Generalized state equation of Petri Nets with priority

Abstract

This article presents a new way of generating a generalized state equation that is useful for analyzing the token flow of the Petri Net (PN) with priority. The transition values in the firing vector as used in the conventional state equation are replaced with transition variables, which are generated by multiplying a series of firing condition functions taking the weighted inhibitor arc into account. The actual value of a transition variable is determined by taking priority and the present marking into account. The proposed state equation generalizes the conventional one by using the transition variable form and by containing the formulation of priority. Given the initial marking, the subsequent marking evolution can be determined successively from the generalized state equation as the simultaneous firings occur. A PN with deadlock is analyzed as an example to establish the validity of the generalized state equation.

A class of generalized Petri nets and its state equation

“…The studies on the state equation of a variety of Petri nets are essential to their applications, leading to a lot of results, [32][33][34][35][36][37][38][39][40][41][42][43][44][45] since they can provide an algebraic approach to the analysis of a Petri net. Burns and Bidanda30 use the concept of transition variables to translate a safe Petri net into sequential Boolean equations but not to formulate the state equation.…”

Embedding an Arbitrary 1-safe Petri Net into a Boolean Petri Net

“…The 'net-like' representation of these logical tools came into the existence in his doctoral thesis "Communication with Automata" at the Technical University of Darmstadt, Germany, in 1962 [1]. Since then Petri nets have been developed and used in many theoretical as well as application areas [2,3,4,5]. A Petri net may be identified as a particular kind of bipartite directed graph having three types of objects.…”