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

Affiliations

  • Departmemt of Mathematics, Annamalai University, Annamalai Nagar, Chidambaram - 608002, Tamil Nadu, India
  • Department of Mathematics, SCSVMV University, Sri Jayendra Saraswathi Street, Enathur, Kanchipuram - 631561, Tamil Nadu, India

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.

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