Real-time control of metro train dynamics with minimization of train time-headway variance

TL;DR

This paper introduces a real-time control model for metro train systems that reduces variability in train headways by incorporating demand-dependent dwell times and run time control, ensuring stable and uniform train intervals.

Contribution

The paper extends a Max-plus linear traffic model with demand-based control laws, enabling elimination of train headway irregularities and guaranteeing uniformity over time.

Findings

Achieves stable train headways with a unique average growth rate.

Guarantees uniformity of train headways at all platforms.

Extends existing models with demand-dependent dwell and run time controls.

Abstract

We present here a real-time control model for the train dynamics in a linear metro line system. The model describes the train dynamics taking into account average passenger arrival rates on platforms, including control laws for train dwell and run times, based on the feedback of the train dynamics. The model extends a recently developed Max-plus linear traffic model with demand-dependent dwell times and a run time control. The extension permits the elimination of eventual irregularities on the train time-headway. The resulting train dynamics are interpreted as a dynamic programming system of a stochastic optimal control problem of a Markov chain. The train dynamics still admit a stable stationary regime with a unique average growth rate interpreted as the asymptotic average train time-headway. Moreover, beyond the transient regime of the train dynamics, our extension guarantees uniformity in time of the train time-headways at every platform.