Title: Bulk queue with Bernoulli vacation and m-optional services under N-policy

Authors: Charan Jeet Singh; Binay Kumar

Addresses: Department of Mathematics, Guru Nanak Dev University, Amritsar-143005, India ' Department of Mathematics, M.L.U. DAV College, Phagwara-144402, India

Abstract: The present investigation deals with a stochastic model of queueing system wherein the customers join the system in bulk with different arrival rates. On arrival in the system, the customer may choose any of the available m-optional services and the server may avail the optional vacation after finishing any one of the service or stay in the system to provide the service to other customers. It is also assumed that the server starts the service, if at least N customers are there in the queue. The steady state behaviour of the system is discussed by using the supplementary variable technique. The mathematical model is analysed by using the probability generating functions of queue size distribution to obtain the performance indices of the system. The principle of maximum entropy is also employed to find the approximate values of waiting time of the system. To validate the results, the numerical illustration is presented.

Keywords: queue; bulk; optional service; vacation; supplementary variable; maximum entropy; queue length.

DOI: 10.1504/IJOR.2017.087826

International Journal of Operational Research, 2017 Vol.30 No.4, pp.460 - 483

Received: 29 Jan 2014
Accepted: 23 Mar 2015
Published online: 06 Nov 2017 *

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