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))

Recursively defined.  Can we reorient the process of recursion to define it as a sum with conditions?  Probably somehow?