Asymptotic approximations for a queueing network with multiple classes

An asymptotic method is described for analyzing the performance of closed, multiple class queueing networks. The networks consist of an infinite server or terminal node, a large number of single-server, fixed-rate nodes. The approximations for the normalization constant or partition function are constructed based on the ray method and are valid for networks with a large number of jobs and nodes. An explicit formula is given for the normalization constant from which the performance measures of the system can be calculated. An extension of the method to a network that includes a load-dependent node is presented. Examples are presented to illustrate the usefulness and accuracy of the approximate formula.