Cost optimization and analysis of retrial queues with hybrid vacation policies and fault correction: a metaheuristic approach

¹ Department of Mathematics, School of Arts and Natural Sciences, Joy University, Tirunelveli, India
² Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India
³ Faculty of Education and Arts, Sohar University, Sohar 3111, Oman
⁴ Department of Mathematics and Computer Science, Menoufia University, Shebin El Koum 32511, Egypt

^* Corresponding author: sherifamar2000@yahoo.com

Received: 29 August 2024
Accepted: 29 June 2025

Abstract

This study presents a comprehensive model for the steady state behavior of an M/G/1 retrial queue with fault correction and hybrid vacation policies, tackling real-world challenges such as system breakdowns, repair delays and cost optimization. By integrating retrial mechanisms, fault-repair processes, and hybrid vacations, the model captures the complexity of systems such as telecommunications networks managing call redials or manufacturing facilities balancing machine downtime and auxiliary tasks. Using the supplementary variable technique (SVT), the study derives probability generating functions (PGFs) and steady-state probabilities, enabling the evaluation of critical performance metrics like queue length, orbit size, and server utilization. Additionally, the work introduces a cost optimization framework that minimizes operational expenses through advanced metaheuristic algorithms such as grey wolf optimizer (GWO), bat algorithm (BA), and whale optimization (WO). Practical applications include optimizing customer call centers to manage retries during peak hours or improving repair strategies for industrial equipment to reduce downtime and costs. This research bridges theoretical advances with real-world applicability, offering robust solutions for enhancing efficiency and cost-effectiveness in queueing systems across industries.