- The data is in the form of sampled
**time series**. Instead of throughput X(N) as a function of N users, the data is in the form X(t) and N(t) as functions of time t.

- The data is
**multi-valued**. Within each sample period there were multiple user loads with the same value but different throughput values. For example:Hr X(t) N(t) 7 12 1 7 12 1 8 166 22 8 462 69 8 680 149 9 282 45 9 310 55 9 291 55

**steady state**to a reasonable approximation. This may not always be valid, so we have to keep it in mind. Next comes the multivaluedness. In the above sample data, you can see that hour-9 has two samples with the same user load i.e., N = 55, but different throughput values. Nonetheless, we press on and normalize all the data to the N = 1 value X(1) = 12 in hour-7. That allows us to calculate the relative capacity function C(N) = X(N)/X(1). Here's that looks like using simulated data: The question is, can we fit the USL nonlinear model to this multi-valued data? The answer is yes, because the regression algorithms shouldn't care. After all, that's generally what raw data looks like. Here's how it looks for the simulated data: The solid curve is produced by the USL model. I used Mathematica, but it should work with any regression package. Typically, I never see data in this form because there is usually only a single throughput value X(N) for each user-load value (N) in a controlled test environment. Chalk up another one to USL, and thanks to the reader for raising the question.

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