Stochastic prediction of train delays in real-time using Bayesian networks

In this paper we present a stochastic model for predicting the propagation of train delays based on Bayesian networks. This method can eciently represent and compute the complex stochastic inference between random variables. Moreover, it allows updating the probability distributions and reducing the uncertainty of future train delays in real time under the assumption that more information continuously becomes available from the monitoring system. The dynamics of a train delay over time and space is presented as a stochastic process that describes the evolution of the time-dependent random variable. This approach is further extended by modelling the interdependence between trains that share the same infrastructure of have a scheduled passenger transfer. The model is applied on a set of historical trac realisation data from the part of a busy corridor in Sweden.We present the initial results and analyse the accuracy of predictions as well as the evolution of probability distributions of event delays over time. The presented method is important for making better predictions for train trac, that are not only based on static, oine collected data, but are able to positively include the dynamic characteristics of the continuously changing delays.

[1]  Erhan Kozan,et al.  Determining operations affected by delay in predictive train timetables , 2014, Comput. Oper. Res..

[2]  Anita Schöbel,et al.  Integer Programming Approaches for Solving the Delay Management Problem , 2004, ATMOS.

[3]  Stuart J. Russell,et al.  Dynamic bayesian networks: representation, inference and learning , 2002 .

[4]  Pavle Kecman,et al.  Predictive modelling of running and dwell times in railway traffic , 2015, Public Transp..

[5]  Thorsten Büker,et al.  Stochastic modelling of delay propagation in large networks , 2012, J. Rail Transp. Plan. Manag..

[6]  Johanna Törnquist Krasemann.  Configuration of an optimization-based decision support for railway traffic management in different contexts , 2015 .

[7]  I. A. Hansen,et al.  Optimizing capacity utilization of stations by estimating knock-on train delays , 2007 .

[8]  Matthias Müller-Hannemann,et al.  Timing of Train Disposition: Towards Early Passenger Rerouting in Case of Delays , 2014, ATMOS.

[9]  Marco Laumanns,et al.  A model predictive control approach for discrete-time rescheduling in complex central railway station areas , 2012, Comput. Oper. Res..

[10]  Francesco Corman,et al.  Stability analysis of railway dispatching plans in a stochastic and dynamic environment , 2013, J. Rail Transp. Plan. Manag..

[11]  Ismail Sahin,et al.  Markov chain model for delay distribution in train schedules: Assessing the effectiveness of time allowances , 2017, J. Rail Transp. Plan. Manag..

[12]  Stephen Graham Ritchie,et al.  TRANSPORTATION RESEARCH. PART C, EMERGING TECHNOLOGIES , 1993 .

[13]  Twan Dollevoet,et al.  Delay Management Including Capacities of Stations , 2012, Transp. Sci..

[14]  Francesco Corman,et al.  Closing the loop in real-time railway control: Framework design and impacts on operations , 2015 .

[15]  Dario Pacciarelli,et al.  A branch and bound algorithm for scheduling trains in a railway network , 2007, Eur. J. Oper. Res..

[16]  Nebojsa J. Bojovic,et al.  Optimal allocation of buffer times to increase train schedule robustness , 2017, Eur. J. Oper. Res..

[17]  Francesco Corman,et al.  A Review of Online Dynamic Models and Algorithms for Railway Traffic Rescheduling , 2014 .

[18]  P. Kecman,et al.  Models for Predictive Railway Traffic Management , 2014 .

[19]  Peter Widmayer,et al.  Online Delay Management on a Single Train Line , 2004, ATMOS.

[20]  Andrew Nash,et al.  Railroad simulation using OpenTrack , 2004 .

[21]  Masoud Yaghini,et al.  Railway Passenger Train Delay Prediction via Neural Network Model , 2013 .

[22]  Matús Mihalák,et al.  Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past , 2015, ATMOS.

[23]  Teshale Fille Bayissa.  How do Delays Along the Way Influence Delays to Final Destination , 2013 .

[24]  Dario Pacciarelli,et al.  Dispatching and coordination in multi-area railway traffic management , 2014, Comput. Oper. Res..

[25]  Daniel Potthoff,et al.  Column Generation with Dynamic Duty Selection for Railway Crew Rescheduling , 2008, Transp. Sci..

[26]  Leo G. Kroon,et al.  A rolling horizon approach for disruption management of railway rolling stock , 2012, Eur. J. Oper. Res..

[27]  Xuesong Zhou,et al.  Simultaneous train rerouting and rescheduling on an N-track network: A model reformulation with network-based cumulative flow variables , 2014 .

[28]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[29]  Paul Schonfeld,et al.  Analyzing passenger train arrival delays with support vector regression , 2015 .

[30]  Dario Pacciarelli,et al.  Job-shop scheduling with blocking and no-wait constraints , 2002, Eur. J. Oper. Res..

[31]  Pavle Kecman,et al.  Online Data-Driven Adaptive Prediction of Train Event Times , 2015, IEEE Transactions on Intelligent Transportation Systems.

[32]  Egidio Quaglietta,et al.  A simulation-based approach for the optimal design of signalling block layout in railway networks , 2014, Simul. Model. Pract. Theory.

[33]  Rob M.P. Goverde,et al.  A delay propagation algorithm for large-scale railway traffic networks , 2010 .

[34]  Wei-Hsun Lee,et al.  A delay root cause discovery and timetable adjustment model for enhancing the punctuality of railway services , 2016 .

[35]  Yong Qin,et al.  Modeling cascade dynamics of railway networks under inclement weather , 2015 .

[36]  Matthias Müller-Hannemann,et al.  Stochastic Delay Prediction in Large Train Networks , 2011, ATMOS.

[37]  Karsten Weihe,et al.  Reliability and Delay Distributions of Train Connections , 2012, ATMOS.

[38]  Giovanni Longo,et al.  A method for using stochastic blocking times to improve timetable planning , 2011, J. Rail Transp. Plan. Manag..

[39]  Francesco Corman,et al.  Evaluating Disturbance Robustness of Railway Schedules , 2014, J. Intell. Transp. Syst..

[40]  Daniel Zelterman,et al.  Bayesian Artificial Intelligence , 2005, Technometrics.

[41]  Johanna Törnquist Krasemann,et al.  Quantifying railway timetable robustness in critical points , 2013, J. Rail Transp. Plan. Manag..

[42]  Davide Anguita,et al.  Dynamic Delay Predictions for Large-Scale Railway Networks: Deep and Shallow Extreme Learning Machines Tuned via Thresholdout , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[43]  Ludolf E. Meester,et al.  Stochastic delay propagation in railway networks and phase-type distributions , 2007 .

[44]  Jan A. Persson,et al.  N-tracked railway traffic re-scheduling during disturbances , 2007 .

[45]  Rob M.P. Goverde,et al.  Railway Timetable Stability Analysis Using Max-plus System Theory , 2007 .

[46]  Francesco Corman,et al.  Train delay evolution as a stochastic process , 2015 .

[47]  Anita Schöbel,et al.  Rules of thumb: practical online-strategies for delay management , 2014, Public Transp..