Towards railway traffic management using switching Max-plus-linear systems

In this paper we present a railway traffic model and a model predictive controller for online railway traffic management of railway networks with a periodic timetable. The main aim of the controller is to recover from delays in an optimal way by changing the departure of trains, by breaking connections, by splitting joined trains, and - in the case of multiple tracks between two stations - by redistributing the trains over the tracks. The railway system is described by a switching max-plus-linear model. We assume that measurements of current running and dwell times and estimates of future running times and dwell times are continuously available so that they can be taken into account in the optimization of the system’s control variables. The switching max-plus-linear model railway model is used to determine optimal dispatching actions, based on the prediction of the future arrival and departure times of the trains, by recasting the dispatching problem as a Mixed Integer Linear Programming (MILP) problem and solving it. Moreover, we use properties from max-plus algebra to rewrite and reduce the model such that the MILP problem can be solved in less time. We also apply the algorithm to a model of the Dutch railway network.

[1]  Riccardo Minciardi,et al.  Generating optimal schedules for an underground railway line , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[2]  B. Schutter,et al.  A permutation-based algorithm to optimally reschedule trains in a railway traffic network , 2011 .

[3]  Bernd Heidergott,et al.  Towards a (Max,+) Control Theory for Public Transportation Networks , 2001, Discret. Event Dyn. Syst..

[4]  Leo G. Kroon,et al.  A Variable Trip Time Model for Cyclic Railway Timetabling , 2003, Transp. Sci..

[5]  Bart De Schutter,et al.  Reducing the time needed to solve the global rescheduling problem for railway networks , 2013, 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013).

[6]  A. Hegyi,et al.  Model Predictive Control Approach for Recovery from Delays in Railway Systems , 2002 .

[7]  Kenneth Holmström,et al.  The TOMLAB Optimization Environment , 2004 .

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

[9]  C. Leake.  Synchronization and Linearity: An Algebra for Discrete Event Systems , 1994 .

[10]  Java Binding,et al.  GNU Linear Programming Kit , 2011 .

[11]  Johanna Törnquist Krasemann.  Design of an Effective Algorithm for Fast Response to the Rescheduling of Railway Traffic During Disturbances , 2012 .

[12]  Geert Jan Olsder,et al.  Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications , 2005 .

[13]  P. R. de Waal,et al.  Control of railway traffic on a single line , 1997, 1997 European Control Conference (ECC).

[14]  B. Schutter,et al.  On max-algebraic models for transportation networks , 1998 .

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

[16]  Bart De Schutter,et al.  Structured modeling, analysis, and control of complex railway operations , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

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

[18]  Dario Pacciarelli,et al.  Bi-objective conflict detection and resolution in railway traffic management , 2012 .

[19]  B. Schutter,et al.  On implicit versus explicit max-plus modeling for the rescheduling of trains ∗ , 2016 .

[20]  B. De Schutter,et al.  Modelling and control of discrete event systems using switching max-plus-linear systems , 2004 .

[21]  Francesco Corman,et al.  Rescheduling models for railway traffic management in large-scale networks , 2013, Public Transport.

[22]  Dario Pacciarelli,et al.  Discrete Optimization A branch and bound algorithm for scheduling trains in a railway network , 2007 .