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A stochastic model for the integrated optimization on metro timetable and speed profile with uncertain train mass

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  • Yang, Xin
  • Chen, Anthony
  • Ning, Bin
  • Tang, Tao

Abstract

The integrated timetable and speed profile optimization model has recently attracted more attention because of its good achievements on energy conservation in metro systems. However, most previous studies often ignore the spatial and temporal uncertainties of train mass, and the variabilities of tractive force, braking force and basic running resistance on energy consumption in order to simplify the model formulation and solution algorithm. In this paper, we develop an integrated metro timetable and speed profile optimization model to minimize the total tractive energy consumption, where these real-world operating conditions are explicitly considered in the model formulation and solution algorithm. Firstly, we formulate a two-phase stochastic programming model to determine the timetable and speed profile. Given the speed profile, the first phase determines the timetable by scheduling the arrival and departure times for each station, and the second phase determines the speed profile for each inter-station with the scheduled arrival and departure times. Secondly, we design a simulation-based genetic algorithm procedure incorporated with the optimal train control algorithm to find the optimal solution. Finally, we present a simple example and a real-world example based on the operation data from the Beijing Metro Yizhuang Line in Beijing, China. The results of the real-world example show that, during peak hours, off-peak hours and night hours, the total tractive energy consumptions can be reduced by: (1) 10.66%, 9.94% and 9.13% in comparison with the current timetable and speed profile; and (2) 3.35%, 3.12% and 3.04% in comparison with the deterministic model.

Suggested Citation

  • Yang, Xin & Chen, Anthony & Ning, Bin & Tang, Tao, 2016. "A stochastic model for the integrated optimization on metro timetable and speed profile with uncertain train mass," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 424-445.
    • Handle: RePEc:eee:transb:v:91:y:2016:i:c:p:424-445
    DOI: 10.1016/j.trb.2016.06.006
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    1. Zhou, Xuesong & Zhong, Ming, 2007. "Single-track train timetabling with guaranteed optimality: Branch-and-bound algorithms with enhanced lower bounds," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 320-341, March.
    2. Meng, Lingyun & Zhou, Xuesong, 2014. "Simultaneous train rerouting and rescheduling on an N-track network: A model reformulation with network-based cumulative flow variables," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 208-234.
    3. Ghoseiri, Keivan & Szidarovszky, Ferenc & Asgharpour, Mohammad Jawad, 2004. "A multi-objective train scheduling model and solution," Transportation Research Part B: Methodological, Elsevier, vol. 38(10), pages 927-952, December.
    4. Bešinović, Nikola & Goverde, Rob M.P. & Quaglietta, Egidio & Roberti, Roberto, 2016. "An integrated micro–macro approach to robust railway timetabling," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 14-32.
    5. Chen, Anthony & Subprasom, Kitti, 2007. "Analysis of regulation and policy of private toll roads in a build-operate-transfer scheme under demand uncertainty," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(6), pages 537-558, July.
    6. Xu, Xiaoming & Li, Keping & Yang, Lixing, 2015. "Scheduling heterogeneous train traffic on double tracks with efficient dispatching rules," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 364-384.
    7. L. Dai & C. H. Chen & J. R. Birge, 2000. "Convergence Properties of Two-Stage Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 489-509, September.
    8. Kim, Myungseob (Edward) & Schonfeld, Paul, 2014. "Integration of conventional and flexible bus services with timed transfers," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 76-97.
    9. Cacchiani, Valentina & Caprara, Alberto & Toth, Paolo, 2010. "Scheduling extra freight trains on railway networks," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 215-231, February.
    10. Niu, Huimin & Zhou, Xuesong & Gao, Ruhu, 2015. "Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 117-135.
    11. Asadi Bagloee, Saeed & Ceder, Avishai (Avi), 2011. "Transit-network design methodology for actual-size road networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1787-1804.
    12. Alan J. King & R. Tyrrell Rockafellar, 1993. "Asymptotic Theory for Solutions in Statistical Estimation and Stochastic Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 148-162, February.
    13. Liu, Rongfang (Rachel) & Golovitcher, Iakov M., 2003. "Energy-efficient operation of rail vehicles," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(10), pages 917-932, December.
    14. Li, Xiang & Lo, Hong K., 2014. "An energy-efficient scheduling and speed control approach for metro rail operations," Transportation Research Part B: Methodological, Elsevier, vol. 64(C), pages 73-89.
    15. Cheng Gong & Shiwen Zhang & Feng Zhang & Jianguo Jiang & Xinheng Wang, 2014. "An Integrated Energy-Efficient Operation Methodology for Metro Systems Based on a Real Case of Shanghai Metro Line One," Energies, MDPI, vol. 7(11), pages 1-25, November.
    16. Li, Xiang & Lo, Hong K., 2014. "Energy minimization in dynamic train scheduling and control for metro rail operations," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 269-284.
    17. Yu, Chunhui & Ma, Wanjing & Lo, Hong K. & Yang, Xiaoguang, 2015. "Optimization of mid-block pedestrian crossing network with discrete demands," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 103-121.
    18. Phil Howlett, 2000. "The Optimal Control of a Train," Annals of Operations Research, Springer, vol. 98(1), pages 65-87, December.
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    11. Zhaoxiang Tan & Shaofeng Lu & Kai Bao & Shaoning Zhang & Chaoxian Wu & Jie Yang & Fei Xue, 2018. "Adaptive Partial Train Speed Trajectory Optimization," Energies, MDPI, vol. 11(12), pages 1-33, November.
    12. Yang, Xin & Chen, Anthony & Ning, Bin & Tang, Tao, 2017. "Bi-objective programming approach for solving the metro timetable optimization problem with dwell time uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 97(C), pages 22-37.
    13. Zhou, Li & Yang, Xin & Wang, Huan & Wu, Jianjun & Chen, Lei & Yin, Haodong & Qu, Yunchao, 2020. "A robust train timetable optimization approach for reducing the number of waiting passengers in metro systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    14. Jianqiang Liu & Nan Zhao, 2017. "Research on Energy-Saving Operation Strategy for Multiple Trains on the Urban Subway Line," Energies, MDPI, vol. 10(12), pages 1-19, December.
    15. Kang, Liujiang & Zhu, Xiaoning & Sun, Huijun & Puchinger, Jakob & Ruthmair, Mario & Hu, Bin, 2016. "Modeling the first train timetabling problem with minimal missed trains and synchronization time differences in subway networks," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 17-36.
    16. Chen, Zhiwei & Li, Xiaopeng & Zhou, Xuesong, 2020. "Operational design for shuttle systems with modular vehicles under oversaturated traffic: Continuous modeling method," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 76-100.
    17. Hu, Yuting & Li, Shukai & Dessouky, Maged M. & Yang, Lixing & Gao, Ziyou, 2022. "Computationally efficient train timetable generation of metro networks with uncertain transfer walking time to reduce passenger waiting time: A generalized Benders decomposition-based method," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 210-231.
    18. Franciszek Restel & Łukasz Wolniewicz & Matea Mikulčić, 2021. "Method for Designing Robust and Energy Efficient Railway Schedules," Energies, MDPI, vol. 14(24), pages 1-12, December.
    19. Canca, David & Zarzo, Alejandro, 2017. "Design of energy-Efficient timetables in two-way railway rapid transit lines," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 142-161.

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