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) without structural restrictions on the enabling of deterministic transitions. The method rests on observation, at equidistant time points, of the continuous-time Markov process that records tangible markings of the DSPN and remaining firing times associated with deterministic transitions. This approach results in the analysis of a general state space Markov chain whose system of stationary equations can be transformed into a system of Volterra equations. The techniques of this paper are also applicable to queueing networks, stochastic process algebras, and other discrete-event stochastic systems with an underlying stochastic process which can be represented as a generalized semi-Markov process with exponential and deterministic events.