A discrete-event model of the train traffic on a linear metro line

Abstract

We present in this article a mathematical model for the traffic on a linear metro line (a metro line without junction), taking into account the train dynamics and the passenger travel demand. The train dynamics are modeled as a discrete event dynamic system, written linearly in the Max-plus algebra. The model permits an analytic derivation of phase diagrams for the train dynamics depending on the passenger travel demand. By this, the physics of traffic on linear metro lines is wholly understood and interpreted. We introduce into the model the passenger capacity of trains, and derive analytically an indicator for the passenger comfort inside the trains, as a function of the number of trains and of the level of the passenger demand. By this model, metro operators can adjust the train dwell times at platforms depending on the level of the passenger demand. They can also optimize the train frequency with respect to the number of trains, and depending on the level of the passenger demand. Furthermore, the level of the passenger comfort inside the trains can be taken as the result of a compromise between the passengers’ satisfaction, in one side, and the number of trains as well as the passenger capacity of trains, in terms of the economic criteria of the operator, in the other side.