The busy period and the waiting time analysis of a MAP/M/c queue with finite retrial group
Stochastic Analysis and Applications
We concentrate on the analysis of the busy period and the waiting time distribution of a multi-server retrial queue in which primary arrivals occur according to a Markovian arrival process (MAP). Since the study of a model with an infinite retrial group seems intractable, we deal with a system having a finite buffer for the retrial group. The system is analyzed in steady state by deriving expressions for (a) the Laplace–Stieltjes transforms of the busy period and the waiting time; (b) the probabiliy generating functions for the number of customers served during a busy period and the number of retrials made by a customer; and (c) various moments of quantites of interest. Some illustrative numerical examples are discussed.
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Artalejo, Jesús R. and Chakravarthy, Srinivas R., "The busy period and the waiting time analysis of a MAP/M/c queue with finite retrial group" (2007). Industrial & Manufacturing Engineering Publications. 39.