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

Author:

Bouchentouf Amina Angelika1,Houalef Meriem2,Guendouzi Abdelhak3

Affiliation:

1. Laboratory Mathematics , Djillali Liabes University of Sidi Bel Abbes , Algeria

2. Laboratory of Mathematics , University of Sidi Bel Abbes, Ecole Supérieure En Sciences Appliquées , B.P. 119, Tlemcen 13000 , Algeria

3. Laboratory of Stochastic Models, Statistic and Applications , Dr. Tahar Moulay University of Saida , Algeria

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

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