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Parametric Inference for Generalized Semi-Markov Processes

Part of the inputs to the simulation of a real-world discrete-event stochastic system will be obtained via a statistical analysis of the system. Also, a number of discrete-event stochastic systems can be modeled as a generalized semi-Markov process. The basic building blocks of a generalized semi-Markov process are the probability distributions of the event lifetimes and the routing probabilities. We assume the form of these distributions and routing probabilities is known but depends on an unknown vector parameter, which must be estimated from the data. In this parametric inference setting we show that, under certain conditions, the maximum likelihood estimator exists, is consistent, and obeys a central limit theorem. A related estimator, easier to compute, is shown to also be consistent. Use of this other estimator results in no loss in statistical efficiency.