On Sat, Jun 5, 2021, 3:44 PM Karl <[1]gmkarl@gmail.com> wrote:

   On Sat, Jun 5, 2021, 3:42 PM Karl <[2]gmkarl@gmail.com> wrote:

   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.

References

   1. mailto:gmkarl@gmail.com
   2. mailto:gmkarl@gmail.com