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

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, place - urban, operations - capacity, operations - performance, economics - operating costs


Transportation systems, modeling, performance evaluation, petri nets, dioid algebra, conflicts, resource sharing, control


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 and dioid algebra. We mainly focused on conflicts resolution using some routing functions in order to evaluate buses timetables and also arrival, boarding, disembarking and waiting times of each passenger. As a second contribution of this paper, we study through the developed models the influence of the buses limited capacity 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 passengers waiting time and transportation company costs by using buses with suitable capacities especially in peak periods.


Permission to publish the abstract has been given by Taylor&Francis, copyright remains with them.