Article: Modelling and simulation of Bernoulli feedback queue with general customers' impatience under variant vacation policy Journal: International Journal of Operational Research (IJOR) 2023 Vol.46 No.4 pp.451 - 480 Abstract: This article deals with a feedback queueing system with variant of a multiple vacation policy, balking, server's states-dependent reneging, and retention of reneged customers. On arrival, if the server is on vacation (respectively, busy), a customer activates an individual timer TV (respectively, TB) and starts his patience time. The patience time of each customer during vacation (respectively, busy) period is a random variable with a general probability distribution function GV (·) (respectively, GB(·)). A customer must leave the system as soon as his patience's time expires. The general distribution of impatience times as well as server's states-dependent reneging makes the analysis of the considered model difficult. We establish the equilibrium analysis of the queueing model, derive its performance measures, and examine it by a series of simulation experiments through a discrete-event simulation. This approach is very appropriate for modelling such complex environment, it attempts to replicate the behaviour of the queueing system providing its characteristic estimations. Inderscience Publishers - linking academia, business and industry through research

Title: Modelling and simulation of Bernoulli feedback queue with general customers' impatience under variant vacation policy

Authors: Mouloud Cherfaoui; Amina Angelika Bouchentouf; Mohamed Boualem

Addresses: Research Unit LaMOS (Modeling and Optimization of Systems), University of Bejaia, 06000 Bejaia, Algeria ' Department of Mathematics, Laboratory of Mathematics, Djillali Liabes University of Sidi Bel Abbes, B.P. 89, Sidi Bel Abbes 22000, Algeria ' Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Technology, University of Bejaia, 06000 Bejaia, Algeria

Abstract: This article deals with a feedback queueing system with variant of a multiple vacation policy, balking, server's states-dependent reneging, and retention of reneged customers. On arrival, if the server is on vacation (respectively, busy), a customer activates an individual timer T_V (respectively, T_B) and starts his patience time. The patience time of each customer during vacation (respectively, busy) period is a random variable with a general probability distribution function G_V (·) (respectively, G_B(·)). A customer must leave the system as soon as his patience's time expires. The general distribution of impatience times as well as server's states-dependent reneging makes the analysis of the considered model difficult. We establish the equilibrium analysis of the queueing model, derive its performance measures, and examine it by a series of simulation experiments through a discrete-event simulation. This approach is very appropriate for modelling such complex environment, it attempts to replicate the behaviour of the queueing system providing its characteristic estimations.

Keywords: queueing; vacation; balking; reneging; general customers' impatience; discrete-event simulation.

DOI: 10.1504/IJOR.2023.129959

International Journal of Operational Research, 2023 Vol.46 No.4, pp.451 - 480

Received: 18 Apr 2020
Accepted: 30 Jul 2020
Published online: 04 Apr 2023 *

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Title: Modelling and simulation of Bernoulli feedback queue with general customers' impatience under variant vacation policy

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