Abstract
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.
Highlights
A flexible manufacturing system (FMS) is a computercontrolled production equipment that consists of a set of workstations and can process different types of parts according to specified sequences of operations
Let n = jPj + jT j denote the size of an FC-sequential processes with resources (S3 PR) (Nb, M0), where P is the set of places and T = P \ P in Nb
This article gives a liveness characteristic analysis including dealing with liveness deciding and initial marking configuration for a class of Petri nets (PNs)
Summary
A flexible manufacturing system (FMS) is a computercontrolled production equipment that consists of a set of workstations and can process different types of parts according to specified sequences of operations. Let n = jPj + jT j denote the size of an FC-S3 PR (Nb , M0), where P is the set of places and T = P \ P in Nb. In the execution process of Algorithm 1, there are two basic operation processes need to be considered: (a) Find new strongly connected RSs by Tarjan’ DFS after deleting l-transitions in each strongly connected RS. By the same analysis for the computation procedures as those of Algorithm 1, it is clear that the main computation cost of Algorithm 2 depends on finding new strongly connected RS by Tarjan’s DFS after deleting the configured resource place in each PRS. The computational complexity of the proposed initial marking configuration method by Algorithm 2 is O(n2)
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