We have developed a simple theoretical model enabling us to estimate the performance, given the raw performance and the workload. This model gives the estimated performance, p, as a function of the workload, w; the raw performance, P; and the number of processors on the machine, n:
To validate this model, we performed several experiments.
The results of the experiments are
plotted in Figure 2,
which shows
the ratio 
versus the workload of the machine.
Each measure gave one of the ``+'' marks.
We then computed the mean
of all the measures for every value of the workload. An asymptotic interpolation
of these mean values is shown with a continuous curve. Our theoretical model
is shown with the dashed line.
In Figure 2a, we can see that the theoretical model is close to the experimental results. In Figure 2b, because the machine has four processors, the beginning of the curve is a flat line, and the performance begins to drop when the four processors are loaded. Our model is less accurate and always optimistic because it does not take into account any operating system delay to manage the different processors. The widely varying behavior of the four-processor machine comes from the fact that the operating system makes process migrations between the processors.
versus workload