Blocking a transition in a free choice net and what it tells about its throughput

摘要

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.