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

Authors

  • Ines Ziad Laboratory of Mathematics of Sidi Bel Abbes, Kasdi Merbah University, Ouargla, Algeria
  • Vijaya P. Laxmi Department of Applied mathematics, Andhra University, Visakhapatnam, India
  • Girija E. 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

Keywords:

Queueing models, matrix analytic method, performance measures, cost model, optimisation

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.

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Published

2023-02-12

Issue

Vol. 33 No. 3 (2023)

Section

Research Articles

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