Performance analysis of an M/G/1 retrial G-queue with balking, optional service and general retrial policy

Department of Mathematics, National Institute of Technology Raipur, Raipur 492010, Chhattisgarh, India

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 11 March 2025
Accepted: 7 April 2026

Abstract

This study examines the steady-state dynamics of an M/G/1 retrial queue that incorpo- rates features such as balking, optional service, negative customer, and general retrial time under a constant retrial policy. The probability generating functions for the orbit length with server status are obtained using the supplementary variable technique at various time epochs. We further extract the orbit size probabilities from these generating functions using the roots method. Additionally, the tail distribution of the orbit length is also presented for different time epochs. We conduct a comprehensive cost analysis to minimize the overall system operation cost. Advanced metaheuristic techniques such as particle swarm optimization and genetic algorithm are employed to determine the optimal system parameters that minimize the total cost. The impact of various system parameters on performance measures is demonstrated through detailed numerical examples.