Traffic Bursts appear to be more pronounced recently and have major consequences for network Quality of Service. We investigate the extreme behavior of bursts and quantify the probabilities of these large bursts. Taking Bellcore internal Ethernet traces as an example, we applied Generalized Extreme Value model over block maxima. The analysis reveals that traffic burst maxima follows GEV model with negative shape parameter. Traffic bursts are in the domain of attraction of Weibull distribution. Our result confirms the conclusion of Norros of storage fed with Gaussian self-similar input. © 2009 IEEE.