Parametric estimation of tail probabilities for the single-server queue

In this paper, the authors consider the question of how long the arrival process to the single-server queue needs to be observed in order to accurately estimate the long-run fraction of time that the workload exceeds y. They assume that the arrival process can be modeled parametrically. In such a parametric context, the present results suggest that one typically needs to observe the arrival process over a time horizon that is large relative to y². This conclusion appears to hold regardless of whether the arrival process model exhibits complex dependencies or not.