A combinatorial approach to performance analysis of a shared-memory multiprocessor

Abstract

A unified approach is proposed for performance analysis of an N × M shared-memory multiprocessor system, consisting of N processors and M memory modules, each of which may be ‘hot’ and/or ‘favorite’. Processors are allowed to have non-uniform memory access patterns and unsatisfied requests are queued up in the buffers of the corresponding modules. The system performance is measured in terms of the effective bandwidth, which is the average number of busy memory modules in one cycle. Our analytical approach, based on the combinatorial arguments as well as queuing models, estimates the bandwidth with good accuracy for arbitrary values of N and M. These estimations tally very well with the simulation results. Since the presence of a hot module almost always leads to an accumulation of memory requests in its direction and thus deteriorates the system performance, one may expect that the hotness should be spread over as many (say, K) modules as possible. However, simulation results showed an upper bound on K beyond which the bandwidth either drops or saturates. From the approximate queuing model, we derive those saturation values in terms of N, M and ph (the probability of accessing a hot module by a processor).