Transforming PEPA Models to Obtain Product Form Bounds

Abstract

This report presents a detailed study of some examples expressed in the PEPA formalism. It has previously been shown that some sub-classes of PEPA models have a product form solution, making them amenable to efficient solution. The models we consider here do not have product form solution because the necessary structural conditions are not satisfied. We demonstrate transformations of these models, based on modifications of the PEPA expressions representing them, which result in new models which are product form. Furthermore we investigate the extent to which performance measures derived from the modified models can be regarded as approximations of the measures pertaining to the original model. We show that if a modeller is interested in one particular performance index, he or she may construct two modified models with product form solutions whose values of this measure are lower and upper bounds of the measure of the initial model.