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Traffic Flow Modeling
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Counting cars, we define flow as the number of cars per hour and concentration as the number of cars per mile. Greenshields model assumes a linear relationship between speed and concentration, which then leads to a concave down parabola as the model of flow as a function of speed. Flow, concentration, and speed occur in the transport equation, a partial differential equation derived from the continuity equation. With this model we can visualize an accelerating platoon of cars, the shock that happens when a fast car meets a slow moving truck, and the diffusion of cars when the stop light flips from red to green. The lecture ends with a proposal for a topic of a project and pointers to the transportation research board special report 165.
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