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.
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?