Performance Analysis of a Bus Network Based on Petri Nets and (Max,+) Algebra

Abstract

This article discusses the modelling and the evaluation of a public transportation network. The main objective of this study is the management of the network connections. For the modelling of this kind of discrete event systems we use, on one hand, the graphical tool called Timed Event Graph that constitutes an important subclass of Petri Nets. On the other hand, we introduce the (max,+) algebra to describe and to analyse the behaviour of our graphical model. By taking into account the network working, some structural conflicts appear in the graphical model. Then we solve them by determining routing equations. Because of these structural conflicts, we obtain a non stationary linear (max,+) mathematical model, to describe the system behaviour. Solving the state representation enables us to evaluate the system performances. An example is worked out to illustrate the results.