Optimal Trajectory Planning and Train Scheduling for Urban Rail Transit Systems (eBook)

Yihui Wang received the B.Sc in control engineering from the School of Electronic and Information Engineering, Beijing Jiaotong University in 2007. She became a Ph.D. student at Delft Center for Systems and Control, Delft University of Technology in September 2010 and obtained the Ph.D. degree in November, 2014. She is currently an assistant professor at the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University. Her main research interests include train scheduling, energy-efficient train control, hybrid systems, and model predictive control. Bart De Schutter received the M.Sc. degree in electrotechnical and mechanical engineering and the Ph.D. degree in applied sciences (summa cum laude with congratulations of the examination jury) from the K.U.Leuven, Leuven, Belgium, in 1991 and 1996, respectively. He is currently a Full Professor with the Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands. His current research interests include the control of intelligent transportation systems, hybrid system control, and multiagent systems. Prof. De Schutter is an Associate Editor for Automatica and for the IEEE Transactions on Intelligent Transportation Systems. Bin Ning received the B.S. degrees from Northern Jiaotong University (now Beijing Jiaotong University), Beijing, China, in 1982, where he received both the M.S. and Ph.D. degrees afterwards. He is currently a full professor with the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, as well as the President of Beijing Jiaotong University. His research interests include intelligent transportation systems, communication-based train control, rail transport systems, system fault-tolerant design, fault diagnosis, system reliability, and safety studies. Prof. Ning is a Fellow of the Institution of Railway Signal Engineers and IET, a Senior Member of the China Railway Society, and a member of the Western Returned Scholars Association. He is the Chair of the Technical Committee on Railroad Systems and Applications of the IEEE Intelligent Transportation Systems Society. Ton van den Boom received the MSc and PhD degrees in Electrical Engineering from Eindhoven University of Technology, Eindhoven, The Netherlands, in 1988 and 1993, respectively. Currently he is an Associate Professor at Delft University of Technology, The Netherlands. His research interests are in the areas of linear and nonlinear model predictive control, control and identification of discrete event systems and hybrid systems with applications in railway, robotics, and printers.

Series Editors’ Foreword 6
Aerospace Control Systems 6
Marine Control Systems 7
Traffic and Automobile Control Systems 7
Bus Urban Transit Systems 8
Rail and Rail-Based Urban Transit Systems 8
Preface 9
Contents 13
Notation 17
Symbols 17
Abbreviations 21
1 Introduction 22
1.1 A Brief Introduction on Railway Operations 22
1.2 Book Outline 25
References 26
2 Background: Train Operations and Scheduling 27
2.1 Operation of Trains 27
2.1.1 Automatic Train Operation 27
2.1.2 Principles of Signaling Systems 29
2.2 Optimal Trajectory Planning of Trains 31
2.2.1 Optimal Trajectory Planning of a Single Train 32
2.2.2 Optimal Trajectory Planning of Multiple Trains 33
2.3 Urban Rail Transit Scheduling Process 34
2.3.1 Passenger Demand 35
2.3.2 Train Scheduling 35
2.4 Summary 38
References 38
3 Optimal Trajectory Planning for a Single Train 42
3.1 Introduction 42
3.2 Model Formulation 43
3.2.1 Train Model 43
3.2.2 An Assumption About the Line Resistance 45
3.3 Mathematical Formulation of the Single Train Trajectory Planning Problem 46
3.4 Solution Approaches 49
3.4.1 Pseudospectral Method 49
3.4.2 Mixed Integer Linear Programming 52
3.5 Case Study 60
3.5.1 Set-Up 60
3.5.2 Results and Discussion 63
3.6 Summary 67
References 69
4 Optimal Trajectory Planning for Multiple Trains 71
4.1 Introduction 71
4.2 Model Formulation 72
4.2.1 Train Dynamics 72
4.2.2 Operation of Trains in a Fixed Block Signaling System 73
4.2.3 Operation of Trains in a Moving Block Signaling System 75
4.3 Mathematical Formulation of the Multiple Trains Trajectory Planning Problem 77
4.4 Solution Approaches 78
4.4.1 Greedy Approach 78
4.4.2 Simultaneous Approach 79
4.5 Mixed Logical Dynamic Formulation for Signaling System Constraints 80
4.5.1 Multiple Trains Under Fixed Block Signaling System 80
4.5.2 Multiple Trains Under Moving Block Signaling System 83
4.5.3 Extension: Mode Vector Constraints 85
4.6 Case Study 86
4.6.1 Set-Up 86
4.6.2 Results for the Fixed Block Signaling System 89
4.6.3 Results for the Moving Block Signaling System 93
4.6.4 Discussion 96
4.7 Summary 96
References 97
5 OD-Independent Train Scheduling for an Urban Rail Transit Line 99
5.1 Introduction 99
5.2 Model Formulation 100
5.2.1 Arrivals and Departures 101
5.2.2 Passenger Demand Characteristics 103
5.2.3 Passenger and Vehicle Interaction 104
5.3 Mathematical Formulation of the Train Scheduling Problem 105
5.4 Solution Approaches 107
5.4.1 Gradient-Free Nonlinear Programming 107
5.4.2 Gradient-Based Nonlinear Programming 108
5.4.3 Mixed Integer Nonlinear Programming 108
5.4.4 Mixed Integer Linear Programming 109
5.4.5 A New Approach: Iterative Convex Programming 110
5.5 Extension: Stop-Skipping at Small Stations 111
5.6 Case Study 113
5.6.1 Setup 113
5.6.2 Results and Discussion 117
5.7 Summary 124
References 124
6 OD-Dependent Train Scheduling for an Urban Rail Transit Line 127
6.1 Introduction 127
6.2 Model Formulation 128
6.2.1 Arrivals and Departures with Stop-Skipping 130
6.2.2 OD-Dependent Passenger Demand Characteristics 132
6.3 Mathematical Formulation of the Scheduling Problem 135
6.4 Solution Approaches 137
6.4.1 Bi-Level Optimization Approach 137
6.4.2 Limited Bi-Level Optimization Approach 138
6.5 Case Study 140
6.5.1 Setup 140
6.5.2 Results and Discussion 142
6.6 Summary 151
References 152
7 OD-Dependent Train Scheduling for an Urban Rail Transit Network 153
7.1 Introduction 153
7.2 Model Formulation 154
7.2.1 Three Types of Events 155
7.2.2 Event-Driven Dynamics 160
7.3 Mathematical Formulation for the Scheduling Problem 165
7.3.1 Performance Criteria 165
7.3.2 Constraints 166
7.4 Rolling Horizon Approach and Initial Conditions 167
7.5 Solution Approaches 168
7.6 Case Study 169
7.6.1 Setup 169
7.6.2 Results and Discussion 173
7.7 Summary 177
References 177
8 Overview and Future Directions 179
Appendix AA General Formulation of the PseudospectralMethod 181
Appendix BBackground—Optimization 185
Index 197