Unstable flow theory and modeling

We use linear stability analysis to develop theory which can predict traffic flow behavior for the unstable flow regime of concentrations. The equilibrium solution of the kinetic equation of Prigogine and Herman is used to obtain closed form models of traffic flow, when viewed under asymptotic (Chapman-Enskog) limit expansions, since it can produce reasonable flows for the whole range of concentrations. A zeroth-order Chapman-Enskog model is found for this range. The Godunov scheme is used to solve this model under a traffic release type of initial condition.