PDE 11: Traffic equations

In this case we have two dependent variables \(\rho=\rho(x,t)\) and \(v=v(x,t) \)

\[\rho_t +(\rho\,v)_x=q(t)\phi(x) \]

\[\rho(v_t+v\,v_x=\frac{\rho}{\tau}(V(\rho)-v)-c_0^2\rho_x+\mu\,v_{xx} \]

Here traffic density and velocity \(( \rho,\;v )\) are modelled as continuous functions of space and time. For a more detailed discussion of the model, see [1] (if you are having trouble accessing this file let me know).

Referance: [1] H.Y. Lee, H.-W. Lee, and D. Kim, Dynamic states of a continuum traffic equation with on-ramp, Phys Rev E, 59 (1999), 5101-5111.

Google: Traffic flow, traffic equations

Challenges: discretization