On Sat, Jun 5, 2021, 1:58 PM Karl <[1]gmkarl@gmail.com> wrote:

   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."

References

   1. mailto:gmkarl@gmail.com