The busy period and the waiting time analysis of a MAP/M/c queue with finite retrial group
Document Type
Article
Publication Date
2-27-2007
Publication Title
Stochastic Analysis and Applications
Abstract
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.
Volume
25
Issue
2
First Page
445
Last Page
469
DOI
10.1080/07362990601139651
ISSN
0736-2994 (print) 1532-9356 (online)
Rights
© 2007 Informa UK Limited. All rights reserved.
Recommended Citation
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.
https://digitalcommons.kettering.edu/industrialmanuf_eng_facultypubs/39
