Paper Title
Optimization of the Randomized Controlling Arrivals for a Finite Queue with Working Breakdowns and Start up

This paper analyzes a randomized control 〈􀢖, 􀡲〉-policy of an M/M/1 queue with working breakdowns and start up. Customers are allowed to enter the system with probability􀢖 or customers are stillunable to enter the system with probability (􀫚 − 􀢖)when the number of customers decreases to a certain threshold value 􀡲.We assume that the serveris subject to working breakdowns only when there is at least one customer in the system. We apply an efficient Maple program to compute the steady-state probabilities and various system performance measures. A cost model is constructed to determine the optimal threshold, 􀡲, and the joint optimal values 􀣆􀫚 and 􀣆􀫛 for the fast and slow service rates simultaneously by means of PSO algorithm. Keywords - Queue, F-Policy, Working Breakdowns, Start up, Pso