10.71932/

Transient Solution of an M/M/1 Variant Working Vacation Queue with Balking

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  • Vijaya Laxmi Pikkala 1,
  • Rajesh Pilla1,
  1. Mathematics Department, Andhra University, Visakhapatnam, India.

Published in Issue 13-07-2025

Copyright (c) 2025 Vijaya Laxmi Pikkala , Rajesh Pilla (Author)

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

How to Cite

Pikkala , V. L., & Pilla, R. (2025). Transient Solution of an M/M/1 Variant Working Vacation Queue with Balking. International Journal of Mathematical Modelling & Computations, 8(01). https://doi.org/10.71932/
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Abstract

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $\bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed to be exponentially distributed and are mutually independent. We have obtained the transient-state probabilities in terms of modified Bessel function of the first kind by employing probability generating function, continued fractions and Laplace transform. In addition, we have also obtained some other performance measures.

Keywords

  • Laplace transform,
  • Queue,
  • balking,
  • probability generating function,
  • transient probabilities,
  • variant working vacations,
  • continued fractions
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