Nonlinear density wave and energy consumption investigation of traffic flow on a curved road**Project supported by the National Natural Science Foundation of China (Grant No. 11372166), the Scientific Research Fund of Zhejiang Province, China (Grant Nos. LY15A020007 and LY15E080013), the Natural Science Foundation of Ningbo, China (Grant Nos. 2014A610028 and 2014A610022), and the K. C. Wong Magna Fund in Ningbo

Abstract

A new car-following model is proposed based on the full velocity difference model (FVDM) taking the influence of the friction coefficient and the road curvature into account. Through the control theory, the stability conditions are obtained, and by using nonlinear analysis, the time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are derived. Furthermore, the connection between TDGL and mKdV equations is also given. The numerical simulation is consistent with the theoretical analysis. The evolution of a traffic jam and the corresponding energy consumption are explored. The numerical results show that the control scheme is effective not only to suppress the traffic jam but also to reduce the energy consumption.