Simulating generalized semi-Markov processes

Abstract : One approach to modeling queueing networks and other complex stochastic systems which has received some attention in the literature is the generalized semi-Markov process (GSMP). This idea is an example of the supplementary variables approach to non-Markovian systems. This approach supplements the natural description of the system by variables which contain information about the past history of the system. In this way, a model of a non-Markovian system can be made Markovian. For GSMPs the supplementary variables are clocks which record the amount of time until the occurrence of various events which could influenece the system. Our approach to this problem is to find closely related regenerative processes on which to base the central limit theorem for the process under study. New results in the theory of Markov chains on a general state space make it clear how these regenerative processes can be constructed.