Isotonic Additive Models for Characterizing Computer Memory Systems

Ilya Gluhovsky, Sun Microsystems Laboratories


Design of a memory system is the first-order effect on performance.  The memory
system includes a multilevel cache hierarchy and the main memory.
Conventionally, a memory system under consideration is simulated to obtain a set
of the corresponding cache miss and writeback rates to be used as inputs to a
memory system model.  However, due to experimental constraints, much of feasible
design space remains unexplored.

We propose an interpolation/extrapolation technique to be used for prediction of
unsimulated cache rates.  The latter are constrained to be nonnegative and
monotone in some predictors.  We first select the best additive model (with
interactions) to explain the data.  Next we apply a monotonizing transformation
to the fit itself.  Since interpretation is crucial for understanding
architectural tradeoffs, we maintain the same additive form.  The monotone fit
matches the original fit as closely as possible and the additive components are
also matched as closely as possible without changing the monotone fit.

Our technique addresses the issues of excessive roughness, overfitting and
implementational complexity present in other methods.  It admits a broader
class of modeling methods.  It is still implementationally easy to monotonize
along a subset of predictors.