Cost Analysis of a two-phase Queue System with Randomized Control Policy

In this paper, we study the optimal management problem of a M/M/1/K queueing system with -policy, where all arriving customers demand the first essential service and some of them may further demand an additional optional service. When the number of customers reaches the system's capacity K, no further arriving customers are allowed to enter the system. Customers are allowed to enter the system with probability p or the customers are still unable to enter the system with probability (1-p) as the queue length decreases to a certain threshold value F. By applying the birth and death technique, some important performance measures are derived. We developed a cost model to determine the optimal control -policy at a minimum cost. A sensitivity analysis is also conducted to investigate the effect of changes in the system parameters on the expected cost function.