Title: M^X/G/1 state dependent arrival queue with optional service and vacation under randomised policy

Authors: Charan Jeet Singh; Binay Kumar; Sandeep Kaur

Addresses: Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India ' Department of Mathematics, MLU DAV College, Phagwara 144402, India ' Department of Applied Sciences, Khalsa College of Engineering and Technology, Amritsar 143002, India

Abstract: The present study deals with the performance analysis of a single server queues with state dependent arrival rates in batches. It is considerable that the units join the system for essential and optional services available in the system. The server can avail the at most m-vacations under randomised vacations policy. The system is analysed by using the supplementary variable technique with the assumptions of probability reasoning for study the steady state behaviour of the system and to obtain various performance indices of queue size distribution. The maximum entropy principle is used to find the approximate results of performance measures and comparative study of exact and approximate waiting times of the units is discussed. The numerical illustration is also carried out to facilitate the minimum cost for optimal parameters and validate the other results of the system.

Keywords: randomised vacation; optional service; supplementary variable; maximum entropy; queue size; cost.

DOI: 10.1504/IJISE.2018.091902

International Journal of Industrial and Systems Engineering, 2018 Vol.29 No.2, pp.252 - 272

Received: 17 Mar 2016
Accepted: 25 Jun 2016
Published online: 21 May 2018 *

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