A semi-empirical model for maximal LINPACK performance predictions

In general, the maximal LINPACK performance of a large cluster depends on the number of processors, the total memory capacities, the problem size, the block size, the middle-ware of message passing, and the BLAS (basic linear algebra subprograms) library. One must handle these multi-variables factors to predict the performance score. In the paper, we propose a semi-empirical weighting function to improve the performance prediction model for high performance Linpack (HPL) for large clusters. In order to better predict the maximal LINPACK performance, we first divide the performance model into two parts: computational power, and message passing overhead. In the latter part, we adopt Xu and Hwang's broadcast model and introduce a weighting function w to account for the other effects. The difference between scores based on our semi-empirical model and the measured scores are less than 5%. The clusters used in the study include Myrinet-based, Quadrics, Gigabits Ethernet, IA64 or IA32 architectures.