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Simple Approximations for the GI/G/c Queue-I: The Steady-State Probabilities

Haim Shore
The Journal of the Operational Research Society
Vol. 39, No. 3 (Mar., 1988), pp. 279-284
DOI: 10.2307/2582610
Stable URL: http://www.jstor.org/stable/2582610
Page Count: 6
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Simple Approximations for the GI/G/c Queue-I: The Steady-State Probabilities
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Abstract

Viewing the GI/G/c queue as a service system alternating between two basic states-that of a loaded (non-empty) GI/G/l queue and that of a GI/G/∞ queue (dependent, respectively, on whether all servers in the GI/G/c queue are busy or otherwise)-approximations for the components of the mixture distribution of the steady-state probabilities are derived. The M/G/c queue is separately treated. Two imposed prerequisites, that only minimal prior information about the queue will be required and that no numeric method be needed other than a root-finding algorithm, are strictly adhered to. The accuracy attained is generally satisfactory, while remarkable algebraic simplicity is preserved.

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