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Journal ArticleDOI

Analysis of multistage M[X]/GK/1 queue with different server’s interruptions and its application in energy consumption

11 Apr 2020-International journal of ambient energy (Informa UK Limited)-Vol. 41, Iss: 6, pp 691-698
TL;DR: This paper considers multistage batch arrival, batch service (fixed batch size) queue having multiple vacation policy subject to server breakdown with the delayed repair, and derives transient and its corresponding steady-state solutions.
Abstract: In this paper, we consider multistage batch arrival, batch service (fixed batch size) queue having multiple vacation policy subject to server breakdown with the delayed repair. In addition, the ser...
Citations
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Journal ArticleDOI
TL;DR: 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 and factors causing service interruption such as unreliable server and server vacation are presented.
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.

16 citations

References
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Journal ArticleDOI
TL;DR: This work studied a queuing system with four different main server interruptions and a stand-by server replaces the main server during any potential stop and the distribution of the service, vacation, extended vacation, repairs and delay times all follow general distributions.
Abstract: This work studied a queuing system with four different main server interruptions and a stand-by server replaces the main server during any potential stop. The main server has five statues in this system where it is either services the customers( active) or it does not work because of one of the four reason; original vacation, extended vacation, it is broken-down but the repairs did not start yet (delay time) and broken-down servers under repairs. The arrivals are assumed to attend the system in batches. All the distributions of the service, vacation, extended vacation, repairs and delay times all follow general distributions while the breakdown times and the stand-by service times are exponentially distributed.

8 citations

Journal ArticleDOI
TL;DR: Using supplementary variable technique and Laplace Stieltjes transform, the probability generating functions has been obtained for finding the steady state solution of bulk arrival queue with fixed batch service.
Abstract: Objectives: To derive a steady state solution of bulk arrival queue with fixed batch service, in addition the server may break down and the server takes compulsory vacation at each service completion points. Methods/Statistical Analysis: Using supplementary variable technique and Laplace Stieltjes transform, the probability generating functions has been obtained for finding the steady state solution. Findings: Using the properties of probability generating function, some performance measures of the queuing model have been obtained at various server state. The model has been compared with existing once by assuming particular distributions to respective random variables. Application/Improvements: The results obtained has been comprehended by illustrating numerical examples.

3 citations


"Analysis of multistage M[X]/GK/1 qu..." refers background in this paper

  • ...In Kalyanaraman and Nagarajan (2016), bulk arrival, batch service queueing model with an unreliable server having compulsory vacation is discussed....

    [...]

Journal ArticleDOI
29 Jan 2012
TL;DR: The single server interdependent queuing models to bulk service queueing models are extended to include costumers/units served k at a time, except when less than k are in the system and ready for service.
Abstract: In this paper we extend the single server interdependent queuing models to bulk service queueing models. Here we consider the costumers/units served k at a time, except when less than k are in the system and ready for service at which time all units are served. In this model various system characteristics like average queue length, variability of the system size are obtained.

3 citations