Mean value analysis for product-form cyclic queueing networks with blocking

The paper analyzes the class of product-form queueing network models with cyclic topology and blocking. For this class of networks, the concept of a dual network was introduced earlier. First we derive a set of properties about the primal and dual performance indices. Then on the basis of the dual network, we are able to define a mean value analysis algorithm to evaluate the mean performance indices of a cyclic network with blocking. The computational time complexity of the algorithm is polynomial in the number of nodes and number of jobs of the network. Finally, we define an equivalence relation for the class of product-form queueing networks with blocking, based on the dual network. This equivalence relation can be used to derive some properties of the equivalent networks, related to the performance indices, which simplify the application of the algorithm.