This is it; most likely the last time I bother the people of this website with my questions on traffic flow.(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to figure out some concrete examples to demonstrate utilization of the conservation equation in traffic flow:

[tex]\frac{\partial \rho }{\partial t} + \frac{\partial q(\rho )}{\partial x} = \frac{\partial \rho }{\partial t} + \frac{\partial \rho v(\rho )}{\partial x} = 0[/tex]

where ##\rho## is density in ##\frac{num. vehicles}{distance}##, ##q## is flow in ##\frac{num. vehicles}{time}##, ##v## is speed/velocity in ##\frac{distance}{time}##, ##t## is time, and ##x## is distance of a segment of road. ##v(\rho )## can be expressed as follows:

[tex]v(\rho ) = v_{max}(1 - \frac{\rho }{\rho_{max}})[/tex]

where ##v_{max}## is maximum velocity and ##\rho_{max}## is maximum density.

Is there anyone here who knows about traffic modelling well enough to suggest some concrete examples for utilization of this equation? Alternatively, could anyone tell me what variables I would need to know to substitute into the equation in order to get something out?

I guess my ultimate question here is just, how do I use this equation for modelling traffic now that I have it?

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# [Traffic Flow] Concrete example of conservation equation?

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