X(t) ~= (number of people who have arrived between 0 and t) - (number of people who have been fully served between 0 and t)
Both of these values are calculable.
S_n is the number of minutes that pass after person (n-1) arrives, before person n arrives.
So the total number of people who
"Let me work the problem!" says DistractionBot. "Oops, I messed it up. Ummm it had to do with a total number of people."