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Analysis of the Busy Period for the M/M/c Queue: An Algorithmic Approach

J. R. Artalejo and M. J. Lopez-Herrero
Journal of Applied Probability
Vol. 38, No. 1 (Mar., 2001), pp. 209-222
Stable URL: http://www.jstor.org/stable/3215752
Page Count: 14
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Analysis of the Busy Period for the M/M/c Queue: An Algorithmic Approach
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Abstract

This paper presents an algorithmic analysis of the busy period for the M/M/c queueing system. By setting the busy period equal to the time interval during which at least one server is busy, we develop a first step analysis which gives the Laplace-Stieltjes transform of the busy period as the solution of a finite system of linear equations. This approach is useful in obtaining a suitable recursive procedure for computing the moments of the length of a busy period and the number of customers served during it. The maximum entropy formalism is then used to analyse what is the influence of a given set of moments on the distribution of the busy period and to estimate the true busy period distribution. Our study supplements a recent work of Daley and Servi (1998) and other studies where the busy period of a multiserver queue follows a different definition, i.e., a busy period is the time interval during which all servers are engaged.

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