Parametric Estimation of Tail Probabilities for the SingleServer QueueP. W. Glynn and M. Torres Book chapter in Frontiers in Queueing: Models and Applicationsin Science and Engineering [J. H. Dshalalow, ed.] CRC Press, New York, 449462 (1997) In this chapter, we consider the question of how long the arrival process to the singleserver queue needs to be observed in order to accurately estimate the longrun fraction of time that the workload exceeds y. We assume that the arrival process can be modeled parametrically. In such a parametric context, our results suggests that one typically needs to observe the arrival process over a time horizon that is large relative to y^{2}. This conclusion appears to hold regardless of whether the arrival process model exhibits complex dependencies or not.
