Approximate solutions to queueing networks with state dependent parameters

A queueing discipline called weighted processor sharing is defined for multiclass queueing networks. This discipline models a first-come, first-serve discipline within each class, with the eligible members of all classes processor shared at the server. The weighted processor shared discipline is shown to result in non-product form networks except for the special case of a single server. Queueing networks with weighted processor shared disciplines are representable as queueing networks with state dependent parameters. Four approximation schemes which may be used to derive the steady state distribution for state dependent queueing networks are presented. Two of the approximation schemes are based on estimates of certain conditional distributions of the model. Conditions are derived under which these estimates yield exact results. In addition, a method for combining these conditional distributions is presented which reduces the storage and time requirements of previous techniques. The second two schemes are based on product form estimates of the steady state distribution. The product form approximations allow more efficient solution algorithms but are not as accurate as the algorithms based on conditional distributions. The approximation schemes are tested on a large number of randomly generated queueing networks. The results indicate that the approximations yield good estimates for the steady state distribution and several performance measures of these networks. The weighted processor shared discipline is used in software level models of computer systems. Reentrant and nonreentrant software modules can be modeled with this technique. An example model of a computer system is presented which incorporates weighted processor sharing. The model is solved with the approximation schemes and the results are compared with a simulation of the model. The approximation schemes are found to adequately model the effects of incorporating reentrant and nonreentrant software modules.