Title: Cost optimisation and maximum entropy analysis of a bulk queueing system with breakdown, controlled arrival and multiple vacations

Authors: R.P. Nithya; M. Haridass

Addresses: Department of Mathematics, PSG College of Technology, Peelamedu, Coimbatore 641004, Tamil Nadu, India ' Department of Mathematics, PSG College of Technology, Peelamedu, Coimbatore 641004, Tamil Nadu, India

Abstract: This article analyses a bulk queueing system with multiple vacations, controlled arrival and breakdown. The service is done in bulk with a minimum of 'a' customers and a maximum of 'b' customers. The server is assigned for secondary jobs (vacations) repeatedly when the number of customers is inadequate to process. The arrivals are accepted with a probability α, β and γ during the busy, vacation and renovation period respectively. During a batch service, if the server breaks down with probability π, the service for the particular batch is processed without interruption. Upon completion of service, the renovation of service station will be considered. The probability generating function for the queue size at an arbitrary time epoch is derived. Various performance measures are obtained. A few particular cases are discussed. Maximum entropy analysis is carried out and validated through numerical illustration. The cost model is also developed to optimise the cost.

Keywords: bulk arrival; batch service; multiple vacations; breakdown; controlled arrival; maximum entropy principle; MEP.

DOI: 10.1504/IJOR.2020.110476

International Journal of Operational Research, 2020 Vol.39 No.3, pp.279 - 305

Accepted: 08 Feb 2018
Published online: 07 May 2020 *

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