Traveling solutions for a multi-anticipative car-following traffic model

In this paper, we consider a steady state multi-anticipative traffic model and we provide necessarily and sufficient conditions for the existence of traveling solutions. In our work, the word traveling means that the distance between two consecutive vehicles travels continuously between two different states. As application to our result, we show that taking a strictly concave optimal velocity, we can construct a traveling solution such that the distance between two vehicles decreases. The existence, uniqueness and the study of the asymptotic behavior of such solutions is done at the level of the Hamilton-Jacobi equation.

Automated summary

In this paper, a steady state multi-anticipative traffic model is considered, and necessary and sufficient conditions for the existence of traveling solutions are provided. The word "traveling" in this work refers to the continuous variation of the distance between two consecutive vehicles between two different states. As an application, it is shown that by taking a strictly concave optimal velocity, a traveling solution can be constructed such that the distance between two vehicles decreases. The existence, uniqueness, and asymptotic behavior of such solutions are studied at the level of the Hamilton-Jacobi equation.