Stochastic and Dynamic Fundamental Diagram for Mixed Traffic

Abstract

This study develops a dynamic fundamental diagram (FD) framework tailored to mixed traffic environments comprising automated vehicles (AVs) and human-driven vehicles (HDVs). Describing function analysis is employed to derive approximate linear transfer functions for nonlinear HDV car-following models. A sequence-based stochastic dynamic FD is then formulated for mixed platoons, enabling the evaluation of hysteresis in the evolution of flow-density relations across different vehicle sequencing scenarios and AV penetration levels. Monte Carlo simulation results reveal that (i) differences in AV-HDV sequencing significantly alter the size of traffic hysteresis loops; and (ii) higher AV shares generally dampen hysteresis magnitude and variability, yet the net impact depends on how AVs are distributed within the platoon. The results suggest that traffic hysteresis in mixed environments is governed not only by the composition of AVs and HDVs, but also by how their interactions unfold through sequencing.