Analysing stability and investments in railway networks using advanced evolutionary algorithms

Abstract

We consider a network of periodically running railway lines. Investments are possible to increase the speed and to improve the synchronisation of trains. The model also includes random delays of trains and the propagation of delays across the network. We derive a cost‐benefit analysis of investments, where the benefit is measured in reduced waiting time for passengers changing lines. We also estimate the actual mean waiting time simulating the train delays. This allows us to analyse the impact that an increasing synchronisation of the timetable has on its stability. Simulation is based on an analytical model obtained from queueing theory. We use sophisticated adaptive evolutionary algorithms, which send off avant‐garde solutions from time to time to speed up the optimisation process. As there is a high correlation between scheduled and estimated waiting times for badly synchronised timetables, we are even able to include the time consuming simulation into our optimisation runs.

The Modeling Power of the Periodic Event Scheduling Problem: Railway Timetables — and Beyond

“…In fact, this condition is quite similar to the symmetry constraints (6). What makes things more complicated is the fact that we must not predict in advance for which pairs (i, j) requirement (17) has to hold, and for which pairs it may be violated.…”

“…Periodic timetabling has also served as a starting point for such attempts. Kolonko and EngelhardtFunke [6] consider investments into infrastructure by using multi-criteria optimization. Nachtigall [20] computes timetables that require only few rolling stock for a specific vehicle schedule.…”

Stability evaluation of a railway timetable at station level

“…Obviously, other delay propagation indicators could be generated with this model. Future research will focus on developing a model for optimizing stability instead of just evaluating it, or on integrating stability evaluation into a multiobjective heuristic scheme as is done in Engelhardt- Funke and Kolonko (2004). In addition to improving the timetable stability, this integration would also allow the trade-off frontier between stability and the number of trains to be studied.…”

Train Timetable Stability Evaluation based on Analysis of Interior and Exterior Factors Information Entropy

“…Engelhardt-Funke and Kolonko considered a network of periodically running railway lines. They built a model to analyze stability and investments in railway networks and designed an advanced evolutionary algorithm to solve the problem [16]. Goverde analyzed the dependence of the timetable on the busy degree of the railway network.…”