A new perspective on the normalization of invariant measures for loss networks and other product form systems

Loss networks have proved to be a vital tool in the study of telecommunication networks, computer performance, and resource allocation problems. For a large subset of these models, the invariant measure is of a product form. The existence of efficient procedures to normalize a product-form invariant measure is essential for analysis of the underlying system. ury et al. [1—4] have recently presented a number of algorithms based upon Fourier analysis for the normalization of product-form invariant measures for specific systems. Bean and Stewart [5] discussed related work for the normalization of product-form invariant measures for closed queueing networks. In this paper, we present a simple unifying framework within which to study these algorithms. This framework is significant as it suggests a number of extensions to these algorithms and simplifies their derivation.