In this paper, we analyze an MX/G/1 with three types of vacation periods including setup
time. Three types of vacations are: N-policy, single vacation, and multiple vacation.
We consider compound Poisson arrival process and general service time, where the
server starts his service when a setup is completed. We find the PGF of the number
of customers in system and LST of waiting time, with which we obtain their means.
A decomposition property for the system size and waiting time is described also.