The output process of an MMPP/M/1 queue

Nigel Geoffrey Bean · Peter G. Taylor

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

Abstract

Olivier and Walrand (1994) claimed that the departure process of an MMPP/M/1 queue is not an MAP unless the queue is a stationary M/M/1 queue. They also conjectured that the departure process of an MAP/PH/1 queue is not an MAP unless the queue is a stationary M/M/1 queue. We show that their proof of the first result has an algebraic error, which leaves open the above question of whether the departure process of an MMPP/M/1 can be an MAP.

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References

1984Matrix-Geometric Solutions to Stochastic Models 1985Matrix-geometric solutions in stochastic models 1987Introduction to Queueing Networks 1956The Output of a Queuing System 1990An Introduction to Queueing Networks 1981The Output of a Queueing System 1993On the Problem of Establishing the Existence of Stationary Distributions for Continuous-Time Markov Chains

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1999Departure processes from MAP/PH/1 queues 2014The intercept term of the asymptotic variance curve for some queueing output processes

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