Particle swarm optimization of a single server retrial queue with balking and immediate feedback under Bernoulli working vacation

Year 2025, Volume: 54 Issue: 5, 1976 - 2006, 29.10.2025

Kalaiselvi J , M C Saravanarajan

https://doi.org/10.15672/hujms.1696033

Abstract

In this study, we investigate a single-server retrial queueing system that incorporates balking, immediate feedback, and a Bernoulli working vacation policy. Customers arriving to find the server busy, under repair, or on working vacation may balk; otherwise, they either join the orbit or receive immediate service if the server is available. Upon completion of the service, the customer can request a finite number of immediate feedback services. When the orbit is empty after the completion of a service, the server initiates a working vacation, serving at a reduced rate. If customers are present in the orbit at the end of the vacation, the server resumes normal operation. If the system is empty, the server remains idle or continues the vacation. We analyze the ergodicity conditions to ensure system stability and derive the stationary distribution of the underlying Markov process. Several key performance measures are computed. Furthermore, a comprehensive cost function is developed and optimized using metaheuristic approaches, including particle swarm optimization and the genetic algorithm. The convergence behavior and optimization results are illustrated through graphical analysis, offering insight into improving the efficiency of complex retrial queueing systems.

Keywords

Balking , Bernoulli working vacation , immediate feedback , particle swarm optimization , retrial queue

Ethical Statement

NIL

Supporting Institution

VIT, Vellore, Tamil Nadu, India.

Project Number

NIL

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