Steady-state analysis of infinite stochastic Petri nets: comparing the spectral expansion and the matrix-geometric method

Abstract

In this paper we investigate the efficiency of two solution approaches to infinite stochastic Petri nets: the matrix-geometric method and the spectral expansion method. We first informally present infinite stochastic Petri nets, after which we describe, using uniform notation, the matrix-geometric and the spectral expansion method. We put special emphasis on the numerical aspect of the solution procedures. Then, we investigate the suitability of these approaches to account for batch-movements of tokens. We then compare the two solution approaches when applied to a larger modelling study of a fault-tolerant computer system. It turns out that the spectral expansion method is favorable in all cases, especially when more heavily loaded systems are studied and when batch arrivals are incorporated in the model. To the best of our knowledge, this paper is the first to compare the spectral expansion method, as advocated by Mitrani and Chakka, with the Latouche-Ramaswami algorithm for the matrix-geometric case. Furthermore, our comparisons go well beyond the usual textbook cases, since we are able to generate, with our tool SPN2MGM, models that are much larger than those that have been assessed in the past.