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The M/M/∞ queue in a random environment

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Abstract

We consider the M/M/∞ queueing system with arrival and service rate depending on the state of an auxiliary semi-Markov process (which can be viewed as an external environment) and find the mean number of customers in the system in steady state. In a particular case when the external environment can be only in two states we find the distribution of the number of customers in the system.

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References

  1. Baykal-Gursoy, M., Xiao, W.: Stochastic decomposition in M/M/∞ with Markov modulated service rates. Queueing Syst. 48, 75–88 (2004)

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Authors and Affiliations

  1. Department of Probability, Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119992, Russian Federation

    G. Falin

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  1. G. Falin
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Correspondence to G. Falin.

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Falin, G. The M/M/∞ queue in a random environment. Queueing Syst 58, 65–76 (2008). https://doi.org/10.1007/s11134-007-9059-0

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  • DOI: https://doi.org/10.1007/s11134-007-9059-0

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