M/M/s와 M/D/s 대기행렬의 점근 근사법 분석을 위한 시뮬레이션 연구

This paper deals with asymptotic approximations analysis of M/M/s and M/D/s queues. For M/M/s queue, we observe economies of scale under the fixed utilization and the fixed probability that customer waits in system, how the average system size vary according to the number of servers (s) increasing. Simulation results show that as s increases, the number of servers who are idling increases, that is, the slack diverges. In addition, through changing the waiting probability under the M/M/s system, this probability was not highly sensitive to the behavior of the system size. And, it is shown that using the relationship between the utilization and the number of servers to handle heavy-traffic regime is only appropriate for the case where the number of customers (k) is one, by observing the effect on the performance of the system with different values of k. For the M/D/s queue, two approximations are used to evaluate the expected system size under the fixed utilization and the fixed waiting probability. Simulations and comparison of these two approximations show that Cosmetatos’approximation performs quite well when s is small and traffic intensity is heavy, but it overestimates the true value for a large s. Meanwhile, the modified approximation gives good results for the steady state count of the system although s grows large.