Performance Modeling of Shared-Resource Array Processors

This paper presents a Markov chain model to analyze the performance of shared-resource array processors for multiple vector processing. Such a parallel processor contains multiple control units sharing a resource pool of processing elements and operating with multiple single-instruction multiple-data streams (MSIMD). In the steady state, the Markov model corresponds to a two-dimensional Markov chain, which can be expressed by a set of equilibrium equations. An iterative method is developed to solve the Markov chain after projecting the equilibrium equations onto a one-dimensional state space. The convergence rate of the iterative method can be greatly enhanced by choosing starting values corresponding to the approximated analytical results obtained earlier by the authors.