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. (2019)

• Record Type: Journal Article
• Authors: Vignesh, P.; Srinivasan, S.; Sundari, S. Maragatha
• Is Part Of: International journal of operational research. Volume 34:Number 1(2019)
• Page Start: 28
• Page End: 53
• Publication Date: 2019
• Subjects: batch arrival -- three stage service -- fourth optional service -- service interruption -- deterministic server vacation; Operations research -- Periodicals; 003.05
• Languages: English
• ISSNs: 1745-7645

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.