A simple approximation method for workload analyses in some queueing systems with control policies

We consider two systems: M/G/1 with a finite workload capacity and an infinite dam model under P^Mi policy. It is necessary to analyze the workload processes for these systems, which is mostly difficult and complex. An efficient and easy approximation procedure for these systems is provided. Our method is based on the idea that the service time of a customer can be approximated as the sum of small deterministic service times of a batch of customers. This enables us to work with system size processes instead of workload processes. The proposed method turns out to be in excellent agreement with simulation results and exact solution.