Title: An M/G/1 retrial queueing system with two phases of service, immediate Bernoulli feedbacks, single vacation and starting failures

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

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

Abstract: This paper analyses an M/G/1 retrial queueing system with second multi-optional services and immediate Bernoulli feedbacks, where the server is subject to starting failure and repair. An arriving customer, who finds the server busy, breakdown or on vacation enters an orbit; otherwise the arriving customer enters into service area. Upon completion of both phases of service in the first round if the customer desires to make a feedback, the customer immediately proceeds for a second round of service. The customer is allowed to make a finite number of such feedbacks before departing from the system. After the completion of both phases of service, if the orbit becomes empty, the server goes for a single vacation. We derive the probability generating functions of number of customers in the orbit for different server states. Important system performance measures are obtained. The effect of various parameters on the system performance are analysed numerically.

Keywords: retrial queues; optional services; immediate feedback; Bernoulli feedback; single vacation; starting failures.

DOI: 10.1504/IJMOR.2016.078823

International Journal of Mathematics in Operational Research, 2016 Vol.9 No.3, pp.302 - 328

Received: 07 Oct 2014
Accepted: 17 Dec 2014
Published online: 03 Sep 2016 *

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