Effect of multi-phase optimal velocity function on jamming transition in a lattice hydrodynamic model with passing

In this paper, we study the effect of multi-phase optimal velocity function on a density difference lattice model with passing. The effect of reaction coefficient is examined through linear stability analysis and shown that it can significantly enlarge the stability region on the phase diagram for any rate of passing. Using nonlinear stability analysis, the critical value of passing constant is obtained and found independent of reaction coefficient. Below this critical value for which kink soliton solution of mKdV equation exists. By varying the density, multiple phase transitions are analyzed, which highly depend on the sensitivity, reaction coefficient and passing constant. It is observed that the number of stages in multi-phase transitions closely related to the number of the turning points in the optimal velocity function. The theoretical findings are verified using numerical simulation, which confirm that phase diagrams of multi-phase traffic in the case of passing highly depend on the choice of optimal velocity function as well as on other parameters such as sensitivity, reaction coefficient and rate of passing.