An extended multi-phase lattice model with consideration of optimal current changes with memory

We present a multi-phase lattice model by considering the optimal current change with memory effect, in which traffic congestion could possibly take place in the cases of both high density and low density. The linear stability condition of the model is obtained by applying the linear stability theory. A modified Korteweg-de Vries (mKdV) equation is also derived through nonlinear analysis to examine the traffic density wave propagation near the critical point. Numerical simulation verified that not only the sensitivity of the optimal velocity change with memory of drivers but also the memory time step could effectively stabilize the traffic flow. The stability of traffic flow could be strengthened by increasing the memory step size of optimal current changes and the intensity of drivers' memory. In addition, the phase transitions and the deviation between the analytical and simulation model is highly dependent on the sensitivity.