Title: Unreliable M^x/G/1 retrial queue with multi-optional services and impatient customers

Authors: Amita Bhagat; Madhu Jain

Addresses: Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India ' Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India

Abstract: The present investigation deals with M^x/G/1 retrial queue with unreliable server and general retrial times. The server is subject to breakdowns and takes some setup time before starting the repair. The server renders first essential phase of service (FES) to all the arriving customers whereas second optional phase services (SOS) are provided after FES to only those customers who opt for it. The impatient customers are allowed to balk depending upon server's status; they may also renege after waiting sometime in the queue. By incorporating the supplementary variables corresponding to service time, repair time, retrial time and setup time and then using generating function method, the queueing analysis has been done to obtain the queue size and orbit size distributions, and some other queueing as well as reliability measures. The effects of several parameters on the system performance are examined numerically by taking an illustration.

Keywords: retrial queues; balking; reneging; setup times; bulk queues; multi-optional services; impatient customers; unreliable servers; service time; repair time; retrial time.

DOI: 10.1504/IJOR.2013.053614

International Journal of Operational Research, 2013 Vol.17 No.2, pp.248 - 273

Published online: 29 Jul 2014 *

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