Further results on equivalence and decomposition in queueing network models

This paper addresses three aspects related to the notion of exact equivalence in queueing models. In many cases the parameters of a system equivalent to a given model involve only a small subset of conditional probabilities of the state of the original model given the equivalent one. It is shown that meaningful bounds may be obtained for the conditional probabilities of interest with little computational effort. Such bounds are useful in assessing processing capacities as well as the accuracy of approximate solutions. As a second point it is shown that the notion of exact equivalence may be easily extended to networks with non-exponential servers. This is done for both the methods of supplementary variables and for the imbedded Markov chain technique. Qualitative analysis of approximation methods is also discussed. Finally, numerical methods based on the notion of exact equivalence, i.e. operating on conditional probabilities, are considered.