In: Performance Evaluation, Vol. 36-37, No. 1-4, pages 35-54. 1999.
Abstract: This paper introduces an efficient numerical algorithms for transient analysis of deterministic and stochastic Petri nets (DSPNs) and other discrete-event stochastic systems with exponential and deterministic events. The proposed approach is based on a general state space Markov chain (GSSMC) whose state expansions constitute a system of multidimensional Fredholm integral equations. Key contributions of this paper constitute the observations that the transition kernel of this system of Fredholm equations is piecewise continuous and separable. Due to the exploitation of these properties, the GSSMC approach shows great promise for being effectively applicable for the transient analysis of large DSPNs with concurrent deterministic transitions. Moreover, for DSPNs without concurrent deterministic transitions, the proposed GSSMC approach requires three orders of magnitude less computational effort than for the previously known approach based on the method of supplementary variables.
Keywords: Markov chains, deterministic Petri nets, stochastic Petri nets, transient analysis.