Abstract
We propose an approximation of the M/G/1 system with finite workload capacity, where those 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 deterministic service time d is small enough. 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.
