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Approximation of the Mean Queue Length of an M/G/c Queueing System

Bobby N. W. Ma and Jon W. Mark
Operations Research
Vol. 43, No. 1, Special Issue on Telecommunications Systems: Modeling, Analysis and Design (Jan. - Feb., 1995), pp. 158-165
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/171768
Page Count: 8
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Approximation of the Mean Queue Length of an M/G/c Queueing System
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Abstract

A relatively robust method for the approximate analysis of the mean queue length of an M/G/c queueing system is proposed. The approximation method is developed based on the following assumptions: the residual service time of one busy server is independent of those of the other busy servers, and the system in which all the servers are busy is treated in the same way as a single-server system with c times the service rate of one of the servers. The application of these two assumptions is coupled through the introduction of a parameter np. If the number of customers in the system is larger than np, assumption 2 is used; otherwise assumption 1 is used. We found that certain properties of np allow an estimation of the mean queue length of a large M/G/c queueing system through the approximate analysis of the mean queue length of a much smaller M/G/c queueing system. Numerical results show that the approximation is accurate even when the coefficient of variation of the service time and the number of channels of the system are as large as 20 and 200, respectively.

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