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 theWestern 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.

• Introduction.- Background: Train Operation and Scheduling.- Optimal Trajectory Planning for a Single Train.- Optimal Trajectory Planning for Multiple Trains.- OD-Independent Train Scheduling for an Urban Rail Transit Line.- OD-Dependent Train Scheduling for an Urban Rail Transit Line.- OD-Dependent Train Scheduling for an Urban Rail Transit Network.- Overview and Future Directions.- Appendix: A General Formulation of the Pseudospectral Method.

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 theWestern 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.

• Introduction.- Background: Train Operation and Scheduling.- Optimal Trajectory Planning for a Single Train.- Optimal Trajectory Planning for Multiple Trains.- OD-Independent Train Scheduling for an Urban Rail Transit Line.- OD-Dependent Train Scheduling for an Urban Rail Transit Line.- OD-Dependent Train Scheduling for an Urban Rail Transit Network.- Overview and Future Directions.- Appendix: A General Formulation of the Pseudospectral Method.

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 theWestern 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.

• Introduction.- Background: Train Operation and Scheduling.- Optimal Trajectory Planning for a Single Train.- Optimal Trajectory Planning for Multiple Trains.- OD-Independent Train Scheduling for an Urban Rail Transit Line.- OD-Dependent Train Scheduling for an Urban Rail Transit Line.- OD-Dependent Train Scheduling for an Urban Rail Transit Network.- Overview and Future Directions.- Appendix: A General Formulation of the Pseudospectral Method.