Novel formulae for GSPN aggregation

J. Freiheit, A. Heindl
Proceedings. 10th IEEE International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunications Systems  
Stationary analysis of Generalized Stochastic Petri Nets (GSPNs) often suffers from the state space explosion problem. Large reachability sets -isomorphic 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, which -if enabled concurrentlycontribute multiplicatively to the size of the state space. This paper examines
more » ... s 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. Examples throughout the paper demonstrate the gains both in drastically reduced state spaces and shortened processing times of the numerical analysis.
doi:10.1109/mascot.2002.1167079 dblp:conf/mascots/FreiheitH02 fatcat:knxq5dmy75a43bp57drurxddme