Embedded processes in stochastic Petri nets

Abstract

Embedded discrete time processes are used to study a class of SPNs (stochastic Petri nets) which have a closed-form equilibrium distribution. These SPNs have probabilistic output bags, colored tokens, and alternating periods of arbitrarily distributing enabling and firing times (periods of time between transitions becoming enabled and absorption of tokens and between transitions absorbing tokens and depositing them in output places, respectively). In addition, an aggregation procedure is proposed which, in certain nets, not only reduces a complex SPN to a much simpler skeleton SPN but also obtains results for the skeleton SPN which are exact marginal distributions for the original SPN.