An extended macro traffic flow model accounting for multiple optimal velocity functions with different probabilities

Due to the maximum velocity and safe headway distance of the different vehicles are not exactly the same, an extended macro model of traffic flow with the consideration of multiple optimal velocity functions with probabilities is proposed in this paper. By means of linear stability theory, the new model's linear stability condition considering multiple probabilities optimal velocity is obtained. The KdV-Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line through nonlinear analysis. The numerical simulations of influences of multiple maximum velocities and multiple safety distances on model's stability and traffic capacity are carried out. The cases of two different kinds of maximum speeds with same safe headway distance, two different types of safe headway distances with same maximum speed and two different max velocities and two different time-gaps are all explored by numerical simulations. First cases demonstrate that when the proportion of vehicles with a larger v(max) increase, the traffic tends to unstable, which also means that jerk and brakes is not conducive to traffic stability and easier to result in stop and go phenomenon. Second cases show that when the proportion of vehicles with greater safety spacing increases, the traffic tends to be unstable, which also means that too cautious assumptions or weak driving skill is not conducive to traffic stability. Last cases indicate that increase of maximum speed is not conducive to traffic stability, while reduction of the safe headway distance is conducive to traffic stability. Numerical simulation manifests that the mixed driving and traffic diversion does not have effect on the traffic capacity when traffic density is low or heavy. Numerical results also show that mixed driving should be chosen to increase the traffic capacity when the traffic density is lower, while the traffic diversion should be chosen to increase the traffic capacity when the traffic density is heavier. (C) 2017 Elsevier B.V. All rights reserved.