NUMERICAL-ANALYSIS OF DETERMINISTIC AND STOCHASTIC PETRI NETS WITH CONCURRENT DETERMINISTIC TRANSITIONS

This paper introduces an efficient numerical algorithm for the steady- state analysis of deterministic and stochastic Petri nets (DSPNs) with out structural restrictions on the enabling of deterministic transitio ns. The method rests on observation, at equidistant time points, of th e continuous-time Markov process that records tangible markings of the DSPN and remaining firing times associated with deterministic transit ions. This approach results in the analysis of a general state space M arkov chain whose system of stationary equations can be transformed in to a system of Volterra equations. The techniques of this paper are al so applicable to queueing networks, stochastic process algebras, and o ther discrete-event stochastic systems with an underlying stochastic p rocess which can be represented as a generalized semi-Markov process w ith exponential and deterministic events.