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Analysis and Design of Loop Service Systems via a Diffusion Approximation

In a loop service system the server cyclically serves a fixed number of peripheral stations. In this paper we consider an operating rule where the server is allowed to service a particular station for a fixed length of time each cycle. Using a diffusion approximation, we obtain expressions for the distribution of the steady state load as well as the expected waiting time at a particular peripheral station. These results are then used to determine the optimal design for the system under a linear cost structure.