Hopf Bifurcation Analysis of Mixed Traffic and Its Implications for Connected and Autonomous Vehicles

Capturing the evolution mechanism of traffic dynamics is of great significance when alleviating traffic congestion and improving traffic efficiency. While several studies have presented stability analyses of various traffic systems, most have relied on linear analysis methods, which cannot capture the complex nonlinear dynamic behavior of heterogeneous traffic flow. To address this shortcoming, this paper derives a generic Hopf bifurcation structure that can be applied to multiclass traffic models. The proposed bifurcation structure is investigated to understand the characteristics of heterogeneous traffic flow in a connected and autonomous environment as case studies. The results, based on selected on- field calibrated traffic models, show that (i) the linear analysis results deviate significantly from the actual instability of the mixed traffic system, which illustrates the necessity of a bifurcation analysis; and (ii) connected human-driven vehicles and connected autonomous vehicles have the ability to alleviate the formation and propagation of traffic oscillations. Finally, the theoretical analysis results are verified through simulation experiments.