Controlling a dioid model of traffic light: a scheduling problem

In this paper, we introduce a new model of urban traffic networks by using Petri Nets. Based on dioid algebra, the behavior of the system is described by M^ax_in γ, δ-linear equations. This will allow to approach the traffic control problems which rise issues of synchronization of traffic lights. As a result, we show how we can model shared resource problems inherent in Discrete Event Dynamic System modeling. Besides, the proposed model provides us with interesting performance evaluations, such as real-time counts of vehicles and bounds of sojourn time in each part of the studied crossroad. Moreover, we propose a control law based on a optimal and polynomial algorithm for the traffic lights to minimize the maximum waiting time of cars. An example is worked out to deal with the control of the crossroad.