Title: Analysis of a non-Markovian single server batch arrival queueing system of compulsory three stages of services with fourth optional stage service, service interruptions and deterministic server vacations

Authors: P. Vignesh; S. Srinivasan; S. Maragatha Sundari

Addresses: Department of Mathematics and As, B.S. Abdur Rahman University, Chennai-600048, Tamilnadu, India ' Department of Mathematics and As, B.S. Abdur Rahman University, Chennai-600048, Tamilnadu, India ' Department of Mathematics, Kalasalingam University, Anand Nagar, Krishnankoil-626126, Tamilndau, India

Abstract: This paper deals with the steady state analysis of a single server batch arrival queueing system with three stages of compulsory service. An additional supposition of a fourth stage optional service is well thought-out. The server may take a vacation after completion of service. In this model, the vacation is of predetermined duration. A busy server may break down at any moment. It is tracked by a repair process. Service time, vacation time and repair time follow general distribution. The steady state probability generating function for the system and also system recital measures is obtained by using a supplementary variable technique. Some special cases of the model are also discussed. The model is justified by means of numerical illustrations followed by graphical representation.

Keywords: batch arrival; three stage service; fourth optional service; service interruption; deterministic server vacation.

DOI: 10.1504/IJOR.2019.096937

International Journal of Operational Research, 2019 Vol.34 No.1, pp.28 - 53

Received: 05 Aug 2015
Accepted: 05 Feb 2016
Published online: 14 Dec 2018 *

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