Modeling Traffic Flow

Traffic flow is not that different from the flow of anything else. Imagine heat flow along an iron rod or water flowing down a pipe. If you observe the traffic (on a highway) from a far enough distance, the mass of cars would appear analogous to a (slowly) flowing fluid.

Let \rho(x,t) be the density (substance per unit length) and let r(x,t) be its rate of flow past x at time t.

The mass present in a segment of length \Delta x is:

    \begin{equation} \[ \int_x^(x+\Delta x) \rho(x,t) \,dx \]  \end{equation}

The rate of flow of this mass

    \begin{equation} \frac{d}{dt} \[ \int_x^(x+\Delta x) \rho(x,t) \,dx \] \end{equation}

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