Stochastic and Dynamic Fundamental Diagram for Mixed Traffic

A new study from Jiwan Jiang and Soyoung Ahn at the University of Wisconsin-Madison introduces a stochastic and dynamic fundamental diagram (FD) for mixed traffic environments combining automated vehicles (AVs) and human-driven vehicles (HDVs). The framework uses describing function analysis to derive approximate linear transfer functions for nonlinear HDV car-following models, enabling a sequence-based evaluation of traffic hysteresis in flow-density relations across different vehicle sequencing scenarios and AV penetration levels.

Monte Carlo simulation results reveal two key insights: first, differences in AV-HDV sequencing can significantly alter the size of traffic hysteresis loops—meaning the order in which AVs and HDVs are arranged within a platoon directly affects congestion patterns. Second, while higher AV shares generally dampen both the magnitude and variability of hysteresis, the net impact depends critically on how AVs are distributed throughout the platoon. The findings suggest that optimizing traffic flow in mixed environments requires not just increasing AV penetration but also strategically sequencing vehicles to minimize hysteresis effects.