajectory associated with this arrival time (Trajectory 2 in Figure 4 7A and Figure Figure 4 7B ) only has an acceleration component at the beginning (for Case T 1A) or only has a deceleration component before the stop bar (for Case T 1B). If T arrival,hypo moves further to the right and locates between T 2 and T 3 , the vehicle trajectory will have two acceleration components (for Case T 1A c) or two deceleration components (for Case T 1B c). For vehicle of this subcase, it first acce lerates/decelerates to a certain speed (lower than v in for Case T 1A and higher than v in for Case T 1B) and maintains this speed until it gets close to the intersection. Then, it accelerates/decelerates again to reach v in . As T arrival,hypo moves from T 2 to T 3 , the time duration of one acceleration/deceleration component keeps increasing while the other acceleration/deceleration component keeps decreasing until T arrival,hypo get to the point T 3 , when the vehicle trajectory only has one acceleration or decelera tion component. As T arrival,hypo moves to the right of T 3 , the vehicle has to slow down to a speed that is less than v in to further extend the travel time. Therefore, the vehicle of Case T 1A - PAGE 108 108 d and Case T 1B d first decelerates to a certain speed and maintai ns it for a while. When it is close to the intersection, the vehicle will accelerate to v in . Case T 2 sfies the following constraints. ( 4 12 ) and/or ( 4 13 ) and ( 4 14 ) In this case, the initial distance to the intersection is not long en ough for vehicles in some subcases to complete the acceleration or deceleration maneuvers even using the maximum acceleration/deceleration rate. Therefore, for some subcases, vehicles cannot arrive at the intersection with the speed v in . Subcase regions, a nd the corresponding threshold arrival times and associated trajectory are illustrated in Figure 4 8 . In Case T 2A, the initial speed v 0 is lower than the desired entering speed v in while in Case T 2B v 0 is greater than v in . The subcases in Case T 2 are: Case T 2A a/Case T 2B a : Case T2A b/Case T2B b : Case T2A c/Case T2B c : Case T2A d/Case T2B d : Case T2A e/Case T2B e : Cas e T2A f/Case T2B f : PAGE 109 10 9 The same as previously defined, T arrival,hypo is the hypothetical intersection arrival time and is also the earliest time that the vehicle can enter the intersection . T 1 through T 5 in the above criterion are the th reshold values that used to identify the trajectory calculation subcase in Case T 2 (including both Case T 2A and Case T 2B). Their values are summarized in Table 4 2. The discussions below only consid er the case when both Equation 4 12 and Equation 4 13 are satisfied. If only Equation 4 12 is satisfied, vehicle trajectories in Case T 2A/B d, Case T 2A/B e and Case T 2A/B f are the same as in Case T 1A/B d. If only Equation 4 13 is satisfied, the trajectory adjustment methods in Case T 2A/B a, Case T 2A/B b are the same as in the corresponding subcases in Case T 1. Trajectory 1 in Figure 4 8 determines the earliest arrival time of all the trajectories in this case . Using this adjustment method, the vehicle first accelerates using the maximum acceleration rate a acc,ma x . After reaching a speed v 2 , the vehicle immediately slows down to ensure it will decelerate to v in when arriving at the intersection stop bar. Since the vehicle have to decelerate before reaching the maximum speed ( v 2 < v max ) and there is no constant spe ed trajectory component, the earliest arrival time in this case is not as early as that in Case T 1, and as the initial distance decreases, T 1 will move to the right. For all vehicles belong to Case T 2A/B a, Trajectory 1 will be used as their adjusted traje ctory. The trajectory adjustment methods for Case T 2A/B b, Case T 2A/B c, and Case T 2A/B d are similar to the corresponding subcases in Case T 1. In those cases, vehicles can reach the speed v in at the stop bar. However, as T arrival,hypo moves to the right i n Figure 4 8 , the vehicle needs to travel at a low speed for a longer time. When it is able to accelerate, there is not enough space to reach the desired speed v in . As T arrival,hypo PAGE 110 110 moves to the right, the speed at the time when the vehicle enters the inte rsection ( T arrival,hypo ) will decrease. The minimum v arrival will be reached when T arrival,hypo gets to the time point T 5 . The vehicle associated with Trajectory 5 first decelerates using the maximum deceleration rate a dec,max . After to decelerating to the speed of 0, the vehicle immediately accelerates and enters the intersection with the minimum v arrival . For vehicles belongs to Case T 2A/B f, they all have to stop for a certain time, and the stopping time increases as T arrival,hypo moves to the right. v ar rival for all vehicles of this subcase is the same as the v arrival in Trajectory 5. Case T 3 the following constraint: ( 4 15 ) For safety concerns, in this study we assume all vehicles could arrive at the intersection with a speed lower or equal to v in. Therefore, this case is only for ve hicles with an initial speed lower than v in . Denote T 0 as the arrival time of the vehicle using its initial speed. If T arrival,hypo PAGE 111 111 trajectories are assumed for the following vehicles. The first and third components have constant acceleration, while the secon d and the fourth one have constant speed. The following equations can be used for calculating the four component trajectories . (4 16) In the above equations, the input variables are: T arrical,hypo = the intersection arrival time of the hypothetical saturation flow curve or the shifted hypothetical saturation flow curve , sec T start = the start time of the optimization stage, sec D = the initial distance of the vehicle to the intersection, ft v 0 = the initial speed of the vehicle, ft/sec v 4 = final speed when the vehicle reach the intersection, ft/sec a 1 = acceleration/deceleration rate for the first component of the traject ory, ft/sec 2 a 3 = acceleration/deceleration rate for the third component of the trajectory, ft/sec 2 t 4 = time duration of the fourth trajectory component, sec d 4 = distance the vehicle passed in the fourth trajectory component, ft The output variabl es that define the trajectories are: v 2 = speed for the constant speed component of the vehicle trajectory, ft/sec PAGE 112 112 t 1 = time duration of the first trajectory component, sec t 2 = time duration of the second trajectory component, sec t 3 = time duratio n of the third trajectory component, sec d 1 = distance the vehicle passed in the first trajectory component, ft d 2 = distance the vehicle passed in the second trajectory component, ft d 3 = distance the vehicle passed in the third trajectory component, ft Among the input parameters, T start , D , and v 0 are given at the beginning of the optimization; v 4 , T arrival, hypo , t 4 , and d 4 can be calculated after getting the hypothetical saturation flow curve using Eq uation 4 1 through Equation 4 9 ; a 1 , a 3 , have to be determined based on the trajectory of the previous vehicle. As discussed earlier in this section, for turning vehicles, the hypothetical saturation flow curve could either be a hypothetical saturation flow departure curve or a hypothetical saturation f low deceleration curve. Therefore, trajectory calculation methods for the following vehicles are developed separately for these two scenarios. Also, since the initial speed v 0 could be either lower or greater than the desired entering speed v in , and the re lationship between the two determines the type of the vehicle trajectory, these two different conditions are also discussed separately. Based on the above analysis, four cases are identified for developing the trajectory calculation algorithm for the follo wing vehicles. They are: Case T F1A: The last non trajectory is an acceleration component, and the initial speed v 0 of the studied vehicle is lower than v in . PAGE 113 113 Case T F1B: The last non constant speed component trajectory is an acceleration component, and v 0 is greater than v in for the studied vehicle. Case T F2A: The last non trajectory is a deceleration component, and v 0 is less than v in for the studied vehicle. Case T F2B: The last non trajectory is a deceleration component, and v 0 is greater than v in for the studied vehicle. Trajectory adjustment algorithms for each of the four cases are d iscussed below in more detail. Case T F1A . For the vehicle in this case, its initial speed v 0 is less than v in , which acceleration component before it reaches the intersec tion. As shown in Figure 4 9A , vehicles in this case are further divided into three subcases based on their initial distance to the intersection (denoted as D ). Assume the vehicle is the j th vehicle of a particular movement. The two threshold values D 1 an d D 2 for this vehicle can be calculated using the following equation. ( 4 17 ) ( 4 18 ) Where v in = the desired speed when the vehicle enters the i ntersection, ft/sec v 0,j = the initial speed for the j th vehicle of a particular movement, ft/sec v max = the maximum allowed speed, ft/sec PAGE 114 114 T enter, j = the earliest time that the j th vehicle of a particular movement can enter the intersection, sec a acc,max = the maximum acceleration rate, ft/sec 2 a dec,max = the maximum deceleration rate, ft/sec 2 For vehicle with an initial distance that is shorter than D 1 , it needs to first location) to a certain speed that is lower than v in , and maintains the speed until it meets the saturation flow departure curve (dashed yellow curve in Figure 4 9A ). Then, it follows the hypothetical saturation flow departure curve to accelerate and enter s the intersection with the speed v in . For vehicle with an initial distance that is between D 1 and D 2 , it needs to first accelerate to a certain speed that is greater than v in but less than v max , and maintains this speed for a certain time. Before its arr ival at the intersection, the vehicle decelerates to meet the saturation flow departure curve to ensure its entering speed is v in . Note that for vehicle in this case, the last component of its trajectory is a deceleration component. Therefore, the hypothet ical saturation flow curve for its following vehicle is a hypothetical saturation flow deceleration curve. For vehicle with an initial distance that is longer than D 2 , they are not able to enter the intersection at the prescheduled T arrival,hypo . Therefore , vehicles of this case should follow its quickest trajectory. It first accelerates to v max and travels with this constant speed. Before entering the intersection, it decelerates to v in using the maximum deceleration rate. The hypothetical saturation flow curve for its following vehicle is also a hypothetical saturation flow deceleration curve. PAGE 115 115 Case T F1B . As shown in Figure 4 9B , vehicles in this case are further divided into three subcases based on their initial distance to the intersection. The two thresh old values D 1 and D 2 for vehicles in this case can be calculated using the following equation. ( 4 19 ) ( 4 20 ) For vehicle with an initial distance t hat is shorter than D 1 , it needs to first decelerate to a certain speed that is lower than v in , and maintains the speed until it meets the hypothetical saturation flow departure curve at its acceleration portion. Then, it follows the hypothetical saturatio n flow departure curve to accelerate and enters the intersection with the speed v in . For vehicle with an initial distance that is between D 1 and D 2 , the vehicle first a certain speed that is greater than v in but less than v max , and maintains this speed for a certain time. Before its arrival at the intersection, the vehicle decelerates to ensure its entering speed is v in . For vehicle with an initial distance that is lo nger than D 2 , its trajectory calculation method is similar to the corresponding subcases in case T F1A. The vehicle first accelerates to v max and travels with this constant speed. Before entering the intersection, it decelerates to v in . The arrival time for vehicles in this case is later than T arrival,hypo . PAGE 116 116 Case T F2A . As shown in Figure 4 10A , vehicles in this case are further categorized into three subcases based on their initial distance to the intersection. Assume the vehicle is the j th vehicle that is c onsidered to depart from this movement. The threshold distance D 1 and D 2 for this vehicle can be calculated using the following equation. ( 4 21 ) ( 4 22 ) Where t vin, j = the time duration of the constant speed portion (with the speed v in ) of the hypothetical saturation flow deceleration curve, sec Other variables are the same as previously d efined. For vehicle with an initial distance that is shorter than D 1 , it needs to first certain speed that is lower than v in , and maintains the speed. Before arriving a t the stop bar, the vehicle accelerates to v in . Since the last component of this vehicle trajectory is an acceleration component, the hypothetical saturation flow curve for its following vehicle is a hypothetical saturation departure curve. This subcase on ly occurs when the hypothetical saturation flow curve is shifted and is far away from the hypothetical saturation deceleration curve of the previous vehicle. For vehicle with an initial distance that is between D 1 and D 2 , the vehicle needs to first acceler ate to a certain speed that is higher than v in , and maintains the speed until it meets the hypothetical saturation flow deceleration curve (dashed blue curve in Figure PAGE 117 117 4 10A ). Then, it follows the hypothetical saturation flow deceleration curve to decelera te and enters the intersection with the speed v in . For vehicle with an initial distance that is longer than D 2 , the vehicle first accelerates to the maximum speed using the maximum acceleration rate a acc,max , and maintains this speed for a certain time. Be fore its arrival at the intersection, the vehicle decelerates to ensure its entering speed is v in . The trajectory of this vehicle may not be able to arrive the intersection at the desired entering time T arrival,hypo if the trajectory cannot meet the hypoth etical saturation flow deceleration curve during the deceleration. Case T F2B . As shown in Figure 4 10B , vehicles in this case are further divided into three subcases based on their initial distance to the intersection. The three subcases are similar to t he corresponding subcases in case F2A. Assume the vehicle is the j th vehicle that is considered to depart from this movement. The two threshold values D 1 and D 2 for this vehicle can be calculated using the following equation. ( 4 23 ) ( 4 24 ) For vehicle with an initial distance that is shorter than D 1 , it needs to decelerate to a certain speed that is lower than v in , and maintains the speed. Before arriving at the stop bar, the vehi cle accelerates to v in . Similar to the corresponding subcase in Case T F2A, since the last component of this vehicle trajectory is an acceleration component, the hypothetical saturation flow curve for its following vehicle is a hypothetical saturation depar ture curve. PAGE 118 118 For vehicle with an initial distance that is between D 1 and D 2 , the vehicle needs to a certain speed that is higher than v in , and maintains the speed u ntil it meets the saturation deceleration curve. Then, it follows the hypothetical saturation deceleration curve to decelerate and enters the intersection with the speed v in . For vehicle with an initial distance that is longer than D 2 , its trajectory calcu lation method is the same as the subcase in case T F1A. The vehicle first accelerates to the maximum speed using the maximum acceleration rate a acc,max , and maintains this speed for a certain time. Before its arrival at the intersection, the vehicle deceler ates to v in . Similarly, the trajectory of this vehicle may not be able to arrive the intersection at the desired entering time T arrival,hypo if the trajectory cannot meet the hypothetical saturation deceleration curve during the deceleration. For all the t urning vehicles discussed above, including both the first vehicles and the following vehicles , if they are able to reach the desired speed v in when arriving at the intersection, they will pass the intersection by following the pre determined passing trajec tory after entering the intersection. For vehicles that enter the intersection with a speed lower than v in (the enter speed cannot be higher than v in for safety concerns), they are required to reach the pre determined speed v mid at the midpoint of the turn ing curve and follow the rest portion of the pre determined passing trajectory to leave the intersection. When calculating the optimum trajectory for a particular vehicle, its trajectory s and the criteria for each trajectory optimization case. Then, the shape of the vehicle trajectories PAGE 119 119 (acceleration rate for each trajectory component) can be determined based on the above discussion. Using E q u ation 4 10 and Equation 4 16 , the parameters t hat define the vehicle trajectories can be calculated. In this research, the optimized trajectory for each vehicle is presented using a four row matrix. The four elements of each column represent the time, and the associated location, speed and acceleratio n rate at each acceleration changing point of the optimized trajectory. 4.2.2 Genetic Algorithm Based Control Optimization The trajectory optimization algorithm discussed in the previous section provides a way for adjusting the vehicle trajectories, such t hat vehicles can leave the intersection as close to the saturation flow rate as possible, while minimizing the ATTD . Trajectory calculations for a particular vehicle are conducted based on the trajectory of the previous vehicle from the same movement and t he exiting time of vehicles that have already left the intersection from conflicting movements. Therefore, given a particular vehicle passing sequence, the optimum trajectories can be calculated vehicle by vehicle. The objective of the optimization problem in this paper is to determine the vehicle passing sequence that optimizes the intersection performance (i.e. minimizes the ATTD). The trajectory optimization algorithm is a scenario based calculation process that cannot be expressed by simple numerical e quations. Therefore, there is very little information about the searching space of the optimization problem. Optimization algorithms that require special characteristics of the candidate solution set cannot be used for this optimization problem . Dynamic p rogramming is a method that can be potentially used for solving this vehicle passing sequencing problem. Instead of determining the passing sequence for PAGE 120 120 all the vehicles at one time, we can break down the problem into multiple stages and only consider one vehicle passing the intersection at each stage. Decisions are made at the beginning of every stage to determine which vehicles and from which movements should enter the intersection. Then, dynamic programming can be adopted to solve this sequential decisio n making problem. This idea works for a two phase intersection that consists of two single lane through movements. However, as the number of movements increases, the size of the feasible solution set increases exponentially. For a twelve movement problem s tudied in this research, the size of the problem is far beyond the capability of the computer. GAs are adaptive heuristic search algorithms that are designed to solve optimization problems using the evolutionary ideas of natural selection and genetic, suc h as inheritance, mutation, selection and crossover (Bajpai & Kumar, 2010) . The evolution of a GA starts from a population of random generated candidate solutions. The fitness of each individual is evaluated. The more fit indivi duals are selected, and then being recombined or possibly randomly mutated to create a new population, which is called a new generation. The new generation will be used for creating the next offspring generation. The iterative process is repeated until a d esired fitness level has been reached or the predefined maximum number of generation has been created. It is a powerful method for problems that have very large set of candidate solutions and complex search spaces. Therefore, GA is is implemented for this optimization problem. Assume there are N vehicles approaching the intersection from different movements. Let X denote the state space, which includes the index for all the movements. For the problem studied in this research, X PAGE 121 121 ( 4 25 ) A candidate solution of the vehicle sequencing problem looks like: ( 4 26 ) represents the movement index of the i th vehicle. The solution should satisfy the following equation. ( 4 27 ) Where i = the i th vehicle that will be scheduled to pass the intersection, i k = the k th movement, k N k = the total number of vehic les from the the k th movement The GA is implemented follow ing the steps shown in Figure 4 11 . A solution generated by GA is called an individual. Assume the population size of each generation is M . First, an initial population of M individuals is generat ed randomly. Then, for each individual (i.e. a string of the vehicle p assing sequence as in Equation 4 26 ), the intersection performance is calculated based on the vehicle trajectories determined using the proposed trajectory optimization algorithm. Indiv idual solutions are then selected from the current population as parents for the next generation. For each selection, a tournament population with a size M t ( M t < M ) is created by randomly selecting M t individuals from the original population. The fittest individual is selected as one parent. In this way, the more fit individuals are typically more likely to be selected. PAGE 122 122 A pair of selected parent solutions is used to create one child solution using the method of crossover and mutation. Uniform crossover t echnique is used in this research and the parameter of uniform rate is defined as the ratio of genes that the offspring will inherit from its first parent. For example if the uniform ratio is 0.5, the offspring will have approximately half of the genes fro m the first parent and the other half from the second parent. A random number between 0 and 1 is generated at each step when looping over the gene size (number of elements in an individual solution). If the random number is smaller than the uniform rate, t he gene from the first parent solution will be used at the corresponding position of the child solution. Otherwise, the gene from the second parent solution will be used for its offspring. The total number of vehicles for each movement is fixed. If the gen e x i inherited from its parent is the movement that all the vehicles from which has already left the intersection, then a random movement index will be selected from the remaining movements. In this way, the child solution can always satisfy Equation 4 27 . The parameter of mutation rate is defined for conducting the mutation process. It determines the percentage of genes in each individual solution that will be replaced. Looping over the genes in one individual solution, a random number between 0 and 1 is generated for each gene. If the generated random number is smaller than the mutation rate, the gene will be saved as a candidate for mutation and its position will be marked. When another candidate gene is selected, the two genes exchange their position. A fter the crossover and mutation process, an individual solution is produced for the new generation. This process will be repeated to create M 1 new individuals, and the last individual for the new generation is the best individual kept from the previous PAGE 123 123 ge neration. The new generation will undergo the same process (i.e. evaluation, selection, crossover and mutation) to produce more generations. This generational process is repeated until a predetermined number of generations is reached. The fittest individua l from the last generation is the optimum solution of the vehicle passing sequence problem. 4.3 Simulation A simulator was coded in Java implementing the proposed algorithm. It consists of 5 components, including vehicle generator, single trajectory optim izer, intersection performance calculator, GA operator, and the main controller that used for reading input, organizing the optimization process and writing output. The flow chart in Figure 4 12 summarizes the steps of the simulation process. At the beginn ing of the simulation, input parameters are read from a separate TXT file. There are four types of input for the simulation: 1) geometric information, including the length of the communication range and the length of the intersection; 2) parameters used fo r vehicle generation, i.e. parameters of the distribution that was used for generating the vehicles; 3) parameters used for optimization operation, such as the length of the optimization period and the length of the warm up period; and 4) vehicle motion pa rameters, including the maximum/minimum speed, maximum/minimum acceleration rate, saturation time headway, and the predefined vehicle turning curve. After reading the input parameters, the system randomly generates the arrival times and speeds for all th e vehicles that enter the communication range during the overall planning horizon (15 minutes). When conducting optimization for a specific stage, only vehicles arrivals since the beginning of the previous stage are considered, along with their associated arrival times and speeds are used as input for the stage PAGE 124 124 optimization. Vehicle arrival is assumed as a Poisson process, and as a result, the inter arrival times follow the exponential distribution. The average time headway is used as the rate parameter o f the follow a triangular distribution, with the maximum speed as the upper limit, the minimum travelling speed as the lower limit and the average travelling speed as the mode. The GA runs fo r 20 generations for each optimization stage with a population size of 100 for each generation. A uniform rate of 0.5 is used for crossover, indicating that each child solution has approximately half of the genes from one parent and the other half from the other parent. The mutation rate is 0.02. So during the mutation step, about 2% of genes in each individual solution are randomly replaced. Using those parameters, it can be observed that for the last several generations, there is no significant improvemen t in the optimization result (average travel time delay) from one generation to the next. There are three major outputs of the proposed algorithm, the optimum vehicle passing sequence, the optimized vehicle trajectory and the intersection average travel ti me delay (ATTD). The optimized vehicle passing sequence is presented by an array as in Equation 4 26 . The optimized trajectory for each vehicle is presented using a four row matrix. The four elements of each column represent the time, and the associated lo cation, speed and acceleration rate at each acceleration changing point of the optimized trajectory. Vehicle trajectories can be plotted based on the trajectory points provided by this matrix. The vehicle trajectory points are recorded until they accelerat e back to the maximum allowed travelling speed in the downstream link. In addition, the travel time delay of each vehicle, average travel time delay of each movement, and PAGE 125 125 throughput of each movement are also calculated and can be presented as outputs at th e end of the simulation if needed. Computational time was also calculated for each optimization stage. It shows that getting the optimum solution for one stage takes about 1 to 2 seconds. 4.4 S ensitivity Analysis Sensitivity analysis was performed to test how sensitive the proposed optimization algorithm is to selected inputs. The following factors were tested: Demand (balanced and un balanced demand) Turning percentage Length of the communication range For each of these factors, various scenarios were tes ted using the Java simulation implementing the proposed intersection control optimization algorithm. The same set of scenarios and intersection configuration was also simulated for an actuated signalized intersection using CORSIM TM . The ATTD and the inters ection throughput were compared for the two intersection control methods. In order to obtain statistically valid results, for each scenario tested in both Java simulation and CORSIM TM , 10 runs were conducted using different random number seeds (these are u sed in our algorithm for vehicle generation, while in CORSIM they are used in vehicle generation and movement.) Figure 4 13 through Figure 4 16 show the comparison between the conventional actuated control and the proposed algorithm under different scenari os. All the test results in the figures are average values of 10 runs. Figure 4 13 presents the comparison results when balanced demands were assigned to all four approaches. For all the scenarios tested in these two figure, the turning percentage was 15% for both the left turning and right turning traffic, and the communication range is 3000 feet from the center of the intersection. It can be observed PAGE 126 126 that, after implementing the proposed optimization algorithm, the ATTD is reduced by 16.3% to 56.0%, and t he intersection throughput is increased by 3.5% to 27.3% depending on the demand scenario, and the improvement is more significant for scenarios with higher demand. It can be note that that under the actuated signal control, the improvement in throughput d ecreases after the demand reaches 1200 vehicle per hour per approach, implying that the demand is getting close to the capacity of the approach. For the proposed algorithm, the throughput increases significantly until the demand reaches about 1400 vehicle per hour per approach . Therefore, it can be concluded that the proposed optimization algorithm increases the capacity of the intersection approach. Figure 4 14 presents how the relative proportions in demand impact the performance of the proposed algorithm . For all the test scenarios in this figure, the total demand of the entire intersection is the same (4000 vehicles per hour for all four approaches combined), but different levels of demand were assigned to the major street approaches and the side street approaches in different scenarios. Figure 4 14 shows that for actuated control, the ATTD slightly increases and the throughput slightly decreases as the demand difference between the major street and side street increases. However, the relative proportions in demand do not have much impact for the proposed algorithm, and there are no significant changes in ATTD or the throughput when there is a higher proportion of demand on the major street. Therefore, as long as the total intersection demand does not chan ge, there is no significant change in ATTD or the intersection throughput . Also, it can be noted that for all test scenarios in Figure 4 14 , the performance of the proposed algorithm is better than the actuated control PAGE 127 127 method. The in ATTD is reduced by 51. 8% to 61.3%, and the intersection throughput is increased by 2.6% to 6.6% depending on the unbalanced demand scenarios. Figure 4 15 presents how the percentage of turning traffic impacts the performance of the proposed algorithm. For all the test scenarios in this figure, the demand is 1000 vehi cles per hour for each approach, and t he right turning traffic takes up 5% of all traffic demand. The left turning traffic demand changes for each test scenario, from 5% to 30%. For all test scenarios, the ATTD is im proved by 60.2% to 68.9% and the intersection throughput is improved by 7.0% to 13.2% after implementing the proposed intersection optimization algorithm. The proposed algorithm is more flexible in allocating time for vehicles to pass the intersection. The figure also shows that for actuated control, the ATTD first increases and the throughput decreases before the turning percentage reaches 15%, and after that the ATTD decreases and the throughput increases as the percentage of turning traffic increases. Th is is because the intersection average performance, and when the demand of turning traffic is relatively high the turning phases are longer to avoid too much waiting time for the turning vehicles. For the proposed algorithm, the ATTD slightly increases as the percentage of turning traffic increases. Because of their turning maneuvers, turning vehicles have a higher delay than the through vehicles when passing the inte rsection. Therefore, the intersection average delay slightly increases as the percentage of turning traffic increases. The increase in the percentage of turning traffic increases does not have significant impact on the throughput. PAGE 128 128 Figure 4 16 and Figure 4 17 presents comparisons of the ATTD and the intersection throughput between the two control algorithms for different communication range/link lengths under different demand levels . For the proposed algorithm, different communication ranges were used for ea ch test scenario. The link length of the actuated test scenarios were modified accordingly to ensure the delay times were calculated inside a link with the same length. For all the test scenarios in this figure, the demand is 1000 vehicles per hour for all approaches, and 15% left turning and right turning traffic were assigned to all the turning movements. Comparison of the ATTD in Figure 4 16 show s that for all the tested scenarios, the proposed algorithm the proposed algorithm works better than the actu ated, and the improvement in the ATTD per unit length (100 feet) decreases (in percentage) as the communication range decreases. This is because the closer the vehicle to the intersection, the more difficult to adjust its trajectory. The extent of the comm unication range limits the trajectory optimization ability of the proposed algorithm. Also, it can be note that, the improvement is most significant for the 1400 vehicle per hour per approach scenario. Figure 4 17 show s the c omparison of throughput for th e same set of test scenarios. It can be note that only for the 1400 vehicle per hour per approach demand scenario, the improvement in throughput increases as the communication range increases. For other demand scenarios, the change in the throughput as the communication range increases does not have a clear trend. This is because under low demand conditions, throughput for all scenarios is relatively high. Therefore, although the delay is improved as the communication range increases, it does not have PAGE 129 129 signi ficant on throughput. Also, when the demand is under a congested condition, throughput is constrained by the capacity of the intersection and cannot be improved by adjusting vehicle trajectories. PAGE 130 130 Table 4 1 . T hreshold vehicle arrival times for Case T 1 . T hreshold Threshold Time T i T 1 T 2 T 3 PAGE 131 131 Table 4 2 . T hreshold vehicle arrival times for Case T 2 . Threshold Threshold Time T i T 1 T 2 T 3 T 4 T 5 PAGE 132 132 Figure 4 1 . Sketch of the intersection and its Communication Range . Figure 4 2 . Layout of the optimization process . PAGE 133 133 A B Figure 4 3 . Hypothetical saturation flow departure curve and shifted hypothetical saturation flow departure curve . A) Hypothetical saturation flow departure curve, B) Shifted hypothetical saturation flow departure curve. PAGE 134 134 Figure 4 4 . Flow chart of the trajectory calculation process . Figure 4 5 . Trajectory and spatial path of turning vehicles . PAGE 135 135 A B Figure 4 6 . Hypothetical saturation flow departure curves and hypothetical sa turation flow deceleration curves for turning vehicles . A) Hypothetical departure curve, B) Hypothetical deceleration curve. PAGE 136 136 A B Figure 4 7 . Illustration of the subcase regions for Case T1 . A) Case T1A, B) Case T1B. PAGE 137 137 A B Figure 4 8 . Illustration of the subcase regions for Case T2 . A) Case T2A, B) Case T2 B. PAGE 138 138 A B Figure 4 9 . Illustration of the subcase regions for Ca se TF1 . A) Case TF1A, B) Case TF1 B. PAGE 139 139 A B Figure 4 10 . Illustration of the subcase regions for Case TF2 . A) Case TF2A, B) Case TF2 B. PAGE 140 140 Figure 4 11 . Genetic Algorithm flowchart . PAGE 141 141 Figure 4 12 . Flow chart of the opt imization process . PAGE 142 142 A B Figure 4 13 . Comparison of the actuated signal control and the proposed signal optimization algorithm under balanced demand scenarios . A) Comparison of ATTD, B) Comparison of throughput. 0 50 100 150 200 250 300 350 Average Travel Time Delay (sec) Demand (veh per hour per approach) Actuated Control Proposed Algorithm 0 200 400 600 800 1000 1200 1400 1600 Throughput (veh) Demand (veh per hour per approach) Actuated Control Proposed Algorithm PAGE 143 143 A B Figure 4 14 . Comparison of the actuated signal control and the proposed signal optimization algorithm under un balanced demand scenarios . A) Comparison of ATTD, B) Compari son of throughput. 0 10 20 30 40 50 60 70 80 90 100 Average Travel Time Delay (sec) Demand (veh per hour for main/side approach ) Actuated Control Proposed Algorithm 500 600 700 800 900 1000 1100 Throughput (veh) Demand (veh per hour for main/side approach) Actuated Control Proposed Algorithm PAGE 144 144 A B Figure 4 15 . Comparison of the actuated signal control and the proposed signal optimization algorithm under different turning percentage scenarios. A) Comparison of ATTD, B) Comparison of throughput. 0 20 40 60 80 100 120 140 5% 10% 15% 20% 25% 30% Average Travel Time Delay (sec) Turning Percentage Actuated Control Proposed Algorithm 500 600 700 800 900 1000 1100 5% 10% 15% 20% 25% 30% Throughput (veh) Turning Percentage Actuated Control Proposed Algorithm PAGE 145 145 A B C D Figure 4 16 . Comparison of the average travel time delay betwee n the two control algorithms under different communication range/link length . A) 600 vph per approach scenario, B) 1000 vph per approach scenario, C) 1400 vph per approach scenario, D) 1800 vph per approach scenario . 0 5 10 15 20 25 30 500 1000 1500 2000 2500 3000 ATTD Per 100 Feet (sec) Communication Range/Link Length (ft) Actuated Control Proposed Algorithm 0 5 10 15 20 25 30 500 1000 1500 2000 2500 3000 ATTD Per 100 Feet (sec) Communication Range/Link Length (ft) Actuated Control Proposed Algorithm 0 5 10 15 20 25 30 500 1000 1500 2000 2500 3000 ATTD Per 100 Feet (sec) Communication Range/Link Length (ft) Actuated Control Proposed Algorithm 0 5 10 15 20 25 30 500 1000 1500 2000 2500 3000 ATTD Per 100 Feet (sec) Communication Range/Link Length (ft) Actuated Control Proposed Algorithm PAGE 146 146 A B C D Figure 4 17 . Comparison of the throughput betwee n the two control algorithms under different communication range/link length . A) 600 vph per approach scenario, B) 1000 vph per approach scenario, C) 1400 vph per approach scenario, D) 1800 vph per approach scenario. 500 700 900 1100 1300 1500 500 1000 1500 2000 2500 3000 Throughput (veh) Communication Range/Link Length (ft) Actuated Control Proposed Algorithm 500 700 900 1100 1300 1500 500 1000 1500 2000 2500 3000 Throughput (veh) Communication Range/Link Length (ft) Actuated Control Proposed Algorithm 500 700 900 1100 1300 1500 500 1000 1500 2000 2500 3000 Throughput (veh) Communication Range/Link Length (ft) Actuated Control Proposed Algorithm 500 700 900 1100 1300 1500 500 1000 1500 2000 2500 3000 Throughput (veh) Communication Range/Link Length (ft) Actuated Control Proposed Algorithm PAGE 147 147 CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS The research presented in this dissertation first developed an optimization algorithm for a simple signalized intersection with two single lan e approaches under a 100% automated vehicle environment. Then, the proposed signal control optimization algorithm was expand ed for a full four leg intersection with the consideration of turning movements, and a full set of possible phases. Simulation code was develope d for both algorithms, and the simulation results were compared against conventional actuated signal control for a variety of scenarios. 5.1 Signal Control Optimization for A Two Approach Intersection A n optimization algorithm was first developed for a sim ple signalized intersection with two single lane approaches under a 100% automated vehicle environment. In order to develop the optimization algorithm, a trajectory optimization algorithm, which is able to optimize the vehicle trajectories for any given si gnal timing plan (the combination of number of phases and phase splits), was first proposed considering through vehicles only. Implementing this algorithm, optimum vehicle trajectories can be developed in conjunction with the optimum signal timing plan usi ng an enumeration technique. A rolling horizon scheme was developed to implement the algorithm over a time horizon and to process the continua lly arriving vehicles. Using the proposed algorithm, vehicle trajectories and the signal timing can be optimized s imultaneously. The proposed signal control optimization algorithm was coded in MATLAB. Actuated signal control was simulated for an intersection with the same configuration using CORSIM TM . Comparison between the two control algorithms was conducted for various scenarios. The results showed that the proposed optimization algorithm is able PAGE 148 148 to improve the intersection performance by reducing vehicle travel time delay, increasing throughput and increasing intersection capacity for both balanced and unbalance d demand scenarios, and it works better for the more congested conditions. However, the proposed algorithm works best when the communication range is bigger than a certain value (2000 ft for the tested scenarios in this research). If the communication range is smaller than that value, improvements brought by the proposed algorithm decrease as the communication range decreases. 5.2 Intersection Control Optimization fo r A General Four Approach Intersection A n intersection control optimization algorithm was developed for a four approach intersection with the consideration of turning movements under an automated vehicle environment. The proposed algorithm is an expansion of the signal control o ptimization algorithm developed for two approach intersections. Traffic signals were not used in the proposed system. Instead, an intersection controller is designed to decide the optimum vehicle passing sequence and to calculate the optimum vehicle trajectories. A trajectory optimization algorithm was developed. Implementing the proposed algorithm, optimum vehicle trajectories can be calculated for any given vehicle passing sequence. Genetic Algorithm was implemented for selecting th e optimum vehicle passing sequence that can optimize the intersection performance. In this way, the proposed intersection control algorithm is able to optimize the system performance and the trajectory of each single vehicle at the same time. The optimizat ion process was designed to repeat over a time horizon in order to process continually arriving vehicles. An intersection simulator was coded in Java implementing the proposed algorithm. An actuated signalized intersection with the same configuration was simulated using CORSIM TM . Comparison between the two control algorithms was PAGE 149 149 conducted for various scenarios. The results showed that the proposed algorithm is able to improve the intersection performance by reducing the average travel time delay and incre asing throughput under various demand scenarios, and it works better for more congested conditions. Compared to the actuated control method, the proposed algorithm is less sensitive to the balances in demand. An increase in the percentage of turning traffi c increases ATTD slightly, since turning movements are slower through the intersection. The proposed algorithm provides greater benefits for longer communication ranges under relative congested conditions, as these allow for more flexibility in adjusting v ehicle trajectories . 5.3 Recommendations for Future Research The two proposed optimization algorithm s were developed for intersections with a configuration where lane changing does not need to be considered. It was also assumed all the vehicles are autom ated vehicles that are able to wirelessly communicate with the intersection controller and strictly follow the trajectories provided to them as optimized by the intersection controller. Future research should expand the proposed algorithm s with the conside ration of lane changing. Also, future work should consider the optimization when non automated vehicles (conventional as well as connected vehicles) are present in the traffic stream. Such research would be very helpful in gradual implementation of the aut omated vehicle technologies. In future research, if the algorithm is expanded for a mi xed traffic environment , the conventional vehicles, which are not capable of wireless communication, will need the presence of traffic signals. In that case, the formula tion of the optimization problem for the four approach intersection (a problem that decides the vehicle passing sequence) can still be used since the signal phasing split can be easily calculated PAGE 150 150 based on the passing time of vehicles from each movement. Ho wever, constraints should be made on the minimum number of vehicles that need to be processed at one time for each movement to guarantee a minimum length of each green time interval. The algorithm should also be further expanded to consider urban networks and the interaction in operations between adjacent intersections (for example, interchanges.) Future work shou ld also consider the impacts of transmission/communication/computational delays and their effect on the algorithm effectiveness. PAGE 151 151 LIST OF REFERENC ES Andrews, C. M., Elahi, S. M., & Clark, J. E. (1997). Evaluation of New Jersey Route 18 OPAC/MIST Traffic Control System. Transportation Research Record (No. 1603), 150 155. 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Service Systems and Service Management, 2008 International Conference on (pp. 1-6). Melbourne, VIC: IEEE. Yi, P. (2011). Application of IntelliDrive Information System to Enhance High-Speed Intersection Safety. Transportation Research Record: Journal of the Transportation Research Board (2215), 105112. Zhao, Y., & Tian, Z. (2012). An Overview of the Usage of Adaptive Signal Control System in the United States of America. Applied Mechanics and Materials , 178 181, 2591-2598 . PAGE 156 156 BIOGRAPHICAL SKETCH Zhuofei Li did her undergraduate study at Tsinghua University, China and started her Ph.D. program at the Transportation Research Center in the University of om the University of Florida in May 2012. analysis, with applications on travel time reliability analysis, signal control optimization, and intersection control optimization for automated vehicles. -authored three journal papers and three project final reports. She won the Outstanding International Students Award from the University of Florida in 2013. She was awarded the International Road Federation (IRF) Executive Fellowship, and the WTS Central Florida Chapter Frankee Hellinger Graduate Scholarship in 2014. |