An extended continuum traffic model with the consideration of the optimal velocity difference

In this letter, we derived an extended continuum model from a car-following model with consideration of the optimal velocity difference called the relative optimal velocity via employing the transformation relation from microscopic variables to macroscopic ones. The stability condition of this continuum traffic model is obtained by performing linear stability analysis. Results show that the optimal velocity difference helps to improve the stability of traffic flow. We make use of the upwind finite difference scheme for simulation. The effects of the optimal velocity difference (the relative optimal velocity) and the velocity difference (the optimal velocity) on local clustering effect and instability are studied and compared each other, respectively. The spatiotemporal evolution patterns of traffic flow for the different initial density, strength of the optimal velocity difference and the velocity-difference are obtained. Their space–time diagrams reveal the local clustering effect induced by the instability of traffic flow and generate the stop&go traffic jams. Numerical simulation result indicates the unstable region is shrunken under the effect of the optimal velocity difference (the relative optimal velocity) and/or the velocity difference (the optimal velocity).