Section 9.1. Performance Models

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9.1 Performance Models

Computer performance models are more complicated than the water problem model, but not so complicated as to be inaccessible. The difficult part of performance modeling is that constructing the model requires some mathematical sophistication. But the hardest work has already been done for you. Over the course of nearly a century, scientists have developed a branch of mathematics called queueing theory to model the performance of systems like yours. This chapter describes how to use one particular queueing theory model that reliably answers questions like these:

• How much faster will the application function f perform for n users if I add k CPUs to my system? What if I replace my existing CPUs with units that are p percent faster?

• How much slower will application function f become if I add n users of f into my system's current workload?

• How many CPUs will my system need if we require that p percent of executions of f must complete in r seconds or less?

• How much faster will f perform for n users if we can eliminate p percent of the code path for f ?

• Which is better suited to my needs, a system with m really fast CPUs? Or a system with m + n slower CPUs?

This book contains no derivations of queueing theory formulas. A number of excellent resources are available to help you if you would like to study why queueing theory works. My aim in this chapter is to explain how to use queueing theory as a tool in real-world Oracle performance improvement projects. To this end, this textbook includes a field- tested queueing theory model implemented in Microsoft Excel. This chapter describes the model and how to use it.

If you are interested in the study of queueing theory, there are several excellent references available. My favorites include [Gross and Harris (1998); Gunther (1998); Jain (1991); Allen (1994); and Kleinrock (1975)].

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