Analysis of a batch arrival multi-server queueing system with waiting servers, synchronous working vacations and impatient customers

Amina Angelika Bouchentouf; Meriem Houalef; Abdelhak Guendouzi

doi:10.2478/ausm-2022-0003

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Analysis of a batch arrival multi-server queueing system with waiting servers, synchronous working vacations and impatient customers

Acta Universitatis Sapientiae, Mathematica

Volume 14 (2022): Issue 1 (November 2022)

By: Amina Angelika Bouchentouf, Meriem Houalef and Abdelhak Guendouzi

Open Access

|Nov 2022

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Abstract

This paper is concerned with the analysis of an infinite-capacity batch arrival multi-server queueing system with Bernoulli feedback, synchronous multiple and single working vacation policies, waiting servers, reneging and retention of reneged customers. The steady-state solution of the queueing system is obtained by using probability generating function (PGF). In addition, important performance measures of the queueing system are derived. Then, a cost model is formulated in order to carry out the parameter optimization using genetic algorithm (GA). Finally, numerical study is presented in which various system performance measures are evaluated based on supposed numerical values given to the system parameters.

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Articles in this issue

DOI: https://doi.org/10.2478/ausm-2022-0003 | Journal eISSN: 2066-7752

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Language: English

Page range: 37 - 60

Published online: Nov 18, 2022

Published in print: Nov 1, 2022

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

multi-server queueing systems,

synchronous working vacation,

batch arrival,

reneging,

cost model

MSC:

60K25,

68M20,

90B22

Related subjects:

Mathematics,

General mathematics

© 2022 Amina Angelika Bouchentouf, Meriem Houalef, Abdelhak Guendouzi, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 14 (2022): Issue 1 (November 2022)