Analysis of optimal velocity deviation with reaction time up to second order in a lattice hydrodynamic model with V2X communication

In real-world driving scenarios, numerous factors such as driver behavior, road conditions, weather conditions and vehicle capabilities contribute to deviations among the driver's actual velocity and the expected velocity. These disparities can often lead to the formation of traffic congestion on a larger scale. Drivers can significantly reduce deviations and maintain smoother traffic flow by reacting properly and promptly to changing traffic conditions. In this work, we investigate the impact of optimal velocity deviation and reaction time effect on traffic systems using lattice hydrodynamic model. The effect of these factors on traffic system stability is examined using the linear perturbation approach and finds that as reaction times increase, the vehicular flow becomes more stable according to both linear and nonlinear stability analysis. When compared to the current lattice models, the results demonstrate that the system becomes more stable when the reaction time effect and ideal velocity deviation are taken into account. We perform sensitivity analysis with respect to the parameters beta and t s , providing insights into their impact on traffic flow stability. Nonlinear analysis of the proposed model reveals jamming transitions among the freely moving phase and coexisting phase with the "kink-antikink wave"in the unstable region solution, which is the solution of the "mKdV equation". The simulation results are consistent with the theoretical analysis of the proposed model. Our findings demonstrate that considering both optimal velocity deviation and reaction time significantly contributes to maintaining smooth traffic flow and reducing congestion, highlighting the importance of these factors in traffic modeling.