The stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow

• Published in: Physica A Vol. 391; no. 19; pp. 4476 - 4482
• Main Authors: Tian, Jun-fang, Yuan, Zhen-zhou, Jia, Bin, Li, Ming-hua, Jiang, Guo-jun
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2012
• Subjects: Burgers equation; Computational fluid dynamics; Density; Density difference; Fluid flow; Hydrodynamics; Lattice hydrodynamic model; Lattices; Mathematical models; MKdV equation; Stabilization; Traffic flow; Lattice hydrodynamic model; Traffic flow; MKdV equation; Burgers equation; Density difference
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2012.04.027

A modified lattice hydrodynamic model of traffic flow is proposed by introducing the density difference between the leading and the following lattice. The stability condition of the modified model is obtained through the linear stability analysis. The results show that considering the density difference leads to the stabilization of the system. The Burgers equation and mKdV equation are derived to describe the density waves in the stable and unstable regions respectively. Numerical simulations show that considering the density difference not only could stabilize traffic flow but also makes the lattice hydrodynamic model more realistic. ► The density difference lattice model of traffic flow has been presented. ► Density difference effects on the stability of traffic flow have been explored. ► The mKdV equation is derived to describe the traffic jam by nonlinear analysis. ► The analytical and numerical results show that density difference can improve the stability of traffic flow.