Approximate closed-form aggregation of a fork-join structure in generalised stochastic petri nets

Nimrod Lilith, Jonathan Billington, Jörn Freiheit

Abstract: In this paper an aggregation technique for generalised stochastic Petri nets (GSPNs) possessing synchronised parallel structures is presented. Parallel processes featuring synchronisation constraints commonly occur in fields such as product assembly and computer process communications, however their existence in closed networks severely complicates analysis. This paper details the derivation of computationally-simple closed-form expressions which permit the aggregation of a GSPN subnet featuring a fork-join structure. The aggregation expressions presented in this paper do not require the generation of the underlying continuous time Markov chain of the original net, and do not follow an iterative procedure. The resulting aggregated GSPN accurately approximates the stationary token distribution behaviour of the original net, and this is shown by the analysis of a number of example GSPNs.