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My company has a software system, which, amongst other things runs payroll for its client companies. In the near future, the number of companies running payroll will jump from 100 to 3000. I'm trying to investigate whether the system will be able to cope with the new load.

I can do a bit of basic analysis on the logs and see that typically on the busiest days of the month, there are about 5x as many payroll runs as on the average day. The peaks could be because there is a group of companies which are connected and all run payroll on the same day, or it could be because if the numbers come out wrong, they have to make corrections and run payroll again until it's right.

When the new companies come online, obviously the average load will increase by 2900%, as almost all companies only run payroll once a month. What I'm trying to estimate is how big the peaks are likely to be. Clearly as volume increases I would expect to see a smoothing effect, and the load charts to look less 'peaky'.

Is there a good method for estimating the peak size, or a confidence value for the peak size, or can I only guess? Even just a point in the right direction would be great.

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First, have you tried plotting number of payroll runs/day, as a histogram? I would guess that your data might look a bit like some form of gamma distribution. If so, you could try to fit such a distribution to your data.

Then, if you feel it's safe to assume that the distribution of payroll runs/day is unlikely to change as clients go up (this is almost certainly untrue, but is probably close enough to the truth to get a decent estimate), you can use this distribution to estimate the probability of getting hit by a heavy run day (i.e. the probability of getting a day with 500 payroll runs).

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  • $\begingroup$ My plot of payroll runs per day does look a bit like the gamma distribution, so I'm going to follow that and see where it gets me. $\endgroup$ Dec 4, 2012 at 16:14
  • $\begingroup$ Well I think I've got to the point where I've got a plausible guess. I fitted the cumulative payroll runs per day to the cumulative gamma distribution, and scaled up to get a set of confidence values. $\endgroup$ Dec 5, 2012 at 11:20
  • $\begingroup$ If corrections need reruns isn't your estimate of 2900% on the low side? $\endgroup$ Mar 4, 2013 at 17:32

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