Title: A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times

Authors: Gautam Choudhury; Mitali Deka

Addresses: Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Paschim Boragoan, Guwahati – 781035, Assam, India ' Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Paschim Boragoan, Guwahati – 781035, Assam, India

Abstract: This paper deals with the steady state behaviour of an Mx/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server. 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. The primary customers finding the server busy, down, or on vacation are queued in the orbit in accordance with first come, first served (FCFS) retrial policy. After the completion of the second phase of service, the server either goes for a vacation of random length with probability p or may serve the next unit, if any, with probability (1 - p). For this model, we first obtain the condition under which the system is stable. Then, we derive the system size distribution at a departure epoch and the probability generating function of the joint distributions of the server state and orbit size, and prove the decomposition property.

Keywords: stationary queue size distribution; random breakdown; repair time; retrial times; Bernoulli vacation; reliability index; batch arrivals; retrial queues; unreliable servers.

DOI: 10.1504/IJMOR.2015.069151

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.3, pp.318 - 347

Received: 14 Oct 2013
Accepted: 24 Jan 2014
Published online: 30 Apr 2015 *

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