Probabilistic interpretations of some duality results for the matrix paradigms in queueing theory

Søren Asmussen · V. Ramaswami

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

Recently, Ramaswami obtained a duality theorem for the Markov renewal processes arising as the matrix analogues of the classical M/G /I and GI/M/1 queues. A new probabilistic proof of that result is provided here in terms of time reversal of sample paths of Markov renewal processes. We also provide a probabilistic proof for a duality theorem for phase type queues obtained earlier by Ramaswami and Neuts.

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1987Applied Probability and Queues 1980The N/G/1 queue and its detailed analysis 1978Markov chains with applications in queueing theory, which have a matrix-geometric invariant probability vector 1990A duality theorem for the matrix paradigms in queueing theory

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