Analysis of deterministic and stochastic Petri nets

Abstract

A time and space efficient algorithm for computing steady state solutions of deterministic and stochastic Petri nets (DSPNs) with both stochastic and structural extensions is presented. The algorithm can deal with different execution policies associated with deterministic transitions of a DSPN. The definition of a subordinated Markov chain (SMC) is refined to reduce the computational cost of deriving the transition probabilities of the embedded Markov chain (EMC) underlying a DSPN. Closed-form expressions of these transition probabilities are presented for some SMC topologies. Moreover, the use of the reward structured defined on the DSPN to reduce memory requirements is proposed. The usefulness of the proposed extensions and the steps of the solution algorithm are illustrated using a DSPN of a simple communication protocol.<>