Blocking a transition in a Free Choice net and what it tells about its throughput

TL;DR

This paper investigates how blocking specific transitions in live, bounded Free Choice Petri nets affects their throughput, demonstrating the existence and computability of transition throughputs in stochastic routed versions.

Contribution

It extends known properties of Free Choice nets to stochastic routed cases, proving throughput existence and explicit computation up to a constant.

Findings

Existence of asymptotic firing throughputs for all transitions.

Explicit computation of throughput ratios up to a multiplicative constant.

Validation of throughput stability in stochastic routed Free Choice nets.

Abstract

In a live and bounded Free Choice Petri net, pick a non-conflicting transition. Then there exists a unique reachable marking in which no transition is enabled except the selected one. For a routed live and bounded Free Choice net, this property is true for any transition of the net. Consider now a live and bounded stochastic routed Free Choice net, and assume that the routings and the firing times are independent and identically distributed. Using the above results, we prove the existence of asymptotic firing throughputs for all transitions in the net. Furthermore the vector of the throughputs at the different transitions is explicitly computable up to a multiplicative constant.