Markov Models for Multiple Bus Multiprocessor Systems

Markovian models are developed for the performance analysis of multiprocessor systems intercommunicating via a set of buses. The performance index is the average number of active processors, called processing power. From processing power a variety of other performance measures can be derived as dictated by the specific processor application. Exact models are first introduced and are illustrated with a simple example. The computational complexity of the exact models is shown to increase very rapidly with system size, thus making the exact analysis impractical even for medium size systems. To overcome the complexity of computation, several approximate models are introduced. The approximate results are compared with the exact ones and found to be surprisingly accurate for a wide range of configurations. Simulation is used to validate the analytic models and to test their robustness.