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I have difficulty understanding how to use Poisson to represent request arrival rate to a server.

Let's say I collected the number of requests coming in to a server every hour. At a certain hour, the server receives 30000 requests per hour. Then I divided this value by 60 to define the base number of average requests per minute for that hour. The result would be 500 requests/min. But how do we represent the requests submitted at each minute, following a Poisson distribution using the base number requests/min for the hour as the average?

The question itself is very confusing to me as I have no background on probability and statistics. I tried to apply this using the Poisson distribution generator on the Internet but I do not know what is the lambda and x (the events if I am not mistaken) supposed to be.

cathy305
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1 Answers1

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Poisson distribution has only one parameter - intensity $\lambda$. In your case $\lambda$ is $30000\;hr^{-1}$ or $500\;min^{-1}$ or $25/3\;s^{-1}$, the only difference is time units. Your process in homogeneous, so for any time interval $[T; T + t]$ you have the probability of observing exactly $n$ requests equal to

$$ \frac{(\lambda t)^n}{n!}e^{-\lambda t}. $$

For example, probability to receive exactly $12$ requests during any $2$-second interval would be

$$ \frac{(25/3\cdot 2)^{12}}{12!}e^{-25/3\cdot 2} \approx 0.05541. $$

Is this what you were looking for?

fanvacoolt
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  • So, when the question says "represents the requests submitted at each minute, following a Poisson distribution", that means my λ = 500, t = 1, and n could be any value that I want, right? – cathy305 Jun 28 '18 at 14:59
  • Yep, if you have requests arriving as per Poisson process, you can get probability of receiving any number $n$ of requests during time interval of length $t$ from formula above. This is true for homogeneous process, when your intensity $\lambda$ doesn't change in time. Poisson process might also be non-homogeneous, when $\lambda$ is a function of $t$ - say, with your server, you receive more requests during daytime, than during night hours. This is a little more complicated. – fanvacoolt Jun 28 '18 at 17:56