Numerical Simulation of Freeway Traffic Flow

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A new high-order continuum model is presented in this paper. This high-order model exhibits smooth solutions rather than discontinuities, is able to describe the amplification of small disturbances on heavy traffic, and allows fluctuations of speed around the equilibrium values. Furthermore, unlike some earlier high-order models, it does not result in negative speeds at the tail of congested regions and disturbance propagation speeds greater than the flow speed. The model takes into account the relaxation time as a function of density and, in the equilibrium limit it is consistent with the simple continuum model. A Riemann-problem-based numerical method is proposed for the solution of the new high-order model. Modeling of interrupted flow behavior such as merging, diverging, and weaving is also investigated. Based on the new high-order model, the proposed numerical method and the modeling of interrupted flow, a versatile code is developed for the numerical simulation of freeway traffic flow that includes several freeway geometries. We compare the high-order model with the simple continuum model and the proposed numerical method with the Lax method based on 30-s and 5 min field data. The model is tested in interrupted flow situations (e.g., pipeline, merging, diverging, and weaving areas). A comparison of numerical results with limited field data shows that the high-order model performs better than the simple continuum model and describes better traffic flow dynamics, and that the proposed numerical method is better than a previously proposed method.