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Analysis of the busy period for the M/M/c queue: an algorithmic approach

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

J. R. Artalejo  and
M. J. Lopez-Herrero
J. R. Artalejo*
Affiliation:
Universidad Complutense de Madrid
M. J. Lopez-Herrero*
Affiliation:
Universidad Complutense de Madrid
*
∗ Postal address: Faculty of Mathematics, Department of Statistics and O.R., Complutense University of Madrid, Madrid 28040, Spain. Email address: jesus_artalejo@mat.ucm.es
∗∗ Postal address: School of Statistics, Complutense University of Madrid, Madrid 28040, Spain.
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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.

Keywords

multiserver queuesbusy periodnumber of customers servedmaximum entropy principle

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 209 - 222
Copyright
Copyright © by the Applied Probability Trust 2001 

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