Analysis of Effective Service Time under MMPP Service Interruptions with State Dependent Interruption Periods

A stochastic model is considered where a service time having a generaldistribution is delayed by service interruptions generated by an MMPP(MarkovModulated Poisson Process). More specifically, such interruptions occur accordingto a Poisson process with intensity λi whenever the underlying Markov chain isin state i. The distribution of the interruption period depends on the state of theMarkov chain at the time of the interruption. The matrix Laplace transform of theeffective service time is derived explicitly, where the matrix is formed for the initialstate i of the Markov chain and the state j of the Markov chain upon completionof the service time. The mean and variance are obtained explicitly