Phase-type representations for matrix-geometric solutions

Abstract

In this note, we re-examine the structured Markov chain {Xk Nk ; k = 0, 1,…} studied by Neuts (1978). We show that the marginal steady state distribution of Xk is discrete phase-type. The implication of the result is that the queue length distribution is phase-type for the large set of queues with such an embedded Markov chain.

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