Title: An M/G/1 two phase multi-optional retrial queue with Bernoulli feedback, non-persistent customers and breakdown and repair

Authors: K. Lakshmi; Kasturi Ramanath

Addresses: A.M. Jain College, Meenambakkam, Chennai-114, Tamilnadu, India ' School of Mathematics, Madurai Kamaraj University, Madurai-21, Tamilnadu, India

Abstract: This paper has been motivated by the interactive voice response system (IVRS). This system has now become a common phenomenon in our everyday life. In this paper, we consider a Poisson arrival queueing system with a single server and two essential phases of heterogeneous service. The customer who completes the first phase has a choice of k-options to choose for the second phase of service. The customer, who finds the server busy upon arrival, can either join the orbit or he/she can leave the system. After completion of both phases, the customer can decide to try again for service by joining the orbit or he/she can leave the system. The server is subject to sudden breakdowns and repairs. We assume that the breakdowns of the system can occur even when the system is idle. By using the supplementary variables technique, we have obtained the steady state probability generating functions of the orbit size and the system size. We obtain a stochastic decomposition law for the system. We present numerical results to illustrate the sensitivity of the system. We obtain some useful performance measures of the system.

Keywords: retrial queues; non-persistent customers; interactive voice response system; IVRS; multi-optional second phase; Bernoulli feedback; stochastic decomposition; breakdowns; repairs; Poisson arrival queueing systems; essential service phases.

DOI: 10.1504/IJOR.2014.057844

International Journal of Operational Research, 2014 Vol.19 No.1, pp.78 - 95

Received: 11 Jan 2012
Accepted: 31 Jul 2012
Published online: 17 Jun 2014 *

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