For a GI/G/c queue, a full busy period is an interval that begins when an arrival finds c − 1 customers in the system, and ends when, for the first time after that, a departure leaves behind c − 1 customers in the system. We present a probabilistic proof of conditions for full busy periods to have finite moments. For queues that empty, this result may be deduced from results in the literature, but our proof is much easier. For queues that do not empty, our proof still applies, and this result is new.
