Title: A two-phase quorum queueing system with Bernoulli vacation schedule, setup, and N-policy for an unreliable server with delaying repair

Authors: Lotfi Tadj; Gautam Choudhury; Kamel Rekab

Addresses: Department of Finance, Information Systems and Management Science, Saint Mary's University, Halifax, NS, B3H 3C3, Canada; School of Business Administration, Dalhousie University, Halifax, NS, B3H 3J5, Canada. ' Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Paschim Boragaon, Guwahati – 781035 Assam, India. ' Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, MO 64110, USA

Abstract: We present in this paper a thorough classified review of queueing system with unreliable server. We then consider a queueing system where service is rendered to groups of customers of fixed quorum size. Service consists of two consecutive phases. The server needs a setup following an idle period, and may take a vacation following the second phase of service. The idle period ends only when at least N customers are in the queue. While providing service, the server may breakdown and a delay period precedes the repair period. This model generalises many of the models available in the literature. For this model, we obtain the steady state system size distributions and discuss the optimal management policy. Illustrative numerical examples are provided.

Keywords: bulk queues; breakdowns; repair; delay; optimal management policy; Bernoulli vacation schedule; two-phase quorum queueing; unreliable servers.

DOI: 10.1504/IJSOM.2012.047103

International Journal of Services and Operations Management, 2012 Vol.12 No.2, pp.139 - 164

Published online: 23 Aug 2014 *

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