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I have a web-site, and I found the distribution of user number in a day have an obvious pattern. Not only my own site, I see almost all usage distributions of web-site fit model like this. They look like sine wave. I would like to use the model to predict how many total bandwidth I will use if I know the peak of usage. What kind of formula do you think it fits the distribution best?

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migrated from math.stackexchange.com Jun 3 '11 at 9:43

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You have time series data and one develops an equation for intra-day usage which may use either an auto-projective ARIMA model or a set of fixed dummies (23 in number) to predict hourly expectations. One has to be concerned with detecting "unusual data" so that your model/parameters reflect the main body of data and not being impacted by the exceptions. You might also be concerned with inter-day activity as different days of the week may have different effects. I have found that there are also interaction effects where the hourly distribution depends on the day-of-the-week. Additionally there may be known events/holidays that need to be accounted for. Upon building a suitable model , the residuals provide an estimate as to the expected variability yielding a "safety stock" which can be useful in guidance. The suggested statistical model for this is called a Transfer Function which is a hybrid between regression and ARIMA modelling.

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