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In this paper we discuss some of the crucial aspects of open restricted queueing networks with special emphasis on the issues of limitations on the capacity of the service provided as well as on the accommodations of the customers. We review the literature bringing together all relevant materials in this problem area. Here we develop the expansion method for approximating the flow process of customers as they travel through this restricted system. Further we present numerical experimentsdoi:10.21172/1.71.014 fatcat:akid62vleja4blh4kedmlpgfrm