Calculation of Open Queueing Networks

Summary

One way to calculate the behavior of computer networks is simulation. It allows to model nearly all problems but it may be rather difficult to prove the correctness of the solution. Therefore the results must be validated by measured values for example. On the other hand an analytical solution that is easier to validate exists for networks that base on Markov processes. A subset of them is characterized by a ‘product form solution’ that is supported by a lot of computational algorithms and that is applicable to a large number of problems. The paper deals with open networks that involve summations of infinite numbers of items. It presents a modified algorithm for an exact or an arbitrary well approximated computation of important performance measures. In order to decrease the computation time without loss of accuracy, special properties of the probability density functions, state aggregation and network decomposition are used.