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Algebraic structure of some stochastic discrete event systems, with applications. (English) Zbl 0738.93068

Summary: Generalized semi-Markov processes (GSMPs) and stochastic Petri nets (SPNs) are generally regarded as performance models (as opposed to logical models) of discrete event systems. Here we take the view that GSMPs and SPNs are essentially automata (generators) driven by input sequences that determine the timing of events. This view combines the deterministic, logical aspects and the stochastic, timed aspects of the two models. We focus on two conditions, (M) and (CX) (which we previously developed to study montonicity and convexity properties of GSMPs), and the antimatroid and lattice structure they imply for the langauge generated by a GSMP of SPN. We illustrate applications of these structural properties in the areas of derivative estimation, simulation variance reduction, parallel simulation, and optimal control.

MSC:

93E03 Stochastic systems in control theory (general)
93B25 Algebraic methods
60J99 Markov processes
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