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.

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

Analysis of the N-policy GI/M/1/K Queueing Systems with Working Breakdowns and Repairs

The present paper deals with the performance evaluation of an M/M/1 retrial queue with collisions, transmission errors and unreliable server. To the best of our knowledge, there are no works that h...

An unreliable single server retrial queue with collisions and transmission errors

This paper presents a steady-state analysis of an M/M/2 queue with heterogeneous servers (Server 1 and Server 2). Server 1 is reliable and may leave for a vacation when the system becomes empty. Se...

Modelling and optimisation of a two-server queue with multiple vacations and working breakdowns

Performance and cost comparative analysis for M/G/1 repairable machining system with N-policy vacation

This paper considers an M/G/1 retrial G-queue with general retrial times, in which the server is subject to working breakdowns and repairs. If the system is not empty during a normal service period, the arrival of a negative customer can cause the server breakdown, and the failed server still works at a lower service rate rather than stopping the service completely. Applying the embedded Markov chain, we obtain the necessary and sufﬁcient condition for the stability of the system. Using the supplementary variable method, we deal with the generating functions of the number of customers in the orbit. Various system performance measures are also developed. Finally, some numerical examples and a cost optimization analysis are presented.

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Tao Li

Papers

An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns