Date of Award

Spring 1-1-2011

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Mathematics

First Advisor

Elizabeth Bradley

Second Advisor

James Meiss

Third Advisor

Bob Easton

Abstract

Recent work in the field of dynamical systems provides evidence that computer systems are nonlinear-deterministic dynamical systems. This implies the existence of a deterministic update rule, which, in turn, implies the existence of a deterministic forecasting rule for the state variables of a running computer. Even a short-term prediction of these quantities, if accurate, could be effective in tailoring system resources on-the-fly to the dynamics of a computing application. For example, a good prediction of processor load could allow a computer to increase its energy efficiency by dynamically turning off unused CPUs, and then turning them back on based on the programs predicted needs. To explore this, I use a custom measurement infrastructure, delay-coordinate embedding and nonlinear time-series analysis to forecast processor load and cache performance of a set of simple C programs running on an Intel Core2 Duo. This proved to be quite effective. However, the use of traditional embedding techniques `on the fly' is impractical due to the time required to correctly perform the processing and post-processing of the data. My alternative to this is to use arbitrary low-dimensional projections. While this is not consistent with the requirements in the current literature, recent work by Mischaikow suggests that this alternative might work. I verified this conjecture, showing that forecasts based on two-dimensional projections are largely as effective as strategies that use the full embedded dynamics. This is in contrast to the current view in the nonlinear dynamics community that a one-to-one delay map is sufficient for successful prediction using delay coordinate embedding. My results suggest that this may not be a necessary condition. The success of the projection-based forecasting schemes brings into questions the need for full topological conjugacy in forecasting schema. The results presented here suggest ways of improving computer design at a systems level; they also provide evidence to support the use of semi-conjugacies in forecasting schemes.

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