Modeling and Optimization of Traffic Flow in Urban Areas - Czech ...

3.2 Continuous Petri Net 21take the value of 0+ and Inhibitor arcs there can be. Both of these conceptsare described by [Davi 04].3.2.1 Conflict ResolutionIn a continuous Petri net, there is an actual conflict among k transitions ina set {T 1 , T 2 , . . . , T k }, if the speed of at least one of them has to be less thanthe maximal speed due to the speeds of the other transitions in this set.When there is an actual conflict between two or more transitions, thenthe priority rule can be used. Another alternative is to use a conflict resolutionmethod based on the maximal speed proportion. The maximal speedproportion means that the flow which runs through the place is divided intothe subsequent transitions in proportion to their maximal speeds, if it is feasiblein regard to other constraints. The method is based on a flow sharingrule, observing the maximum firing speed described by [Hanz 03] and can beused only in simple Petri nets. A simple Petri net is a net in which eachtransition can only be concerned with one conflict at most.In order to illustrate the conflict resolution method we have shown anexample in Fig. 3.1. There are three places P 1 , P 2 and P 3 with zero marking.These places are supplied by the transitions T 1 , T 2 and T 3 with a speedv 1 = 35, v 2 = 40 and v 3 = 18, respectively. Place P 2 is supplied with asmaller speed than the sum of the maximal speed of the transitions P2◦ i.e.v 2 < V 4 + V 5 . Therefore, there is an actual conflict between transitions T 4and T 5 .A geometrical interpretation of the conflict resolution is given in Fig. 3.2.Fig. 3.1: Continuous Petri net example with actual conflict