Probability Question

TCARobb

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Sep 13, 2007
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We’re trying to determine the number of users we can have on our site on any given time without exceeding the maximum concurrent clicks the system can support.

Here is the data I have.

Our system can support 90 simultaneous clicks.

The request time for each click takes 1 second.

On average, users make one click every 200 seconds.

This means that, if we had an even distribution, our system could support 90 * 200 (18,000) users at any given time. We know that we will NOT have an even distribution.

So the question is; is there a formula that would help us determine how many users could be on the system at any given time before 90 of them were to click at the same time?

I know there is a chance (however small) that 90 users could click at the exact same time and use up all 90 connections. I’m looking for some kind of number that works within the bounds of probability. Maybe something like, “There’s a 99% chance that you with 9,000 users on the system you would not exceed 90 concurrent clicks.”

Thanks for your help!
 
I believe the distribution is a rayleigh distribution

probability[x]=xe^-x^2/[2s^2]

distribution[x]=1-e^-x^2/[2s^2]

Arthur
 
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