Improved High-Order Model for Freeway Traffic Flow

An improved high-order continuum model is developed based on hyperbolic conservation laws with relaxation, linearized stability analysis, and more realistic considerations of traffic flow. The improved high-order model allows smooth traveling wave solutions as well as contact shocks (different densities moving at the same speed), 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 because the improved model has a zero characteristic speed and a nonnegative characteristic speed that is equal to the traffic flow velocity. The relaxation time is a function of density and, in the equilibrium limit, the improved high-order model is consistent with the simple continuum model. The improved high-order model is compared with the simple continuum model. Exemplary test results suggest that the improved high-order model is intuitively correct. Comparison of numerical results with field data suggests that the improved high-order model yields lower error levels than the simple continuum model.