Towards a (max,+) control theory for public transportation networks (Q5949610)

A public transportation network governed by a timetable is modeled within the framework of a (max,+) algebra. The control problem considered consists in minimizing the propagation of a delay (occurred to a train) through the network, while maintaining as many connections as possible. Solutions to this control problem are presented for both the deterministic and the stochastic case. The deterministic version relies on (max,+) techniques for analyzing the propagation of delays, which also allow a noticeable reduction of the search space. The stochastic version exploits a parameterized control policy that is turned into an optimization problem. Illustrative examples are given for both types of control.