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International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 673642, 20 pages
http://dx.doi.org/10.1155/2012/673642
Research Article

A Feedback Retrial Queueing System with Two Types of Batch Arrivals

Department of Mathematics, Annamalai University, Annamalainagar 608002, India

Received 8 September 2012; Revised 15 November 2012; Accepted 18 November 2012

Academic Editor: Ho Lee

Copyright © 2012 R. Kalyanaraman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A retrial queueing system with two types of batch arrivals, called type I and type II customers, is considered. Type I customers and type II customers arrive in batches of variable sizes according to two different Poisson processes. Service time distributions are identical and independent and are different for both types of customers. If the arriving customers are blocked due to the server being busy, type I customers are queued in a priority queue of infinite capacity, whereas type II customers enter into a retrial group in order to seek service again after a random amount of time. A type I customer who has received service departs the system with a preassigned probability or returns to the priority queue for reservice with the complement probability. A type II call who has received service leaves the system with a preassigned probability or rejoins the retrial group with complement probability. For this model, the joint distribution of the number of customers in the priority queue and in the retrial group is obtained in a closed form. Some particular models and operating characteristics are obtained. A numerical study is also carried out.