A Stochastic Model for Railway Network Reliability: Analysis of a Periodic Train Timetable

Şahin İ., Artan M. Ş.

8th International Symposium on Transportation Network Reliability (INSTR), Stockholm, Sweden, 16 - 18 June 2021, pp.1-10

  • Publication Type: Conference Paper / Full Text
  • City: Stockholm
  • Country: Sweden
  • Page Numbers: pp.1-10
  • Yıldız Technical University Affiliated: Yes


Urban and intercity railway networks constitute nodes, and links between them. The physical inter-connectivity within the network is further complicated with the interaction of train lines running over the network. Trains operating with respect to a timetable are expected to arrive and depart at times in their schedules. However, trains are subject to primary and secondary (knock-on) delays causing deviations from their schedules. Reliability is one of the common performance measures for evaluating the effectiveness (delays) of train arrivals and departures at scheduled nodes of a railway network.
Vromans (2005) points out that various definitions exist for reliability. In the railway context, it is defined as the positive difference between the actual and scheduled arrival times. Increasing reliability requires minimizing this difference. Other performance measures associated with reliability are the robustness, stability, and punctuality. Carey and Carville (2000) proposed a simulation model to test schedule performance and reliability for trains by predicting probability distributions of knock-on delays at stations due to exogenous (primary) delays. This model can be used to test schedule changes, various operating policies and changes in infrastructure. The model provides reliability outcomes for trains types, lines and platforms. Vromans et al. (2003) attempt to increase rail network reliability, focusing on decreasing heterogeneity in train traffic by reducing running time differences in track sections. The authors create more homogeneous timetables and test them using a simulation model for evaluation. Luethi et al. (2007) develop a network rescheduling method for increasing the capacity utilization and stability without making substantial infrastructure investments using microscopic simulation technique. The basic idea in this method is to minimize the reserve times in timetable without reducing the stability, hence increasing network capacity. A report of OECD/ITF (2009) distinguish the link and network reliability performance from the perspectives of user and network provider/operator for surface transportation networks. Various policy options are recommended to improve reliability, including physical capacity expansion and better management of capacity. Landex (2012) expands the reliability of railway operations by incorporating passenger delay models, which contributes to overall reliability. Şahin (2017) developed a stochastic model based on Markov chains to evaluate the performance of time allowances embedded in train timetables. The performance measures of the Markov models allow to quantify punctuality and adequacy of running time supplements and buffer times.
The current research is aimed to expand the utilization of the Markov model towards measuring the operational quality and on-time performance of cyclic trains subject to a periodic timetable. For example, considering aggregate train arrival and departure times at terminal stations help us analyze the reliability (including punctuality and robustness) of a periodic timetable. For this purpose we have selected a railway line portion between Haarlem and Den Haag Centraal terminal stations in the Dutch railways.