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



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Artalejo, Jesús R. and Lopez-Herrero, M. J. (2001) Analysis of the busy period for the M/M/c queue: An algorithmic approach. Journal of Applied Probability, 38 (1). pp. 209-222. ISSN 0021-9002

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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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The authors thank the referee for his detailed comments on an earlier version of this paper. This work was supported by the European Commission through INTAS 96-0828, by the
DGES through project 98-0837 and by the Complutense University of Madrid through project PR64/99-8501.

Uncontrolled Keywords:Multiserve queues; busy period; number of customers served; maximum; entropy principle
Subjects:Sciences > Mathematics > Operations research
ID Code:15826
Deposited On:04 Jul 2012 09:50
Last Modified:06 Aug 2018 08:45

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