Asymptotic analysis of memory interference in multiprocessors with private cache memories

A closed Markovian queueing network model of a multiprocessor system with a two-level memory hierarchy is considered. Performance measures are introduced and obtained from the partition function. With a special structure of branching probabilities the network model is reduced to a nonlinear machine interference model. Asymptotic representation of the stationary distribution for heavy traffic conditions in the latter model is used for deriving approximate formulas for the performance measures when the number of processors and memory modules is large. For normal usage the approximations are obtained from asymptotic expansions of the partition function.