Control of a Public Transport Network by the Max-Plus Algebra: case of a system constrained by maximal connection times

The theory of linear systems in the max-plus algebra is developed for the analysis of discrete event systems. The timed event graphs are one of the tools used for modelling these systems, and their behaviour can be described by (max, plus )-linear equations. This paper proposes a control structure for a public transport system. We mainly based the research of this control on the Residuation theory. This control aims at conceiving a timetable of buses such that: the connection time at interchange points respects an upper bound corresponding to a tolerance for passengers, and it limits the number of buses required to ensure the connections. Key-Words: Public transport system, Petri Nets, Max-Plus algebra, Discrete Event Systems, Control, Connection time.