In: Discrete Event Dynamic Systems: Theory & Applications, Vol. 1, No. 1, pages 7-35. May 1991.
Abstract: Generalized semi-Markov processes (GSMPs) and stochastic Petri nets (SPNs) are generally regarded as performance models of discrete event systems. The authors treat them as generators driven by input sequences that determine the timing of events. The focus is on two conditions, (M) and (CX) and the antimatroid and lattice structure they imply for the language generated by a GSMP or SPN. The authors present applications of these structural properties in the areas of derivative estimation, simulation variance reduction, parallel simulation, and optimal control.
Keywords: algebraic structure (of) stochastic discrete event system; generalized semi-markov process; stochastic net; antimatroid; lattice; parallel simulation; optimal control.