On approximating the generalized occupancy of the G/M/K queueing system

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Abstract

The G/M/K is one of very few multiserver queueing systems for which analytical results exist. In 1951 Kendall [4] showed how to compute the steady-state probabilities of a G/M/K queueing system. Later, Takacs [6] suggested an iterative procedure for the evaluation of a needed component in Kendall's scheme; namely, the generalized occupancy ω*. However, Takàcs' algorithm requires the computation of a general integral for each of its interations.

In this paper we propose a simple and explicit approximation for the generalized occupancy of the G/M/K system. Several numerical results are also included.

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Baruch Halachmi gained his B.A. in Statistics & Economics from The Hebrew University of Jerusalem, his M.A. in Operations Research & Statistics from Tel Aviv University and Ph.D. in Computer Science from the University of Minnesota. Currently an Assistant Professor of Computer Science at the University of Kansas. Areas of interest include: Simulations and Modeling, Computer Performance Evaluation, Optimization and Queueing Theory.

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