We propose a probabilistic characterization of network traffic. This characterization can handle traffic with heavy-tailed distributions in performance analysis. We show that queue size, output traffic, virtual delay, aggregate traffic, etc. at various points in a network can easily be characterized within the framework. This characterization is measurable and allows for a simple probabilistic method for regulating network traffic. All of these properties of the proposed characterization enable a systematic approach for providing end-to-end probabilistic QoS guarantees.