Parametric Estimation of Tail Probabilities for the Single-Server 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, 449-462 (1997) In this chapter, we 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. 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 y2. This conclusion appears to hold regardless of whether the arrival process model exhibits complex dependencies or not.
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