Simulating Delays for Realistic Time-Table Optimization

Abstract

We present; a method for the macroscopic simulation of the accumulated delay along a sequence of tracks ("supertrack") in a railway network. In a naive approach perturbations in tracks or stations would be simulated separately to calculate their accumulation in the presence of slack times. Instead we analyze the delay process using results from queuing theory to approximate the distribution of the net delay on such a "supertrack". This allows to simulate on a reduced network. Simulating the performance of time-tables becomes faster and can be included in optimization schemes. We compared scheduled and "real" transfer waiting times including delays during the optimization of time-tables. As was to be expected, there is a strong correlation between scheduled and "real" waiting time for time-tables with high waiting times. For time-tables with better scheduled waiting times that appear during the iterative optimization however, the variance of the "real" waiting time increases and time-tables with good scheduled waiting times behave increasingly poor with respect to "real" waiting time.