Two calculations the number of concurrent users.
1. Eric Man Wong
Eric Man Wong published as "Method for Estimating the Number of Concurrent Users" in 2004
$$
C = nL / T
$$
n the total number of users represents the start to the end
L represents the length of time the average user online
T total time indicates the beginning to the end of a long
2. Little's Law
Little's Law states that "the average number of objects in the system is equal to the product of the average time to reach the object of system objects and the average rate stays in the system. --- Baidu Encyclopedia
$$
N=X*R
$$
N represents simultaneously active users in the system, including being processed in the queue and
X represents user rate were arriving in the system, when the equilibrium state is the system throughput (= departure arrival)
R represents the average residence time of each user in the system
3. Examples
There is a forum system, every day there are 500 active users, active users are mainly concentrated in time 19:00 to 12:00, the average person to sign out once, landing 30 minutes long, please establish that system performance test model.
Eric solution using the estimation formula:
Suppose the system back-end maintenance session, then the session is the length of this 30 minutes, L = 30minutes
When the user is already known active length of from 7:00 to 12:00 total five hours, T = 5 hours
Then the number of concurrent users C = n * L / T = 500 * 30 / (5 * 60) = 50
Little's law to use the system to estimate the number of concurrent users:
500've found that the user needs to sign one after another 7 to 12 points this time, the arrival rate of X = 500 / (5 * 60) = 5/3 user / min
30 minutes longer residence time for the user in the system during landing, R = 30 minutes
Then the system while being concurrent service is N = X * R = 5/3 * 30 = 50
Eric let's break down the estimation formula from another angle:
C = n * L / T can be expressed as C = (n / T) * L
n / T and is not the same as in the first step we have just above Little is calculated arrival rate of X.
And R L is not it? They are equivalent to the length of the session.
That is C = (n / T) * T = X * R = N
Conclusion: that from the above, Eric's estimation formula with Little's law are equivalent.