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In an attempt to examine the effect of dependencies in the arrival process on the steady state queue length process in single server queueing models with exponential service time distribution, four different models for the arrival process, each with marginally distributed exponential inter-arrivals to the queueing system, are considered. Two of these models… (More)

The derivation of mean first passage times in Markov chains involves the solution of a family of linear equations. By exploring the solution of a related set of equations, using suitable generalized inverses of the Markovian kernel I – P, where P is the transition matrix of a finite irreducible Markov chain, we are able to derive elegant new results for… (More)

The distribution of the " mixing time " or the " time to stationarity " in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reach a state sampled from the stationary distribution of the Markov chain. Expressions for the probability generating function, and hence the probability distribution of the… (More)

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