An operator-analytic approach to product-form networks

The product-form stationary distributions of open Markovian networks of queues are characterised in terms of eigenvalues and eigenvectors of appropriately defined rate matrices in an operator-analytic formulation. For a Jackson network, the conditions enforced by such a formulation are shown to be equivalent to the conditions imposed by the standard traffic equations. Generalisations to a wider class of product-form networks are also given.