Simple Models of Memory Interference in Multiprocessors, Part II: Asymptotics and Limit Theorems

A basic widely used stochastic model of memory interference in multiprocessors is considered. No useful closed form solutions are known for the key performance measures such as the effective memory bandwidth. In part I of this paper an approximate analysis of the model and several generalizations is presented, along with experimental results showing the approximations appear to be accurate. In this part, we consider the behavior of the model as the number of processor and memory modules become large, with their ratio tending to a limit. We prove that the approximations become exact in this limit.