Effects of uncertain historical information on traffic dynamics in the lattice model

Several real-time feedback tactics have been presented and applied for traffic dynamics, such as historical density information, historic flux information, etc. Moreover, complex uncertainties such as equipment malfunctions, network fluctuations, driver personalities, and traffic disruptions may affect traffic information. Therefore, this article is devoted to reflecting better the reality of traffic situations in the transportation system by considering uncertainty about historical information of density (UHDI) based on the lattice approach. The UHDI effect is probed using linear stability analysis and nonlinear stability analysis. The instability is found with an increased value of the UHDI coefficient. The modified Korteweg-de-Vries equation is obtained to describe the characteristics of traffic congestion. Finally, numerical simulations are implemented to analyze the results of theoretical findings. The numerical and hypothetical results show that the UHDI factor significantly affects traffic flow.