On the Balance between Accuracy and Robustness for Online Estimation of Delay Tail Probability

In the Internet, premium services require to keep a very small delay tail probability with respect to some delay threshold. Such a small probability is difficult to measure in real time due to the large measurement variability. Practical approaches measure the traffic statistics instead and derive the tail probability by queueing analysis. In this paper, we show that an accurate estimator based on in-depth queueing analysis can amplify the measurement errors and cause robustness problem. A simple and less-accurate estimator is proposed to achieve much better robustness while still keeping a satisfying accuracy. The balance between the accuracy and robustness is thus not only an issue of parameter configuration for an estimator, but also a crucial point in designing the method for online estimation. This insight illuminates a potential new way for the development of online tail probability estimators.