Analytical Solution of the Mixed Traffic Flow Cellular Automaton FI Model with the Next-Nearest-Neighbor Interaction

Abstract

Based on a one-dimensional (1D) traffic flow cellular automaton (CA) FI model, a deterministic next-nearest-neighbor interaction FI model (NIFI model) is proposed. Using the mean-field analysis, the analytical solution of the NIFI model in one-dimensional traffic flow is derived under periodic boundary conditions. For the mixed traffic flow, the occupancy and the mixing ratio are introduced to describe the mixing effect. Similarly, using the mean-field method, the exact solution of the mixed traffic flow is derived from the long-time evolution to reach the steady state. The numerical simulations are carried out for the mixed traffic flow with different vehicle lengths, maximum velocities, and mixing ratios to verify the analytical solutions. The results show that the numerical simulation results agree well with the analytical solution.