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

Bobby N. W. Ma and Jon W. Mark
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Bobby N. W. Ma: Ryerson Polytechnical Institute, Toronto, Ontario, Canada
Jon W. Mark: University of Waterloo, Waterloo, Ontario, Canada

Operations Research, 1995, vol. 43, issue 1, 158-165

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 n p . If the number of customers in the system is larger than n p , assumption 2 is used; otherwise assumption 1 is used. We found that certain properties of n p 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.

Keywords: queues; approximate analysis: robust approximation of mean queue length for large systems; queues; multiserver: M/G/c for modeling multiple access systems (search for similar items in EconPapers)
Date: 1995
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