Petri nets conflicts resolution for performance evaluation and control of urban bus networks: a (max, +) based approach

International audience; This paper deals with the modeling, analysis, performance evaluation and control of urban bus networks characterized by conflicts, synchronization and concurrency using two complementary formalism Petri nets (PN) and dioid algebra. We mainly focused on conflicts and resource sharing resolution using some routing functions in order to evaluate some passengers metrics within various stations of the bus network. More precisely, we evaluate arrival, boarding, disembarking and waiting times of each passenger at any network station. As a second contribution of this paper, we study through the developed models the influence of the limited capacity of the buses on passengers travel time. The objective is to find an optimal threshold from which the buses capacity has no longer impact on passengers waiting time. Finally, we propose a control approach enabling to determine a compromise between the capacity and number of buses to use on the network in order to minimize both waiting time of passengers and transportation company costs by using buses with suitable capacities especially in peak periods. An illustrative example is given to show the applicability of the proposed approach and the obtained results are promising.