Title: A note on a bulk arrivals quorum queuing system with an unreliable server

Authors: Lotfi Tadj, Gautam Choudhury, Kamel Rekab

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

Abstract: This paper considers a service system with bulk service and an unreliable server, generalising the work of Tadj and Choudhury [Applied Mathematics Letters, 22 (2009) 1710-1714]. While Tadj and Choudhury assume single arrivals, we allow arrivals to occur in bulk, which increases the analytical challenge. The first objective is to derive the probability generating function of the number of customers in the system at a service completion epoch and at an arbitrary instant of time as well as the performance characteristics of the system. The second objective is to develop an optimal management policy to obtain the optimal value of the parameter which minimises a suitable cost structure. This model is useful in different real-world operational management problems to minimise the organisation costs while keeping a high customer satisfaction level.

Keywords: bulk arrivals; bulk service queues; quorum queuing; breakdowns; repair; optimal management policy; unreliable servers; organisation costs; customer satisfaction.

DOI: 10.1504/IJAMS.2011.041320

International Journal of Applied Management Science, 2011 Vol.3 No.3, pp.316 - 325

Published online: 30 Sep 2014 *

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