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Diffusion Approximations for Queues with Markovian Bases

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  • Toshikazu Kimura

Abstract

Consider a base family of state-dependent queues whose queue-length process can be formulated by a continuous-time Markov process. In this paper, we develop a piecewise-constant diffusion model for an enlarged family of queues, each of whose members has arrival and service distributions generalized from those of the associated queue in the base. The enlarged family covers many standard queueing systems with finite waiting spaces, finite sources and so on. We provide a unifying explicit expression for the steady-state distribution, which is consistent with the exact result when the arrival and service distributions are those of the base. The model is an extension as well as a refinement of the M/M/s-consistent diffusion model for the GI/G/s queue developed by Kimura [13] where the base was a birth-and-death process. As a typical base, we still focus on birth-and-death processes, but we also consider a class of continuous-time Markov processes with lower-triangular infinitesimal generators. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Toshikazu Kimura, 2002. "Diffusion Approximations for Queues with Markovian Bases," Annals of Operations Research, Springer, vol. 113(1), pages 27-40, July.
    • Handle: RePEc:spr:annopr:v:113:y:2002:i:1:p:27-40:10.1023/a:1020997509178
    DOI: 10.1023/A:1020997509178
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    Cited by:

    1. Dae W. Choi & Nam K. Kim & Kyung C. Chae, 2005. "A Two-Moment Approximation for the GI / G / c Queue with Finite Capacity," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 75-81, February.
    2. Ward Whitt, 2004. "A Diffusion Approximation for the G/GI/n/m Queue," Operations Research, INFORMS, vol. 52(6), pages 922-941, December.

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