Closed queueing networks with finite capacities: blocking types, product-form solution and performance indices

Abstract

Queueing network models with blocking are used to represent systems with finite capacity resources, such as production, communication and computer systems. By comparing different types of blocking models, which have been defined in various application fields, the conditions under which equivalence properties hold are derived. These properties are defined as exact transformation functions between steady-state solutions of closed networks with different blocking types. A direct consequence of these equivalence relations is an extension of the class of product-form networks with blocking. This class also includes models where different nodes work under different blocking types and which can be used as models of complex systems, e.g. integrated computer-communication systems. Moreover equivalence relations between blocking types in terms of mean performance indices (i.e., utilization, throughput, mean response time) are discussed.