Generalized state equation of Petri Nets with priority

• Published in: International journal of intelligent systems Vol. 18; no. 11; pp. 1145 - 1153
• Main Authors: Lee, Gi Bum, Zandong, Han, Lee, Jin S.
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.11.2003; Wiley
• Subjects: Algebra; Algorithmics. Computability. Computer arithmetics; Applied sciences; Computer science; control theory; systems; Exact sciences and technology; Linear and multilinear algebra, matrix theory; Mathematics; Sciences and techniques of general use; Theoretical computing; Transition; Equations of state; Weight function; Priority; Linear algebra; Petri net
• ISSN: 0884-8173; 1098-111X
• DOI: 10.1002/int.10135

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. © 2003 Wiley Periodicals, Inc.