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A Quasi-Steady Model fro Congested Highway Traffic Flow


Y. Wang

IfA Internal Seminar Series

Hysteresis is one of the most predominant behaviors in the transitions between the free flow and the congested flow for highway traffic. In this talk, we propose a low order nonlinear model to explain the hysteresis behavior qualitatively. The main assumption of quasi-steady traffic is when the traffic flow deviates from the equilibrium flow, the local flow rate has a finite time response to local density disturbances. The other key assumption is the inlet-diffuser assumption of traffic flow near ramps, where the upstream of on/off ramp is modeled as an inlet to a section of highway and the main road at on/off ramp as a diffuser. The resulting model for a section of highway is composed of a partial differential equation coupled with an ordinary differential equation. By assuming periodic boundary conditions, the equations are projected to the space of zeroth and the first modal wave via a Galerkin procedure, resulting in a lower order nonlinear model. In this truncated model and for a range of parameter values, the onset of congested flow is identified as a subcritical Hopf bifurcation, where the amplitude of the first modal traveling wave of density grows to a finite value. The local Hopf bifurcation can be investigated via center manifold analysis. Possibility of using feedback control to change the bifurcation characteristic is discussed.


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