| In this thesis, a new high-order continuum model is developed based on hyperbolic conservation laws with relaxation, linearized stability analysis and more realistic considerations. The new 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 existing high-order models, it does not result in negative speeds at the tail of congested regions and disturbance propagation speeds greater than the traffic flow velocity since the new model has a zero characteristic speed and a nonnegative characteristic speed which is equal to the traffic flow velocity. The relaxation time is a function of density and, in the equilibrium limit, the new high-order model is consistent with the simple continuum model.; In addition, 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 investigated. Based on the new high-order model, the proposed numerical method and the modeling of interrupted flow, a comprehensive and versatile computer code is developed for the numerical simulation of freeway traffic flow that includes several freeway geometries. An optimization procedure for parameter calibration that requires no user interface is also developed. The new model and the proposed numerical method have been tested against hypothetical data, 30-second and 5-minute field data for various geometric cases (including pipeline, entrance with or without exclusive lane(s), exit with or without exclusive lane(s), weaving areas, lane adds and lane drops). We have compared the high-order model with the simple continuum model and the proposed numerical method with the Lax method. Exemplary test results have suggested that the new high-order model is intuitively correct. Comparison of numerical results with field data has shown that the new high-order model yields lower error levels than the simple continuum model and describes well traffic flow dynamics, while the proposed numerical method is better than the Lax method for numerically implementing the new high-order model. |
