Novel formulae for GSPN aggregation

Abstract

Stationary analysis of generalized stochastic Petri nets (GSPNs) often suffers from the state space explosion problem. Large reachability sets somorphic to continuous-time Markov chains - are not only expensive to generate, but related high-dimensional data structures also put excessive demands on numerical algorithms. In particular, sequences of transitions and alternative branches contribute multiplicatively to the size of the state space - if enabled concurrently. The paper examines under which circumstances such structures can be merged into a single timed transition while preserving the stationary token distributions in the embedding environment. For these aggregation steps on net level, novel formulae for the (locally) marking-dependent rates of the merged transition are developed, which solely rely on parameters of the aggregated subnet. These formulae bear a strong relation to flow equivalence. Examples throughout the paper demonstrate the gains both in drastically reduced state spaces and shortened processing times of the numerical analysis.