In this paper, we constract a new dynamic model for the Token Bucket (TB) algorithm used in computer networks and use systems approach for its analysis. This model is then augmented by adding a dynamic model for a multiplexor at an access node where the TB exercises a policing function. In the model, traffic policing, multiplexing and network utilization are formally defined. Based on the model, we study such issues as (quality of service) QoS, traffic sizing and network dimensioning. Also we propose an algorithm using feedback control to improve QoS and network utilization. Applying MPEG video traces as the input traffic to the model, we verify the usefulness and effectiveness of our model.