A class of queueing models is considered here which in general do not give rise to a product from solution but can nevertheless be decomposed into their components, subject to a property referred to as quasi-separability. Such a decomposition gives rise to expressions for marginal probabilities which may be used to derive potentially interesting system performance measures, such as the average number of jobs in the system. It is very important that some degree of confidence in such measures can also be given, however, we show here that it is not generally possible to calculate the variance exactly from the marginal probabilities. In this paper a simple approximation for the variance of the state a system of quasi-separable components is presented and evaluated.
Information from pubs.doc.ic.ac.uk/decomposing-queues.