Analysis of an M/G1G2/1 Queue with Bernoulli Vacation and Server Breakdown

In this article, an M / G 1 G 2 / 1 queue with service interruption consisting of a definite repairability is analyzed in the steady-state regime. Here, the server, after completion of a service, is allowed to take in a single vacation under the Bernoulli schedule. For this model, probability genera...

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Bibliographic Details
Published in:International journal of applied and computational mathematics 2023, Vol.9 (1)
Main Authors: Begum, Anjana, Choudhury, Gautam
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied mathematics
Computational mathematics
Computational Science and Engineering
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Queues
Theoretical
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Summary:In this article, an M / G 1 G 2 / 1 queue with service interruption consisting of a definite repairability is analyzed in the steady-state regime. Here, the server, after completion of a service, is allowed to take in a single vacation under the Bernoulli schedule. For this model, probability generating function (PGF) for queue length distribution at arbitrary and service completion epoch are derived. Laplace Stieltjes Transform (LST) of a busy period distribution and waiting time distribution are obtained. In addition to these, some important performance measures such as the mean queue size and the mean waiting time of a customer are achieved. The reliability indices for this model are carried out and are included in the study. An optimal operation policy of the model in terms of total expected cost is developed at a lower cost. Finally, various numerical examples are presented in support of the theory.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-022-01481-4