Liveness characteristic analysis of a class of Petri nets

Petri nets are an effective tool for analyzing and modeling the dynamic behavior of flexible manufacturing systems. Finite capacity systems of simple sequential processes with resources are an important subclass of Petri nets, for which this article gives a liveness characteristic analysis. First, an effective algorithm for deciding the liveness of finite capacity systems of simple sequential processes with resources is developed by analyzing the relation between the structural properties of resource subnets and the strict minimal siphons. Then, a liveness condition of finite capacity systems of simple sequential processes with resources is accordingly established. Based on the proposed liveness condition, an algorithm for configuring an initial marking for a finite capacity systems of simple sequential processes with resources is given, and therefore, a live finite capacity systems of simple sequential processes with resources net with a configured initial marking can be obtained, which avoids the siphon enumerations and the addition of any control actions. It is shown that the computational complexity of both the developed liveness deciding and the initial marking configuration algorithms is polynomial. Examples are finally provided to illustrate the mentioned results.