Bulk Arrival, Fixed Batch Service Queue with Unreliable Server and with Compulsory Vacation

R  Kalyanaraman  and P  Nagarajan

doi:10.17485/ijst/2016/v9i38/101793

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Bulk Arrival, Fixed Batch Service Queue with Unreliable Server and with Compulsory Vacation

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2016/v9i38/101793

Year: 2016, Volume: 9, Issue: 38, Pages: 1-8

Original Article

Bulk Arrival, Fixed Batch Service Queue with Unreliable Server and with Compulsory Vacation

R. Kalyanaraman¹ and P. Nagarajan²

¹ Departmemt of Mathematics, Annamalai University, Annamalai Nagar, Chidambaram - 608002, Tamil Nadu, India; [email protected]
² Department of Mathematics, SCSVMV University, Sri Jayendra Saraswathi Street, Enathur, Kanchipuram - 631561, Tamil Nadu, India, Email: nagarajandixit@gmail

This work is licensed under a Creative Commons Attribution 4.0 International License.

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.
Keywords: Batch Arrival, Batch Service, Compulsory Vacation, Probability Generating Function and Operating Characteristics, Unreliable Server