How to calculate flow completion time?

[antique refer]

Recently, I was doing some experiments.

But, I had trouble with setting the environment.

My main problem is that if I set the simulation time to 1 second.

And during the entire one second, there will be new flow be initiated base on poison process.

And it'll probability have some flows aren't completed in 1 second simulation time. (Especially, when there are some congestion states in the network) 

So, I do not know how to calculate the average flow completion time, since there are some flows haven't be completed yet.

What is the right way to simulate and calculate the flow completion time?