Road Traffic Models using Petri Nets and Minplus Algebra

We present in this paper a road traffic model based on Petri nets and minplus algebra in order to study the fundamental traffic diagram of regular city (american like city). The obtained dynamic is simulated using an extension of the maxplus toolbox of Scilab able to simulate general Petri nets with negative multipliers. The Petri net model corresponding to an intersection with traffic lights is described first. Then the construction of the regular city dynamics is done. An algebra point of view is used. Systems are seen as operators corresponding to Petri nets with named inputs and outputs which can be represented by a set of matrices in standard and maxplus algebra. On such systems standard operations parallel series composition feedback and contraction (a feedback generalization) are defined. Then a regular city dynamic is obtained by combining three elementary systems with these combinators. The fundamental diagrams of some regular cities are shown to illustrate the possibilities of the toolbox.