Equivalent queueing networks and their use in approximate equilibrium analysis

Most Markovian queueing networks that arise as models of stochastic congestion systems (e.g., communication networks and multiprogrammed computer systems) do not have a product form in their stationary probability distributions, and hence are not amenable to the simplicity of product-form analysis. In this paper we suggest an approach for systematically examining the validity of a class of approximation schemes that is based on the idea of equivalent networks and is used for the approximate equilibrium analysis of nonproduct-form networks. We study equivalent networks, and prove a generalization of the so-called “Norton's” Theorem for closed product-form networks in order to study and generalize the equivalent flow method for the approximate analysis of nonproduct-form queueing networks. We then present the results of a study of the approximation scheme as applied to a type of network model (called a central-server model) that arises frequently in modeling multiprogrammed computer systems. In this model the central server uses a priority discipline, so the resulting network is nonproduct form. This study demonstrates the situations under which the approximation can be expected to do well or poorly and the kinds of errors it introduces.