November 2006 B
High Productivity Computing Systems and the Path Towards Usable Petascale Computing
Declan Murphy, Sun Microsystems, Inc.
Thomas Nash, Sun Microsystems, Inc.
Lawrence Votta, Jr., Sun Microsystems, Inc.
Jeremy Kepner, MIT Lincoln Laboratory

2. The Productivity Figure of Merit

In factoring out the productivity contributors, we take an approach that, like the blind men and the elephant, focuses on what can be measured at defined parts of the beast and builds to a picture of the whole productivity equation for a system in a particular environment. This assumes that our elephant is reasonably smooth and predictable between those points we can feel with our measurements. 7

We start with

Productivity = Utility/Cost

We expand the utility into system level and job level components


As a convention, we use the letters U, E, A, R, C to denote variables of utility, efficiency, availability, resources, and cost, respectively. The subscripts indicate the variables that address system level (including administrative and utility) and job level factors.

We recognize that some aspects of the system level efficiency will never be amenable to measurement and will always require subjective evaluation. Only subjective evaluation processes can address the first two variables in the utility numerator. In principle one can measure the last four variables and the HPCS research program is addressing such measurements.

We have been emphasizing that this is to be a figure of merit, including estimates and evaluations of what we expect the productivity output of an installation to be. For clarity, in explaining this formulation, we will start by talking as if we know what happened over the lifetime, as if we are doing a post-mortem. We will mention in passing how the components relate to ongoing work on productivity estimators. We will return to discuss these estimators in more detail in Section 4.

The goal of those optimizing utility at the job level is to maximize resources they can effectively apply to their problem. This will enable them to bring their project to a successful conclusion with higher utility (larger scale or finer granularity solutions or higher throughput of data intensive problems) or more rapidly (allowing more problems of similar utility to be accomplished within the lifetime of the resources). It is “not in their job description” to address the relative utility of their problem compared to others (though they may be inclined to do so). So, we consider utility at the job level, Ujob, to be just the cost ($) of the resources that they have effectively used, and the job level efficiency Ejob = Ujob/Csys, with Csys the total lifetime system cost. As defined below and in the Appendix, Ujob and Ejob are averaged over all jobs.

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Reference this article
"A System-wide Productivity Figure of Merit," CTWatch Quarterly, Volume 2, Number 4B, November 2006 B. http://www.ctwatch.org/quarterly/articles/2006/11/a-system-wide-productivity-figure-of-merit/

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