Performance Analysis and Cost Optimization of an M/M/1 Queue with N-Policy and Working Breakdown

This paper examines the impact of operational breakdown in an $$\varvec{M}\varvec{/}\varvec{M}\varvec{/}\varvec{1}$$ queueing system with $$\varvec{N}$$ -policy. The system is initially idle. Once $$\varvec{N}$$ customers have arrived, it begins to provide service, which continues until the system becomes empty. An exponentially distributed pre-service task is introduced following each idle period. Subsequently, the server may encounter breakdown during busy period, wherein it continues to operate at a slower pace. We establish a stability condition for the existence of a steady state, and using the probability generating function method, we obtain the steady state probabilities in closed form. Key performance measures are then derived. Numerical examples demonstrate the variations in system performance, and performance metrics are validated through simulation using Arena software. A cost function is formulated, and the particle swarm optimization algorithm is applied to reduce the overall cost by determining the optimal decision variables. Furthermore, different parameters are investigated to analyze how they influence the anticipated overall cost. The optimization results highlight that the service rates surpass the customer arrival rate, while an optimal service rate ensures efficient operation. Additionally, an application related to wireless sensor networks and robotic manipulators is discussed.