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A Quasi-Steady Model fro Congested Highway Traffic Flow

Author(s):

Y. Wang
Conference/Journal:

IfA Internal Seminar Series
Abstract:

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.

Year:

2008
Type of Publication:

(06)Talk
Supervisor:



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