Title: Analysis of M^[X]/G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown

Authors: P. Rajadurai; M. Varalakshmi; M.C. Saravanarajan; V.M. Chandrasekaran

Addresses: School of Advanced Sciences, VIT University, Vellore – 632 014, Tamil Nadu, India ' School of Advanced Sciences, VIT University, Vellore – 632 014, Tamil Nadu, India ' School of Advanced Sciences, VIT University, Vellore – 632 014, Tamil Nadu, India ' School of Advanced Sciences, VIT University, Vellore – 632 014, Tamil Nadu, India

Abstract: This paper investigates the steady state behaviour of an M^[X]/G/1 retrial queue with two phases of service under Bernoulli vacation schedule and breakdown. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters the service immediately while the rest join the orbit. After completion of each two phases of service, the server either goes for a vacation with probability p or may wait for serving the next customer with probability (1-p). While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. We construct the mathematical model and derive the probability generating functions of number of customers in the system when it is idle, busy, on vacation and under repair. Some system performances are obtained.

Keywords: batch arrival; retrial queues; Bernoulli vacation; random breakdowns; stochastic decomposition; two phase services; mathematical modelling.

DOI: 10.1504/IJMOR.2015.065946

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.1, pp.19 - 41

Received: 19 Mar 2013
Accepted: 14 Jul 2013
Published online: 11 Jan 2015 *

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