Analysis of P-time Event Graphs in (Max,+) and (Min,+) Algebras

TL;DR

This paper investigates P-time event graphs using (max,+) and (min,+) algebraic descriptions to determine extremal periodic trajectories, with applications demonstrated in electroplating process modeling.

Contribution

It introduces a combined (max,+) and (min,+) algebraic framework for analyzing P-time event graphs, providing necessary and sufficient conditions for extremal trajectories.

Findings

Derived conditions for fastest and slowest periodic trajectories.

Applied the framework to a real electroplating process example.

Established a new dual algebraic approach for P-time event graph analysis.

Abstract

In this work we investigate the behavior of P-time event graphs, a class of time Petri nets with nondeterministic timing of places. Our approach is based on combined linear descriptions in both (max,+) and (min,+) semirings, where lower bounds on the state vector are (max,+)-linear and upper bounds are (min,+)-linear. We present necessary and sufficient conditions for the existence of extremal (fastest and slowest) periodic trajectories that are derived from the new description. The results are illustrated by a realistic example of an electroplating process.