Computing Optimal Coverability Costs in Priced Timed Petri Nets

TL;DR

This paper investigates the problem of computing minimal costs in priced timed Petri nets, where tokens have clocks and transitions are constrained by time intervals, and demonstrates that the infimum of costs is computable.

Contribution

It introduces a method to compute the infimum of costs in priced timed Petri nets, addressing the challenge of cost optimization in unbounded, clocked Petri nets.

Findings

The infimum of costs in priced timed Petri nets is computable.

Cost-optimal runs may not always exist, but their infimum can be determined.

The approach handles unbounded nets with real-valued clocks and cost models.

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.