Single Server Markovian Queue With Time‐Homogeneous Partial and Complete Breakdowns and Cost Optimization by Genetic Algorithm

Abstract

This paper investigates the steady‐state performance of an queueing system subject to random and time‐homogeneous partial and complete server breakdowns. Under partial breakdown conditions, the server continues to provide service at a reduced rate, while service is entirely suspended during complete breakdown periods. By applying the Probability Generating Function (PGF) methodology, the joint probability distribution of the server state and the number of customers in the system is obtained. Several key performance measures are derived and numerically illustrated to highlight the influence of system parameters on overall performance. In addition, a structured cost model is developed to account for service, breakdown, and holding costs. A Genetic Algorithm (GA) is then employed to optimize the cost function and identify effective operational strategies for handling partial and complete breakdowns.