This paper treats the threshold policy for an M/G/1 queue with an exception
al first vacation. Under this policy, the server takes a vacation when he f
inishes serving all customers in the system. Upon returning from the vacati
on, the server takes another vacation if the number in the system is below
a certain level; otherwise, he resumes service. The distribution function o
f the first vacation is different from that of the subsequent vacations. Th
ere is a startup cost for starting a series of vacations, a linear customer
waiting cost, and type-dependent vacation reward rates. Renewal theory is
used to develop expressions for the average system cost, and a provably fin
ite search procedure is developed for determining the optimal threshold pol
icies.