Difference between revisions of "Traffic Waves"
From WikiWaves
Jump to navigationJump to search| Line 2: | Line 2: | ||
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
