We obtain sufficient conditions for the finiteness of the moments of the single-server queue busy period in discrete and continuous time. In the cases of power and exponential moments, the conditions found coincide with the known necessary ones.
S. Foss, A. Sapozhnikov, (2004) On the Existence of Moments for the Busy Period in a Single-Server Queue. Mathematics of Operations Research 29(3):592-601.
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