A (Max, +)-linear model for the analysis of urban traffic networks

In this paper, we introduce a new model of urban traffic networks by using timed event graphs (TEG). Based on dioid algebra, the behavior of the system is described by (Max, +)-linear equations. This will allow to approach the traffic control problems which rise issues of cycle times and of synchronization. As a result, we show how we can solve a non-null initial marking problem inherent in dioid modeling. Besides, the proposed model provides us with interesting performance evaluations, such as realtime counts of vehicles and bounds of sojourn time in each part of the studied street. An example is worked out to validate the model