Title: Simulation of batch service lateness queues with multiple vacations and two Bernoulli catastrophes using the developed 'goLHS' generator

Authors: Anfal Rezgui; Hafida Saggou; Megdouda Ourbih-Tari; Meriem Boubalou

Addresses: Laboratory of RIIMA, Faculty of Mathematics, USTHB, PB 32 El Alia 16111 Algiers, Algeria ' Laboratory of RIIMA, Faculty of Mathematics, USTHB, PB 32 El Alia 16111 Algiers, Algeria ' Institut des Sciences, Centre Universitaire Morsli Abdellah de Tipaza, Tipaza, 42020, Algeria; Laboratory of Applied Mathematics, Faculty of Exact Sciences, Bejaia University, Bejaia, 06000, Algeria ' Institut des Sciences, Centre Universitaire Morsli Abdellah de Tipaza, Tipaza, 42020, Algeria; Laboratory of Applied Mathematics, Faculty of Exact Sciences, Bejaia University, Bejaia, 06000, Algeria

Abstract: This paper considers a new model of a single server queue subject to two different Bernoulli catastrophes with service lateness which represents the control duration and the service duration where both are in batches of fixed size K. We assume that catastrophes can occur when the server is in service or when it is on vacation. This proposed model is then solved using the appropriate generating functions, which gives steady state probabilities and some performance measures. Numerical results are sketched out to illustrate the effect of the system parameters on the main performance measures. To manage the proposed model with large batches, a Monte Carlo simulation is performed. For this purpose, a Latin hypercube sampling (LHS) generator called 'goLHS' is developed under MATLAB and it has been well tested. The 'rand' and 'goLHS' generators are used to compute the performance measures of the model when the batch size is large.

Keywords: batch service; Bernoulli catastrophe; multiple vacations; service lateness; Monte Carlo simulation; Latin hypercube sampling; LHS.

DOI: 10.1504/IJMOR.2023.128631

International Journal of Mathematics in Operational Research, 2023 Vol.24 No.1, pp.128 - 153

Received: 25 Jun 2021
Accepted: 24 Dec 2021
Published online: 31 Jan 2023 *