A new lattice model for single-lane traffic flow with the consideration of driver's memory during a period of time

In order to investigate the effect of driver's memory during a period of time upon traffic dynamics, an extended lattice hydrodynamic model for traffic flow is proposed and studied analytically and numerically in this paper. The linear stability analysis reveals that the time length of driver's memory has an important effect on stability of traffic flow. The factor will lead to the occurrence of traffic congestion. Three typical nonlinear wave equations including Burgers, Korteweg-de Vries and modified Korteweg-de Vries equation are derived to describe the evolution of density wave for traffic flow in three different regions, which are stable, meta-stable and unstable region, respectively. The simulations are given to illustrate and clarify the analytical results. The results indicate that the time length of driver's memory has a negative effect upon stability of traffic flow.