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Optimal Trajectory Planning and Train Scheduling for Railway Systems Optimal Trajectory Planning and Train Scheduling for Railway Systems Yihui Wang . Optimal Trajectory Planning and Train Scheduling for Railway Systems Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op maandag 3 november 2014 om 12:30 uur door Yihui WANG Bachelor of Science in Automation, Beijing Jiaotong University, geboren te Huize, Yunnan, China. Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. ir. B. De Schutter Copromotor: Dr. ir. T.J.J. van den Boom Samenstelling promotiecommissie: RectorMagnificus voorzitter Prof. dr. ir. B. De Schutter Technische Universiteit Delft, promotor Dr. ir. T.J.J. van den Boom Technische Universiteit Delft, copromotor Prof. dr. B. Ning Beijing Jiaotong University Prof.dr.ing.I.A.Hansen TechnischeUniversiteitDelft Prof. dr. ir. C. Vuik Technische Universiteit Delft Prof. dr. ir. D. Pacciarelli Universit`adegli Studi Roma Tre Prof. dr. B.F. Heidergott Vrije Universiteit Amsterdam Prof. dr. R. Babuˇska Technische Universiteit Delft (reservelid) This thesis has been completed in partial fulfillment of the requirements of the Dutch In- stitute of Systems and Control (DISC) for graduate studies. The support of the Chinese Scholarship Council (CSC) is greatly acknowledged, as well as the support of the European Union 7th Framework Network of Excellence “Highly-complex and networked control sys- tems (HYCON2)” program. TRAIL Thesis Series T2014/7, The Netherlands TRAIL Research School P.O. Box 5017 2600 GA Delft, The Netherlands T: +31 (0) 15 278 6046 T: +31 (0) 15 278 4333 E: [email protected] Published and distributed by: Yihui Wang E-mail: [email protected] ISBN 978-90-5584-176-9 Keywords: trajectory planning, train scheduling, passenger demand, urban rail transit, op- timization. Copyright c 2014 by Yihui Wang All rights reserved. No part of the material protected by this copyright notice may be re- produced or utilized in any form or by any means, electronic or mechanical, including pho- tocopying, recording or by any information storage and retrieval system, without written permission of the author. Printed in the Netherlands, Haveka B.V. Acknowledgments It has been a wonderful experience to stay in Delft for four years and to finish my thesis. I feel so blessed since many people have helped me, supported me, accompanied me, and shared the happiness and the sadness together with me. Here, I wish to express my gratitude to all of these people. I would like to sincerely thank my main supervisor, Prof. Bart De Schutter, for his thoughtful guidance, great inspiration, and warm support throughout this study. His enthu- siasm for research and teaching, kindness and care to students, and wide range of knowledge encouraged me to pursue an academic career. Thank you for the nice discussions we had in these four years and your efficient and precise comments on equations and English writing. I especially appreciated the confidence that you have in me. I would also like to thank my second thesis supervisor Dr. Ton van den Boom for his in- sights on railways and control theories. His ideas, questions, and comments were important to ensure the research went in the right direction. I appreciated the nice discussions about daily life, cultural differences, technology, etc. My wholehearted gratitude goes to Prof. Bin Ning for being my Ph.D. supervisor and bringing me into the academic world. I have appreciated you for giving me the opportunity to study abroad and to pursue my Ph.D. degree in Delft. Thank you for the freedom, the trust, and the unconditional support you have given to me. I am also gratefulto Prof. Tao Tang for all the valuablediscussionswe had and for all the opportunities he provided me to participate in the projects of train control systems. Further, I greatly appreciate Prof. Robert Babuˇska, Prof. Ingo Hansen, Prof. Bernd Heidergott, Prof. Dario Pacciarelli, and Prof. Kees Vuik for being part of my defense committee. Thank you all for the nice discussions and valuable comments. During these four years, I enjoyed working with my colleagues at DCSC. A special thanks goes to my office mate Noortje for her company and for translating my summary and propositions into Dutch. I am thankful to Anil, Anna, Anqi, Arne, Bart, Dieky, Jia, Juan, Jun, Kim, Le, Mernout, Mohammad, Patricio, Pieter, Renshi, Sadegh, Shu, Shuai, Subramanya, Yashar, Yiming, Yu, Yue, Yuping, Zhao, Zhe, Zulkifli, and the colleagues from other departments and other universities for the good memories of the conferences, special events, discussions, lunches, dinners, and games. I appreciated Hans Hellendoorn for his help and kindness. Here I would also like to thank those who work in our secretariat (Kitty, Esther, Saskia, Marieke, and Heleen) for being kind and helpful. Further, I am gratefulto therailway peoplein TU Delft for nice presentations and discus- sions in our monthly meetings: Bart, Daniel, Dewei, Egidio, Fei, Francesco, Ingo, Jeroen, Lingyun, Nadjla, Nikola, Pavle, Rob, and Ton. I would also like to thank my colleagues in v vi the State Key Laboratory of Rail Traffic Control and Safety, especially to Fang Cao, Lijie Chen, Chunhai Gao, Qing Gu, Youneng Huang, Bo Liu, Jiang Liu, Chao Liu, Lianchuan Ma, Ru Niu, Shuai Su, Wumei Tang, Cheng Wang, Hongwei Wang, Jing Xun, Lei Yuan, Zhenyu Yu, Bobo Zhao, Xianqiong Zhao, and Li Zhu. I would like to thank my friends from the church and fellowship, especially to Chang, David & Fera, Didy & Fera, Fei, Gerrit, Guojie, Hanning, Henk & Zhuna, Jizhe, Joanne, Liang, Lisa, Lu, Michael & Gracelyn, Philip, Priscilla, Qianrong, Quanquan, Shasha, Weis- han, Xiucheng, Yanchun, Zhaoyuan for the wonderful times we had together. Special thanks to Yanchun for helping me drawing the picture on the thesis cover. I would also like to thank my friends Linfeng Chen, Jianbin Fang, Ping Liu, Yan Ni, Meng Ma, Shuhong Tan, Chang Wang, Jianbin Xin, Yong Zhang, and Lilan Zhou for being a nice fun community in Delft. I would like to thank to my parents and my parents-in-law for their unconditional love, support, and encouragement. Thank you for giving me strength and freedom to chase my dreams. My sister, Xiaoyan Wang, and my brother-in-law, Gang Xu, deserve my whole- hearted thanks as well. Last but not least, I would like to congratulate my husband Jian Xu on getting his Ph.D. degree a few months before me. I am very lucky to have met you. I thank you for always being there for me, even though we have been almost eight thousand kilometers away from each other for four years. Your love, full understanding, and wise encouragements helped me go through tough moments and brought me peace and joy in these years. Delft, October 2014 Yihui Wang Contents Acknowledgments v 1 Introduction 1 1.1 Abriefintroductiononrailwayoperations . ....... 1 1.2 Motivationandaimofthethesis . .. 3 1.3 Scopeandcontributionsofthethesis . ..... 4 1.4 Thesisoutline................................. 7 2 Background: Train Operations and Scheduling 9 2.1 Operationoftrains .............................. 9 2.1.1 Automatictrainoperation . 9 2.1.2 Principlesofsignalingsystems. .. 11 2.2 Optimaltrajectoryplanningoftrains . ...... 13 2.2.1 Optimaltrajectoryplanningofasingletrain . ..... 13 2.2.2 Optimaltrajectoryplanningof multipletrains . ....... 15 2.3 Urbanrailtransitschedulingprocess . ...... 15 2.3.1 Passengerdemand .......................... 16 2.3.2 Trainscheduling ........................... 17 2.4 Summary ................................... 19 3 Optimal Trajectory Planning for a Single Train 21 3.1 Introduction.................................. 21 3.2 Modelformulation .............................. 22 3.2.1 Trainmodel.............................. 22 3.2.2 Anassumptionaboutthelineresistance . ... 24 3.3 Mathematical formulation of the single train trajectoryplanningproblem. 24 3.4 Solutionapproaches.... .... .... .... ... .... .... ... 27 3.4.1 Pseudospectralmethod . 27 3.4.2 Mixedintegerlinearprogramming . 29 3.5 Casestudy................................... 36 3.5.1 Set-up................................. 36 3.5.2 Resultsanddiscussion . 39 3.6 Conclusions.................................. 44 3.A A general formulationof the pseudospectralmethod . ......... 45 3.A.1 Themultiple-phaseoptimalcontrolproblem. ..... 45 3.A.2 The solution process of the optimal control problem . ...... 46 vii viii Contents 4 Optimal Trajectory Planning for Multiple Trains 49 4.1 Introduction.................................. 49 4.2 Modelformulation .............................. 50 4.2.1 Traindynamics............................ 50 4.2.2 Operationof trains in a fixed block signaling system . ...... 50 4.2.3 Operation of trains in a moving block signaling system ....... 53 4.3 Mathematical formulation of the multiple trains trajectory planning problem 54 4.4 Solutionapproaches.... .... .... .... ... .... .... ... 55 4.4.1 Greedyapproach ........................... 55 4.4.2 Simultaneousapproach. 56 4.5 Mixed logical dynamic formulation for signaling system constraints . 56 4.5.1 Multipletrains underfixed blocksignalingsystem . ...... 57 4.5.2 Multiple trains under moving block signaling system . ....... 59 4.5.3 Extension:modevectorconstraints . .. 61 4.6 Casestudy................................... 62 4.6.1 Set-up................................. 62 4.6.2 Resultsforthefixedblocksignalingsystem . .... 64 4.6.3 Resultsforthemovingblocksignalingsystem . .... 68 4.6.4 Discussion .............................
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