Weak consistency of P-time event graphs

TL;DR

This paper introduces the concept of weak consistency in P-time event graphs, providing an algorithm to verify this property and determine the maximum number of transition firings before violating time constraints.

Contribution

It defines weak consistency for P-TEGs, formulates a polynomial-time verification algorithm, and offers a method to compute the maximum firings before constraint violation.

Findings

Weak consistency allows indefinite transition firings without violating time constraints.

An efficient polynomial-time algorithm verifies weak consistency in P-TEGs.

The approach enables calculating the maximum number of firings before violations occur.

Abstract

P-time event graphs (P-TEGs) are event graphs where the residence time of tokens in places is bounded by specified time windows. In this paper, we define a new property of PTEGs, called weak consistency. In weakly consistent P-TEGs, the amount of times a transition can fire before the first violation of a time constraint can be made as large as desired. We show the practical implications of this property and, based on previous results in graph theory, we formulate an algorithm of strongly polynomial time complexity that verifies it. From this algorithm, it is possible to determine, in pseudo-polynomial time, the maximum number of firings before the first constraint violation in a P-TEG.