Conditions for finite moments of waiting times in \(G/G/1\) queues (Q1339070)

\textit{J. Kiefer} and \textit{J. Wolfowitz} [Ann. Math. Stat. 27, 147-161 (1956; Zbl 0070.366)] proved that the \(\gamma\)-th moment of the stationary waiting time \(W\) in a stable \(GI/GI/1\) queue is finite if and only if the \((R+1)\)st moment of the service time is finite. The authors find sufficient conditions for the \(\gamma\)-th moment to be finite in a stable \(G/G/1\) queue with dependent service and interarrival times. This extends the earlier work of the first and third authors [Ann. Appl. Prob. 2, No. 4, 987-1008 (1992; Zbl 0772.60073)] on \(G/GI/1\) systems.