A Petri Net Model of Train Operation Simulation for Harmonizing Train Timetables of Neighbor Dispatching Sections

  • Xuelei Meng Lanzhou Jiaotong University
  • Limin Jia Beijing Jiaotong University
  • Wanli Xiang
Keywords: train operation, Petri net, simulation, neighbor dispatching section


Train timetable is the key document to regulate railway traffic through sequencing train movements to keep the appropriate order. Timetable stability and on-schedule rate are closely related. Delays caused by disturbances in train operations can be absorbed by a high quality timetable with high stability, and the on-schedule rate then can be assured. This paper improves the stability of timetables of several connected railway sections to assure the on-schedule rate with a simulation method. Firstly, we build a macroscopic network model of train operation in a railway network using the Petri net theory. Then we design the train tracking subnet model, the station subnet model and arrival-departure track subnet model. At last we propose a computing case, simulating the train operation process based on the presented models, and the simulation results prove the feasibility and availability of the models. The approach presented in this paper can offer valuable decision-support information for railway operators preparing train timetables.

Author Biographies

Xuelei Meng, Lanzhou Jiaotong University

Xuelei Meng received the PhD degree in planning and
management of traffic and transportation at State Key
Laboratory of Rail Traffic Control and Safety, Beijing
Jiaotong University in 2011. He is currently an associate
professor in Lanzhou Jiaotong University. His research interests are in the areas of train timetable design, optimization and evaluation, line planning for railway. He has published research papers in reputed international journals, such as Transportation Research Record.

Limin Jia, Beijing Jiaotong University

Limin Jia is a professor responsibility and doctoral supervisor of State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University. He received his PhD degree at China Academy of Railway Science in 1991. He is the member of the Chinese national intelligent transportation expert advisory committee, China systems engineering society, China railway society, China operations research society. He is also an editorial member of China Railway Science. His main research interests are: application of intelligent control and intelligent systems, railway intelligent
automation, railway intelligent transportation system.

Wanli Xiang

Wan-li Xiang received the Ph.D.degree fromTianjin University,Tianjin,China, in2014. He is an Associate Professor of the School of Traffic and Transportation,Lanzhou Jiaotong University. His research interests include datamining,evolutionary computation and their applications to logistics and transportation.


[1] Keijia K, Naohikob H, Shigerub M. Simulation analysis of train operation to recover knock-on delay under high-frequency intervals. Case Studies on Transport Policy. 2015;3(1): 92-98.
[2] Flynn D, Hemida H, Soper D, Baker C. Detached-eddy simulation of the slipstream of an operational freight train. Journal of Wind Engineering and Industrial Aerodynamics. 2014;132: 1-12.
[3] Mihailovs F, Sansyzbajeva Z, Mezitis M. Simulation of the interaction of railway station and harbor. Procedia Computer Science. 2017;104: 222-226.
[4] Warg J, Bohlin M. The use of railway simulation as an input to economic assessment of timetables. Journal of Rail Transport Planning and Management. 2016;6(3): 255-270.
[5] Debois S, Hildebrandt T, Sandberg L. Experience report: constraint-based modelling and simulation of railway emergency response plans. Procedia Computer Science. 2016;83: 1295-1300.
[6] Nagel K, Schreckenberg M. A cellular automaton model for freeway traffic. Journal of Physics I France. 1992;2: 2221-2229.
[7] Spyropoulou I. Modelling a signal controlled traffic stream using cellular automata. Transportation Research Part C: Emerging Technologies. 2007;15(3): 175-190.
[8] Kheldoun A, Barkaoui K, Ioualalen M. Formal verification of complex business processes based on high-level Petri nets. Information Sciences. 2017;385-386: 39-54.
[9] Wang P, Fang W, Guo B. A colored Petri nets based workload evaluation model and its validation through Multi-Attribute Task Battery-II. Applied Ergonomics. 2017;60: 260-274.
[10] Pachpor PS, Shrivastava RL, Seth D, Pokharel S. Application of Petri nets towards improved utilization of machines in job shop manufacturing environments. Journal of Manufacturing Technology Management. 2017;28(2): JMTM-05-2016-0064.
[11] Milinković S, Marković M, Vesković S, Ivić M, Pavlović N. A fuzzy Petri net model to estimate train delays. Simulation Modelling Practice and Theory. 2013;33: 144-157.
[12] Ahmad F, Khan SA. Specification and verification of safety properties along a crossing region in a railway network control. Applied Mathematical Modelling. 2013;37(7): 5162-5170.
[13] Boudi Z, Miloudi E, Koursi E, Collart-Dutilleul S. From place/transition Petri nets to B abstract machines for safety critical systems. IFAC-PapersOnLine. 2015;48(21): 332-338.
[14] Khan SA, Zafar NA, Ahmad F, Islam S. Extending Petri net to reduce control strategies of railway interlocking system. Applied Mathematical Modelling. 2014;38(2): 413-424.
[15] Ricci S. The use of Petri nets models in railway traffic applications. IFAC Proceedings Volumes. 2009;42(5): 151-156.
[16] Basile F, Cabasino MP, Seatzu C. Diagnosability Analysis of Labeled Time Petri Net Systems. IEEE Transactions on Automatic Control. 2017;62(3): 1384-1396.
[17] Kaakai F, Hayat S, Moudni AE. A hybrid Petri netsbased simulation model for evaluating the design of railway transit stations. Simulation Modelling Practice and Theory. 2007;15(8): 935-969.
[18] Quiroga LM, Wegele S, Schnieder E. Benefit of railway infrastructure diagnosis systems on its availability. IFAC Proceedings Volumes. 2009;42(5): 146-150.
[19] Marrone S, Rodríguez RJ, Nardone R, Flammini F, Vittorinic V. On synergies of cyber and physical security modelling in vulnerability assessment of railway systems. Computers and Electrical Engineering. 2015;47: 275-285.
[20] Wang P, Ma L, Goverde RMP, Wang Q. Rescheduling trains using Petri nets and heuristic search. IEEE Transactions on Intelligent Transportation Systems. 2016;17(3): 726-735.
[21] Durmuş MS, Yildirim U, Söylemez MT. Interlocking system design for ERTMS/ETCS: an approach with Batches Petri Nets. IFAC Proceedings Volumes. 2012;45(29): 110-115.
[22] Goverde RMP. Railway timetable stability analysis using max-plus system theory. Transportation Research Part B: Methodology. 2007;41(2): 179-201.
[23] Delorme X, Gandibleux X, Rodriguez, J. Stability evaluation of a railway timetable at station level. European Journal of Operational Research. 2009;195(3): 780-790.
[24] Engelhardt-Funke O, Kolonko M. Analysing stability and investments in railway networks using advanced evolutionary algorithm. International Transactions in Operational Research. 2004;11(4): 381-394.
[25] Niu H, Zhou X, Gao R. 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: Methodology. 2015;76: 117-135.
[26] Hansen IA. Station capacity and stability of train operations. Advances in Transport, Computers in Railways VII. 2000;7: 809-816.
[27] Cicerone S, D'Angelo G, Stefano GD, Frigioni D, Navarra A. Recoverable robust timetabling for single delay: complexity and polynomial algorithms for special cases. Journal of Combination Optimization. 2009;18(3): 229-257.
[28] Liebchen C, Stille S. Delay resistant timetabling. Public Transport. 2009;1(1): 55-72.
[29] D'Angelo G, Stefano GD, Navarra A, Pinotti CM. Recoverable robust timetables: An algorithmic approach on trees. IEEE Transactions Computers. 2011;60(3): 433-446.
[30] Cicerone S, Stefano GD, Schachtebeck M, Schöbel A. Multi-stage recovery robustness for optimization problems: A new concept for planning under disturbances. Information Sciences. 2012;190: 107-126.
How to Cite
Meng X, Jia L, Xiang W. A Petri Net Model of Train Operation Simulation for Harmonizing Train Timetables of Neighbor Dispatching Sections. Promet - Traffic & Transportation [Internet]. 21Dec.2018 [cited 21Jan.2019];30(6):647-60. Available from: https://traffic.fpz.hr/index.php/PROMTT/article/view/2713