Journal of Scheduling

, Volume 22, Issue 1, pp 85–105 | Cite as

An efficient train scheduling algorithm on a single-track railway system

  • Xiaoming Xu
  • Keping Li
  • Lixing YangEmail author
  • Ziyou Gao


Since scheduling trains on a single-track railway line is an NP-hard problem, this paper proposes an efficient heuristic algorithm based on a train movement simulation method to search for the near-optimal train timetables within the acceptable computational time. Specifically, the time–space statuses of trains in the railway system are firstly divided into three categories, including dwelling at a station, waiting at a station and traveling on a segment. A check algorithm is particularly proposed to guarantee the feasibility of transition among different statuses in which each status transition is defined as a discrete event. Several detailed operation rules are also developed to clarify the scheduling procedure in some special cases. We then design an iterative discrete event simulation-based train scheduling method, namely, train status transition approach (TSTA), in which the status transition check algorithm and operation rules are incorporated. Finally, we implement some extensive experiments by using randomly generated data set to show the effectiveness and efficiency of the proposed TSTA.


Train scheduling Single-track railway Train status transition Discrete event model 



This research was supported by the National Natural Science Foundation of China (Nos. 71701062, 71431003, 71422002), the Anhui Provincial Natural Science Foundation of China (No. 1708085QG167), and the State Key Laboratory of Rail Traffic Control and Safety (No. RCS2017K004), Beijing Jiaotong University.

Supplementary material


  1. Cacchiani, V., Caprara, A., & Toth, P. (2010). Scheduling extra freight trains on railway networks. Transportation Research Part B, 44(2), 215–231.CrossRefGoogle Scholar
  2. Cacchiani, V., Huisman, D., Kidd, M., Kroon, L., Toth, P., Veelenturf, L., et al. (2014). An overview of recovery models and algorithms for real-time railway rescheduling. Transportation Research Part B, 63, 15–37.CrossRefGoogle Scholar
  3. Cacchiani, V., & Toth, P. (2012). Nominal and robust train timetabling problems. European Journal of Operational Research, 219(3), 727–737.CrossRefGoogle Scholar
  4. Cai, X., & Goh, C. (1994). A fast heuristic for the train scheduling problem. Computers & Operations Research, 21(5), 499–510.CrossRefGoogle Scholar
  5. Cai, X., Goh, C., & Mees, A. (1998). Greedy heuristics for rapid scheduling of trains on a single track. IIE Transactions, 30(5), 481–493.CrossRefGoogle Scholar
  6. Caprara, A., Fischetti, M., & Toth, P. (2002). Modeling and solving the train timetabling problem. Operations research, 50(5), 851–861.CrossRefGoogle Scholar
  7. Carey, M. (1994a). A model and strategy for train pathing with choice of lines, platforms, and routes. Transportation Research Part B, 28(5), 333–353.CrossRefGoogle Scholar
  8. Carey, M. (1994b). Extending a train pathing model from one-way to two-way track. Transportation Research Part B, 28(5), 395–400.CrossRefGoogle Scholar
  9. Carey, M., & Lockwood, D. (1995). A model, algorithms and strategy for train pathing. Journal of the Operational Research Society, 46(8), 988–1005.CrossRefGoogle Scholar
  10. Corman, F., D’Ariano, A., & Hansen, I. (2014a). Evaluating disturbance robustness of railway schedules. Journal of Intelligent Transportation Systems, 18(1), 106–120.CrossRefGoogle Scholar
  11. Corman, F., D’Ariano, A., Hansen, I., & Pacciarelli, D. (2011). Optimal multi-class rescheduling of railway traffic. Journal of Rail Transport Planning Management, 1(1), 14–24.CrossRefGoogle Scholar
  12. Corman, F., D’Ariano, A., Marra, A. D., Pacciarelli, D., & Samà, M. (2017). Integrating train scheduling and delay management in real-time railway traffic control. Transportation Research Part E, 105, 213–239.CrossRefGoogle Scholar
  13. Corman, F., D’Ariano, A., Pacciarelli, D., & Pranzo, M. (2010a). A tabu search algorithm for rerouting trains during rail operations. Transportation Research Part B, 44(1), 175–192.CrossRefGoogle Scholar
  14. Corman, F., D’Ariano, A., Pacciarelli, D., & Pranzo, M. (2010b). Centralized versus distributed systems to reschedule trains in two dispatching areas. Public Transport, 2(3), 219–247.CrossRefGoogle Scholar
  15. Corman, F., D’Ariano, A., Pacciarelli, D., & Pranzo, M. (2012). Optimal inter-area coordination of train rescheduling decisions. Transportation Research Part E, 48(1), 71–88.CrossRefGoogle Scholar
  16. Corman, F., D’Ariano, A., Pacciarelli, D., & Pranzo, M. (2014b). Dispatching and coordination in multi-area railway traffic management. Computers & Operations Research, 44, 146–160.CrossRefGoogle Scholar
  17. Cordeau, J. F., Toth, P., & Vigo, D. (1998). A survey of optimization models for train routing and scheduling. Transportation Science, 32(4), 380–404.CrossRefGoogle Scholar
  18. Danna, E., Rothberg, E., & Pape, C. (2005). Exploring relaxation induced neighborhoods to improve MIP solutions. Mathematical Programming, 102(1), 71–90.CrossRefGoogle Scholar
  19. Dessouky, M., & Leachman, R. (1995). A simulation modeling methodology for analyzing large complex rail networks. Simulation, 65(2), 131–142.CrossRefGoogle Scholar
  20. D’Ariano, A. (2009). Innovative decision support system for railway traffic control. IEEE Intelligent Transportation Systems Magazine, 1(4), 8–16.CrossRefGoogle Scholar
  21. D’Ariano, A., Pacciarelli, D., & Pranzo, M. (2007). A branch and bound algorithm for scheduling trains in a railway network. European Journal of Operational Research, 183(2), 643–657.CrossRefGoogle Scholar
  22. Dollevoet, T., Corman, F., D’Ariano, A., & Huisman, D. (2014). An iterative optimization framework for delay management and train scheduling. Flexible Services and Manufacturing Journal, 26(4), 490–515.CrossRefGoogle Scholar
  23. Dorfman, M. J., & Medanic, J. (2004). Scheduling trains on a railway network using a discrete event model of railway traffic. Transportation Research Part B, 38(1), 81–98.CrossRefGoogle Scholar
  24. Fang, W., Yang, S., & Yao, X. (2015). A survey on problem models and solution approaches to rescheduling in railway networks. IEEE Transactions on Intelligent Transportation Systems, 16(6), 2997–3016.CrossRefGoogle Scholar
  25. Fischetti, M., & Lodi, A. (2003). Local branching. Mathematical Programming, 98(1–3), 23–47.CrossRefGoogle Scholar
  26. Garey, M., & Johnson, D. (1979). Computers and intractability: A guide to the theory of NP-completeness (pp. 90–91). San Francisco, CA: W.H. Freeman.Google Scholar
  27. Goverde, R., Corman, F., & D’Ariano, A. (2013). Railway line capacity consumption of different railway signalling systems under scheduled and disturbed conditions. Journal of Rail Transport Planning & Management, 3(3), 78–94.CrossRefGoogle Scholar
  28. Kroon, L., Huisman, D., & Maróti, G. (2014). Optimisation models for railway timetabling. In I. A. Hansen & J. Pachl (Eds.), Railway timetabling and operations: Analysis, modelling, optimisation, simulation, performance evaluation (2nd ed., pp. 155–173). Hamburg: DVV Media Group.Google Scholar
  29. Higgins, A., Kozan, E., & Ferreira, L. (1996). Optimal scheduling of trains on a single line track. Transportation Research Part B, 30(2), 147–161.CrossRefGoogle Scholar
  30. Lu, Q., Dessouky, M., & Leachman, R. (2004). Modeling train movements through complex rail networks. ACM Transactions on Modeling and Computer Simulation, 14(1), 48–75.CrossRefGoogle Scholar
  31. Li, F., Gao, Z., Li, K., & Yang, L. (2008). Efficient scheduling of railway traffic based on global information of train. Transportation Research Part B, 42(10), 1008–1030.CrossRefGoogle Scholar
  32. Li, F., Sheu, J., & Gao, Z. (2014). Deadlock analysis, prevention and train optimal travel mechanism in single-track railway system. Transportation Research Part B, 68, 385–414.CrossRefGoogle Scholar
  33. Liu, L., & Dessouky, M. (2017). A decomposition based hybrid heuristic algorithm for the joint passenger and freight train scheduling problem. Computers & Operations Research, 87, 165–182.CrossRefGoogle Scholar
  34. Lusby, R., Larsen, J., Ehrgott, M., & Ryan, D. (2011). Railway track allocation: Models and methods. OR Spectrum, 33(4), 843–883.CrossRefGoogle Scholar
  35. Mazzarello, M., & Ottaviani, E. (2007). A traffic management system for real-time traffic optimisation in railways. Transportation Research Part B, 41(2), 246–274.CrossRefGoogle Scholar
  36. Meng, L., & Zhou, X. (2014). Simultaneous train rerouting and rescheduling on an N-track network: A model reformulation with network-based cumulative flow variables. Transportation Research Part B, 67, 208–234.CrossRefGoogle Scholar
  37. Pachl, J. (2007). Avoiding deadlocks in synchronous railway simulations. In 2nd international seminar on railway operations modelling and analysis (pp. 28–30).Google Scholar
  38. Pellegrini, P., Marlière, G., & Rodriguez, J. (2014). Optimal train routing and scheduling for managing traffic perturbations in complex junctions. Transportation Research Part B, 59, 58–80.CrossRefGoogle Scholar
  39. Samà, M., Corman, F., & Pacciarelli, D. (2017). A variable neighbourhood search for fast train scheduling and routing during disturbed railway traffic situations. Computers & Operations Research, 78, 480–499.CrossRefGoogle Scholar
  40. Samà, M., Pellegrini, P., D’Ariano, A., Rodriguez, J., & Pacciarelli, D. (2016). Ant colony optimization for the real-time train routing selection problem. Transportation Research Part B, 85, 89–108.CrossRefGoogle Scholar
  41. Szpigel, B. (1973). Optimal train scheduling on a single track railway. In M. Ross (Ed.), Operational research ’72 (pp. 343–352). Amsterdam: North-Holland.Google Scholar
  42. Törnquist, J., & Persson, J. (2007). N-tracked railway traffic re-scheduling during disturbances. Transportation Research Part B, 41(3), 342–362.CrossRefGoogle Scholar
  43. Wang, Y., Li, K., Xu, X., & Zhang, Y. (2014). Transport energy consumption and saving in China. Renewable and Sustainable Energy Reviews, 29, 641–655.CrossRefGoogle Scholar
  44. Xu, X., Li, K., & Li, X. (2016). A multi-objective subway timetable optimization approach with minimum passenger time and energy consumption. Journal of Advanced Transportation, 50(1), 69–95.CrossRefGoogle Scholar
  45. Xu, X., Li, K., & Yang, L. (2015). Scheduling heterogeneous train traffic on double tracks with efficient dispatching rules. Transportation Research Part B, 78, 364–384.CrossRefGoogle Scholar
  46. Xu, X., Li, K., Yang, L., & Ye, J. (2014). Balanced train timetabling on a single-line railway with optimized velocity. Applied Mathematical Modelling, 38(3), 894–909.CrossRefGoogle Scholar
  47. Yang, L., Li, K., & Gao, Z. (2009). Train timetable problem on a single-line railway with fuzzy passenger demand. IEEE Transactions on Fuzzy Systems, 17(3), 617–629.CrossRefGoogle Scholar
  48. Yang, L., Li, K., Gao, Z., & Li, X. (2012). Optimizing trains movement on a railway network. Omega, 40(5), 619–633.CrossRefGoogle Scholar
  49. Yang, L., Zhou, X., & Gao, Z. (2013). Rescheduling trains with scenario-based fuzzy recovery time representation on two-way double-track railways. Soft Computing, 17(4), 605–616.CrossRefGoogle Scholar
  50. Yang, L., Zhou, X., & Gao, Z. (2014). Credibility-based rescheduling model in a double-track railway network: A fuzzy reliable optimization approach. Omega, 48, 75–93.CrossRefGoogle Scholar
  51. Zhou, X., & Zhong, M. (2007). Single-track train timetabling with guaranteed optimality: Branch-and-bound algorithms with enhanced lower bounds. Transportation Research Part B, 41(3), 320–341.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Xiaoming Xu
    • 1
    • 2
  • Keping Li
    • 2
  • Lixing Yang
    • 2
    Email author
  • Ziyou Gao
    • 2
  1. 1.School of Automotive and Transportation EngineeringHefei University of TechnologyHefeiChina
  2. 2.State Key Laboratory of Rail Traffic Control and SafetyBeijing Jiaotong UniversityBeijingChina

Personalised recommendations