Finiteness of waiting-time moments in general stationary single-server queues (Q1203755)

Consider a stable single-server queue in which the arrivals occur at the epochs of a stationary point process that is not necessarily a renewal process and the service times are i.i.d. random variables \(\{S_ n\}\). Let \(W\) be a random variable distributed as the stationary customer waiting time. A classical result shows that when the arrival process is renewal, for \(\gamma>0\), \(EW^ \gamma<\infty\) if and only if \(ES_ 1^{\gamma+1}<\infty\). Analogues of this result for the case when the arrivals no longer form a renewal process are developed. Two special cases are considered in detail: when the arrivals are generated by a Cox process and when the sequence of interarrival times contains an embedded regenerative phenomenon.