Inspired by this question, the asker assumes that the users of a system would very rarely take some action at the exact same time as each other.
Given what I know of making assumptions like that I can guarantee that users would infact do things at the same time. However, I am at a loss as to how you would actually calculate the expected frequency of collisions.
E.g. If we assume each user is taking an action every 3 minutes and our timer is really only accurate to the millisecond, what is the formula for calculating the frequency of collisions?
Given the Wikipedia entry for the birthday problem can be generalised into the formula
Where d is the 180,000 milliseconds and p the probability of a collision.
So with 3 users say, we get a probability of 2.4996E-05 in any given 3 minute period that there is a collision.
The issue then becomes what are the chances of a collision during the day?
There being 60-*60*8/3 = 9600 3 minute periods in the working day, the probability of a collision in any given day then be comes 1-((1-2.4996E-05)^9600) = 21%. A pretty good chance of things going pear shaped.
In 3 minutes you will have 180000 milliseconds. If you know the number of users, you can use the probability of the Birthday Paradox to determine the odds of a collision.
Consider too that your timer might not be accurate to the millisecond, even though it might be measured in milliseconds. Many timers are based on a tick that runs much less than 1000 times a second.