コロキウム

In terms of traffic problems, we present a new model that incorporates a position mean-field. The Bando model of a previous paper [1] considers legal safe velocity according to the motion of the preceding vehicle. Recently, global control of vehicles has become possible due to the development of communication technology. In another previous paper [2], a mean-field velocity difference model using multi-vehicle interaction is presented. In this research, we propose a global control model by a position mean-field because it is considered to be meaningful to solve the traffic congestion problem. In this model, the state in which the vehicles running at equal intervals and equal speeds is the equilibrium state. The stability of this equilibrium state is analyzed by linearizing the equation of motion and performing the Fourier-Laplace transform.

[1] Dynamical model of traffic congestion and numerical simulation, M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Physical Review E 51(2), 1035 (1995). DOI: 10.1103/PhysRevE.51.1035
[2] Mean-field velocity difference model considering the average effect of multi-vehicle interaction, Y. Guo, Y. Xue, Y. Shi, F. P. Wei, L. Z. Lü, and H. Di. He, Commun. Nonlinear Sci. Numer. Simulat. 59, 553 (2018). DOI: https://doi.org/10.1016/j.cnsns.2017.11.026