A Simple Concept for the Performance Analysis of Cluster-Computing

There seems to be a lack of reliable thumb rules to estimate the size and performance of clusters with respect to applications. Since modern cluster architecture is based on multi-cores we follow a concept derived by S. Williams et. al. for the analysis of such systems. The performance is described by the dimensionless speed-up in dependence on important hardware and application parameters. The hardware parameters are the number and the theoretical performance of each processing unit and the bandwidth of the network. The application parameters are the total number of operations performed on a number of bytes and the total number of bytes communicated between the processing units. In order to test our theoretical concept we apply our model to the scalar product of vectors, matrix multiplication, Linpack and the TOP500-list.