Bi-Weekly Guest Talk: Florian Schanzenbächer: Feedback control for metro lines with a junction, based on a discrete event traffic model of the train dynamics
Wednesday, December 11, 2019, 10:30am
Location: RWTH Aachen University, Department of Computer Science - Ahornstr. 55, building E3, room 9u10
Speaker: Florian Schanzenbächer (RATP, Paris Ecole des Ponts)
In this talk, a mathematical model for the train dynamics in a mass-transit metro line system with one symmetrically operated junction will be presented. Three parts are distinguished: a central part and two branches. The tracks are spatially discretized into segments (or blocks) and the train dynamics are described by a discrete event system where the variables are the kth departure times from each segment. The train dynamics are based on two main constraints: a travel time constraint modeling run and dwell times, and a safe separation constraint modeling the signaling system in case where the traffic gets very dense. In a first step, the travel times considered are the theoretic travel times. These will be replaced in a second step by passenger travel demand-dependent dwell times and controlled run times.
The Max-plus algebra model allows to analytically derive the asymptotic average train headway/ frequency as a function of many parameters, including train travel times, the passenger travel demand, minimum safety intervals, the total number of trains on the line and the number of trains on each branch. This derivation permits to understand the physics of traffic in a metro line with a junction.