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Asymptotics for the sojourn time distribution in the queue defined by a general QBD process with a countable phase space

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Abstract

We consider a FIFO queue defined by a QBD process. When the number of phases of the QBD process is finite, it has been proved that the stationary distribution of sojourn times in that queue can be represented as a phase-type distribution. In this paper, we extend this result to the case where the number of phases of the QBD process is countably many and obtain several kinds of asymptotic formula for the steady-state tail probability of sojourn times in the queue when the tail probability decays in exact exponential form.

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Acknowledgments

The author would like to thank the anonymous reviewer for his/her valuable comments.

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  1. Faculty of Business Administration, Komazawa University, 1-23-1 Komazawa, Setagaya-ku, Tokyo, 154-8525, Japan

    Toshihisa Ozawa

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  1. Toshihisa Ozawa
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Correspondence to Toshihisa Ozawa.

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Ozawa, T. Asymptotics for the sojourn time distribution in the queue defined by a general QBD process with a countable phase space. Queueing Syst 76, 73–103 (2014). https://doi.org/10.1007/s11134-013-9359-5

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  • DOI: https://doi.org/10.1007/s11134-013-9359-5

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