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

Abstract
This paper analyzes a randomized control 〈p,F〉-policy of an M/M/1 queue with working breakdowns and startup.Customers are allowed to enter the system with probabilityp or customers are stillunable to enter the system with probability (1-p)when the number of customers decreases to a certain thresholdvalue F.We assume that the serveris subject to workingbreakdowns only when there is at least onecustomer in the system.We apply an efficient Maple program to compute the steady-state probabilities and various system performance measures. A costmodel is constructed to determine the optimal threshold, F, and the joint optimal values μ_1 and μ_2 for the fast and slow service rates simultaneously by means of PSO algorithm. Keywords - Queue, F-policy, working breakdowns, startup, PSO