Asymptotic expansion for large closed queuing networks

Reviewer: Jean Walrand

The authors address the numerical evaluation of the partition function of a product-form network with one infinite server queue and a large number of single-server queues and customers. Using simple limiting arguments and assuming that the nodes can be divided into classes with nearly equal utilizations, they derive a partial differential equation that approximates Buzen's recursive formula. The authors then employ the methods of characteristics and asymptotic expansions. Simulations are used to evaluate the results and compare them to those of McKenna and Mitra. The paper proposes a novel approach to the important problem of evaluating partition functions. The case of a large number of single-server nodes may find many applications. Some familiarity with the method of characteristics is helpful when reading the paper. References are prov ided.