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On-line traffic, including conversational call, videoconference call, and live video, is becoming an important kind of traffic in Internet. On-line traffic has no traffic trace pre-recorded and has little information available in advance, which means it is hard to be characterized by existing deterministic traffic models. In order to anticipate and capture the burstiness property of on-line traffic, we proposed a confidence-level-based statistical bounding interval-length dependent (S-BIND) traffic model. However, S-BIND's statistical property prevents it from being policed by existing deterministic regulators. In this paper, we design a state-dependent token bucket based statistical regulator to police the S-BIND modeled traffic. Simulation results show that the newly designed statistical regulator outputs traffic with S-BIND parameter values below or at most 5% above the desired rates when the original input traffic has rates up to 85% higher than the desired rates. The regulated traffic can prevent the QoS degrading in other co-existing traffic and is still able to receive its reserved QoS service.