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Posted on by Anuj Varma
Modeling Traffic Flow

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Specializing in high volume web applications, Anuj Varma has helped architect, re-architect and troubleshoot some of the largest web applications out there.
His customer base includes Fortune 100 companies ( British Petroleum, dell.com, Schlumberger) as well as smaller to mid size firms within the United States. He can also be found on – technicalarchitect.us

Anuj Varma – who has written posts on Anuj Varma, Technical Architect.


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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