Title: An M^X/G/1 retrial queue with two-phase service subject to active server breakdowns and two types of repair

Authors: M. Senthil Kumar, R. Arumuganathan

Addresses: Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore 641 004, Tamil Nadu, India. ' Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore 641 004, Tamil Nadu, India

Abstract: This paper analyses a single server batch arrival retrial queue with active breakdowns, two types of repair and second optional service (SOS). The server provides preliminary first essential service (FES) to the primary arriving customers or customers from retrial group. The server is subject to breakdowns. The customer under service during the failure decides, with probability q, to join the orbit (impatient customer) and, with complementary probability |p|, to remain in the server for repair in order to conclude his remaining service (patient customer). It is considered that the repair time of server during the presence of patient customer and the repair time of the server while the customer (impatient customer) joining the orbit due to failure are different. On completion of FES successfully, the customer may opt for SOS with probability α. Reliability of the proposed model is analysed. Some particular cases are also discussed. Other performance measures are also obtained. The effects of several parameters on the system are analysed numerically.

Keywords: first essential service; reliability analysis; second optional service; steady-state distribution; unreliable servers; server breakdowns; repair; single server queues; batch arrival queues; retrial queues.

DOI: 10.1504/IJOR.2010.033540

International Journal of Operational Research, 2010 Vol.8 No.3, pp.261 - 291

Published online: 04 Jun 2010 *

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