Traffic dynamics (traveling wave)


by anotherghost
Tags: dynamics, traffic, traveling, wave
anotherghost
anotherghost is offline
#1
Nov30-10, 10:57 PM
P: 12
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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jackmell
jackmell is offline
#2
Dec1-10, 05:13 AM
P: 1,666
Quote Quote by anotherghost View Post
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:

[tex]\rho_t+M(1-2\frac{\rho}{d})\rho_x=0[/tex]

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


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