대기 부하량에 제한이 있는 M/G/1 시스템의 근사법

An approximation of the M/G/1 system with finite workload capacity

In this paper, we propose an approximation of the M/G/1 system with finite workload capacity, where customers whose admission to the system would increase the workload beyond a prespecified finite capacity limit are not accepted. Our approximation method is based on the idea that the service time of a customer in the M/G/1 system can be approximated as the sum of service times of a batch of customers in the $M^{X}/d/1$ system where the service time is deterministic and very small. That is, the original service time is discretized and approximated by the batch size. We exemplified our method by obtaining the average workload of the M/M/1 system by means of the $M^{X}/d/1$ system, where the batch size is geometric. In addition, the approximate blocking probabilities of the M/M/1 and $M/E_{k}/1$ system with finite workload capacities are sought. The proposed method turns out to give a good approximation, which is compared with a simulation.