On the Product Form Solution of a Class of Multiple Bus Multiprocessor System Models

Recursive relations are derived for the exact computation of the steady-state probability distribution of some queuing models with passive resources that can be used to analyze the performance of multiple-bus multiprocessor system architectures. The most general case that can be shown to admit a product-form solution is described, and a recursive solution is obtained taking into account, considering different processor access rates, different memory selection probabilities, and a first-come-first-served bus scheduling policy. Several simpler cases allowing easier model solutions are also considered. Numerical evaluations for large computing systems with nonuniform memory references show the usefulness of the results.