  We present a new tool, GPA, that can generate key performance measures for
very large systems. Based on solving systems of ordinary differential equations
(ODEs), this method of performance analysis is far more scalable than
stochastic simulation. The GPA tool is the first to produce higher moment
analysis from differential equation approximation, which is essential, in many
cases, to obtain an accurate performance prediction. We identify so-called
switch points as the source of error in the ODE approximation. We investigate
the switch point behaviour in several large models and observe that as the
scale of the model is increased, in general the ODE performance prediction
improves in accuracy. In the case of the variance measure, we are able to
justify theoretically that in the limit of model scale, the ODE approximation
can be expected to tend to the actual variance of the model.
