Fast approximate solution of multiprogramming models

Abstract

Queueing network models of computer systems with multiprogramming constraints generally do not possess a product-form solution in the sense of Jackson. Therefore, one is usually led to consider approximation techniques when dealing with such models. Equivalence and decomposition is one way of approaching their solution. With multiple job classes, the equivalent network may be viewed as a set of interdependent queues. In general, the state-dependence in this equivalent network precludes a product-form solution, and the size of its state space grows rapidly with the number of classes and of jobs per class. This paper presents two methods for approximate solution of the equivalent state-dependent queueing network. The first approach is a manifold application of equivalence and decomposition. The second approach, less accurate than the first one, is a fast-converging iteration whose computational complexity grows near-linearly with the number of job classes and jobs in a class. Numerical examples illustrate the accuracy of the two methods.