Traffic Waves: Difference between revisions
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We consider a single lane of road. We define the following variables | We consider a single lane of road. We define the following variables | ||
<center><math> | |||
\begin{matrix} | |||
&\rho &: &\mbox{car density (cars/km)} \\ | |||
& v(\rho) &: &\mbox{car velocity (km/hour)} \\ | |||
& q =\rho v &: &\mbox{car flow rate (cars/hour)} \\ | |||
\end{matrix} | |||
</math></center> | |||
If we consider a finite length of road <math>x_1\leq x \leq x_2</math> then the net flow of cars | |||
in and out must be balanced by the change in density. This means that | |||
<center><math> | |||
\begin{matrix} | |||
&\rho &: &\mbox{car density (cars/km)} \\ | |||
& v(\rho) &: &\mbox{car velocity (km/hour)} \\ | |||
& q =\rho v &: &\mbox{car flow rate (cars/hour)} \\ | |||
\end{matrix} </math></center> | |||
[[Category:789]] | [[Category:789]] | ||
Revision as of 23:07, 20 July 2008
Equations
We consider a single lane of road. We define the following variables
If we consider a finite length of road [math]\displaystyle{ x_1\leq x \leq x_2 }[/math] then the net flow of cars in and out must be balanced by the change in density. This means that
