## Traffic dynamics (traveling wave)

The problem:
You are given the problem of analyzing the dynamics of a line of cars moving on a one-lane highway. One approach to this problem is to assume that the line of cars behaves like a group of coupled oscillators. How would you set this problem up in a tractable way? Make lots of assumptions.

Can anyone help me get started on this? I'm having trouble even setting up the differential equation.

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 Quote by anotherghost The problem: You are given the problem of analyzing the dynamics of a line of cars moving on a one-lane highway. One approach to this problem is to assume that the line of cars behaves like a group of coupled oscillators. How would you set this problem up in a tractable way? Make lots of assumptions. Can anyone help me get started on this? I'm having trouble even setting up the differential equation.
There is a write-up on traffic flow using first order PDEs in "Basic Partial Differential Equations" by Bleecker and Csordas. Try and find it in the library. This is the equation that is derived:

$$\rho_t+M(1-2\frac{\rho}{d})\rho_x=0$$

Although maybe you're looking for just an ODE model.