Petri Nets with Time and Cost

TL;DR

This paper studies timed Petri nets with cost models, demonstrating that while optimal runs may not exist, the minimal achievable cost can be effectively computed, aiding in resource optimization.

Contribution

It introduces a cost framework for timed Petri nets and proves the computability of the infimum of costs for reaching control states.

Findings

The infimum of costs in timed Petri nets is computable.

Optimal runs may not always exist, but minimal cost bounds are obtainable.

The model integrates timing constraints with cost analysis for Petri nets.

Abstract

We consider timed Petri nets, i.e., unbounded Petri nets where each token carries a real-valued clock. Transition arcs are labeled with time intervals, which specify constraints on the ages of tokens. Our cost model assigns token storage costs per time unit to places, and firing costs to transitions. We study the cost to reach a given control-state. In general, a cost-optimal run may not exist. However,we show that the infimum of the costs is computable.