A Better Crystal Ball

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The Beauty of Large Numbers

The rule of large numbers is the name given to the mathematical property that makes it possible to statistically model complex systems with millions of events or components accurately, even when individual events or components are unpredictable, i.e. describable only in terms of probabilities. For example, physicists can create ‘equations of state’ to model specific forms of matter even though the behavior of individual atoms or molecules is unpredictable. This principle can even be applied to large groups of people. The actuaries at large insurance companies have statistical models that can accurately predict how many individuals out of a large group will die from various causes over the next year, how many will crash their cars, how many will lose their house to fire and so on. Of course these models don’t predict which individuals will experience calamities, but nevertheless are quite useful to help set the price of insurance policy premiums to be commensurate with the risk.

In a similar manner, it is possible to analyze and model the performance of modern processors sufficiently accurately to make useful predictions. The secret is to identify and control, or at least account for, all the factors that determine processor performance. Computers are used in many classes of applications, and these often have their own performance metrics. In a real-time embedded control application the maximum response time to certain events is a critical performance metric. In throughput oriented applications, like banking or airline reservation management, the maximum number of transactions per unit of time may be of most interest (often with a maximum response time provided as a constraint). But the most common concept of computer performance is the time it takes to complete a specific task. That task may be to predict the weather 24 hours into future, simulate airflow over a wing, calculate a chess move, or update a 3D image in an interactive game. The less time it takes a computer to perform the task, the higher its performance is judged to be.

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