A survey of product form queueing networks with blocking and their equivalences

Queueing network models have been extensively used to represent and analyze resource sharing systems, such as production, communication and information systems. Queueing networks with blocking are used to represent systems with finite capacity resources and with resource constraints. Different blocking mechanisms have been defined and analyzed in the literature to represent distinct behaviors of real systems with limited resources. Exact product form solutions of queueing networks with blocking have been derived under special constraints for different blocking mechanisms. In this paper the authors present a survey of product form solutions of queueing networks with blocking and equivalence properties among different blocking network models. By using such equivalence they can extend product form solutions to queueing network models with different blocking mechanisms. The equivalence properties include relationships between open and closed product form queueing networks with different blocking mechanisms.