# Probability of users polling a server at the same time

Discussion in 'Scientific Statistics Math' started by Chris, Nov 25, 2011.

1. ### ChrisGuest

Hi,

I'm trying to model the probability of users polling a server at the
same time.

The scenario is we have 500 concurrent users which poll a server
system. Lets assume the poll takes 1 second. The polling period is 2
minutes, so every user will poll the server once every 120 seconds and
continue to do so. Assuming that they do not all connect (i.e. start
polling) at the same time. What is the probability within a 1 hour
period, that any of these users will poll at the same time?

How does this probability change when we change the polling period,
for example from 2 minutes, to 3 or 4 minutes?

Thanks for any help,
Chris.

Chris, Nov 25, 2011

2. ### Rich UlrichGuest

It looks like there are several red herrings here - clues that
actually don't help the problem at all.

Polling "once every 120 seconds" sets up an interval.
One user, it says, polls for 1 second out of every 120.

There are 500 "concurrent users" but they might not
start at the same time. Well, "concurrent" says that
they are operating at the same time. 500 polls every
120 seconds is 4+ polls per second. And it is *unavoidable*
that there will be multiple polls at the same time "within
a 1 hour period" or even "within every 2 minute period"
while there are 500 concurrent users.

The number polling at any given instant is Poisson, with
the mean as you figure it.

Rich Ulrich, Nov 26, 2011