A Matrix Geometric Solution of a Multi-Server Queue With Waiting Servers and Customers’ Impatience Under Variant Working Vacation and Vacation Interruption

  • Ines Ziad Laboratory of Mathematics of Sidi Bel Abbes, Kasdi Merbah University, Ouargla, Algeria
  • P. Vijaya Laxmi Department of Applied mathematics, Andhra University, Visakhapatnam, India
  • E. Girija Bhavani Department of Applied mathematics, Andhra University, Visakhapatnam, India
  • Amina Angelika Bouchentouf Mathematics Laboratory, Djillali Liabes University of Sidi Bel Abbes, Algeria Laboratory of Stochastic Models, Statistic and Applications, University of Saida-Dr. Moulay Tahar, Algeria
  • Shakir Majid Department of Mathematics, University of Ladakh, India
DOI: https://doi.org/10.2298/YJOR220315001Z

Abstract

This paper deals with a M/M/c queueing system with waiting servers, balking, reneging, and K-variant working vacations subjected to Bernoulli schedule vacation interruption. Whenever the system is emptied, the servers wait for a while before synchronously going on vacation during which services are offered with a lower rate. We obtain the steady-state probabilities of the system using the matrix-geometric method. In addition, we derive important performance measures of the queueing model. Moreover, we construct a cost model and apply a direct search method to get the optimum service rates during both working vacation and regular working periods at lowest cost. Finally, numerical results are provided.

Published
2023-02-12
How to Cite
ZIAD, Ines et al. A Matrix Geometric Solution of a Multi-Server Queue With Waiting Servers and Customers’ Impatience Under Variant Working Vacation and Vacation Interruption. Yugoslav Journal of Operations Research, [S.l.], v. 33, n. 3, p. 389-407, feb. 2023. ISSN 2334-6043. Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1079>. Date accessed: 04 dec. 2024. doi: https://doi.org/10.2298/YJOR220315001Z.
Citation Formats
Issue
Vol 33 No 3 (2023)
Section
Research Articles
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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