S_n and a 1 minute delay.
St(n): time person n arrives.
Sts(n): time person n begins being served
Stf(n): time person n is done being served and leaves
Stf(n) = Sts(n) + 1
Sts(n) = max(St(n), Stf(n -1))
Sts(n) = max(St(n), Sts(n - 1) + 1)
Each iteration, the final value is either one more than the previous, or a newly defined value.
St(n) = Sum[j=1...infinity, S_j * I{j <= n}]
In the end, we want the number of people as a function of time. How many people have arrived by time t?
Arrived(t) = Sum[j=0...infinity, 1 I{St(j) < t}]
Using the impulse function to do everything is new to me. Not easily accessible.