Dynamical Analysis of Car-Following Model Considering Anticipation, Time Delay and Feedback Effect

Traffic problems are a major concern for many cities and towns worldwide. This problem can be overcome with the help of an intelligent transport system by taking the information about the anticipated and time-delay feedback control. This study proposes a car-following model by considering anticipation and delayed time-feedback effects depending on both optimal and local velocity differences to suppress traffic jams. The linear and nonlinear analyses are conducted for the proposed model and it is found that the anticipation effect enhances the stable region of the traffic flow. On the other hand, the unstable region enhances with an increase in the delay time value, indicating that longer delays in the system's response can lead to more congestion and instability. It is also seen that the congestion induced by delay time can be overcome by considering the role of feedback gains. By optimizing feedback control based on anticipated and delayed information, the proposed model effectively regulates traffic flow, reduces congestion, and improves overall flow stability. From a comparison of the current study with the existing one, it is noticed that the proposed model is more efficient in regulating the flow. Numerical simulation shows that the proposed model can improve traffic flow stability and reduce traffic congestion by forecasting future vehicle headway and speed, which is by the theoretical examination. Therefore, the anticipated and delay time feedback effect provides a more efficient solution for traffic management systems that will result in fewer delays, improved safety conditions, and reduced costs for transportation networks.