Modeling Traffic Flow

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Posted on October 1, 2011 by Anuj Varma

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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