Analytic modeling of cache coherence based parallel computers

In this paper, we propose an analytic model using a semi-markov process for parallel computers which provides hardware support for a cache coherence mechanism. The model proposed here, the Semi-markov Memory and Cache coherence Interference model, can be used for the performance prediction of cache coherence based parallel computers since it can be easily applied to descriptions of the waiting states due to network contention or memory interference of both normal data accesses and cache coherence requests. Conventional analytic models using stochastic processes to describe parallel computers have the problem of numerical explosion in the number of states necessary as the system size increases even for simple parallel computers without cache coherence mechanisms. The number of states required by constructing our proposing analytic model, however, does not depend on the system size but only on the kind of cache coherence protocol. For example, the number of states for the Synapse cache coherence protocol is only 20, as is described in this paper. Using the proposed analytic model, we investigate several comparative experiments with widely known simulation results. We found that there is only a 7.08 % difference between the simulation and our analytic model, while our analytic model can predict the performance of a 1,024 processor system in the order of microseconds.