Multiclass queueing networks with population constrainted subnetworks

A Multiclass Queueing Network model (MQN) is partitioned into a set of disjoint subnetworks. Population constraints are applied to each subnetwork such that within each subnetwork each population chain is either subject to an individual population constraint, or a group of chains may be subject to a common (shared) population constraint. Such population constraints are necessary in order to model multiprogramming level constraints in mainframe computer systems and window flow control mechanisms in computer communication networks. A computationally efficient approximate solution method is developed for solving MQN's with population constraints. Each subnetwork is reduced to a single approximately flow equivalent composite centre by assuming that the effect of other chains on a given chain can be adequately represented by their average customer populations. The accuracy of the population constraint approximation is compared against previous techniques by applying it to a set of test cases for which simulation solutions have previously been reported. The accuracy of the approximation technique is found to be good and in general is an improvement over previously published concurrency constraint approximations.