Performance Optimization of M/M/1 Queues with Working Vacations and Server Breakdowns in Wireless Communication Systems

This paper presents a unified analytical and simulation framework for optimizing the performance of M/M/1 queueing systems that incorporate differentiated working vacations, server breakdowns, and customer balking behavior. Other features of the solution include dynamical transitions between full-service mode, two levels of working vacation (with reduced service rates) phases, and random breakdown-repair cycles. Customers arrive via a Poisson process and decide to join or balk based on the server's current state. Embedded Markov chains, probability generating functions, and Matlab based discrete event simulation are applied to analyze key performance metrics, including average waiting time, queue length, and server utilization. A particle swarm optimization (PSO) algorithm is used to identify parameter configurations that minimize congestion and delay. Application scenarios in 5G/6G networks and service platforms demonstrate how adaptive vacation scheduling and resilience strategies improve energy efficiency and throughput. The results offer valuable information for performance tuning in resource-constrained telecommunication systems.