Forecast of Train Delay Propagation Based on Max-Plus Algebra Theory

Abstract

The forecast of delay time is of great assistance to decision making in train operation adjustment when the schedule is disturbed either by infrastructure fault or natural hazard. This paper presents a railway delay propagation model to forecast the delay time, described by discrete event dynamic system (DEDS) and formulated by max-plus algebra theory. On the basis of the train operation regulations and headway constraints, a system matrix of max-plus algebra is acquired to illustrate the mechanism of delay propagation. And then a function to predict the delay time is proposed to solve the model, with two advantages: Firstly, the specific delay time is able to be calculated; secondly, the result of the prediction is comparatively precise due to the highly match of the model to the actual operation. Finally, by analysis of the prediction, this paper offers the decision support in train adjustment, from which the dispatcher can proactively conduct countermeasures to alleviate the propagation and even stop it.