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Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)

Madhu Jain (), Sandeep Kaur () and Parminder Singh ()
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Madhu Jain: Indian Institute of Technology Roorkee
Sandeep Kaur: Guru Nanak Dev University
Parminder Singh: Guru Nanak Dev University

Operational Research, 2021, vol. 21, issue 4, No 1, 2203-2246

Abstract: Abstract In most of the queueing models, service is considered to be complete without any interruption. But in reality, queueing systems are subject to interruptions due to failure of server or any other cause. In the present article, we present an overview and literature survey on the performance modeling and analysis of single server, general service queueing system with service interruption using supplementary variable technique. The factors causing service interruption such as unreliable server and server vacation are elaborated. The brief of supplementary variable technique to establish the queue size distribution is explained for single server non-Markovian queueing models by incorporating the features of service interruption. The basic concepts and review of literature on the queues with server breakdown and/or vacationing server are described. The research works done during last 10 years (2010–2019) on queues with service interruption involving many other key concepts namely Bernoulli vacation, multiple vacation, bulk arrival, discouragement, etc. and queueing scenarios of service interruption are reported. Some specific applications are also highlighted.

Keywords: Non-Markovian; Unreliable server; Vacation; Supplementary variable; Queue length; Bulk input (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s12351-019-00519-8

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