Platoon Fundamental Diagram estimation can be Markovian: evidence from human- and self-driven vehicle trajectories

TL;DR

The paper addresses deriving a robust Fundamental Diagram (FD) from platoon trajectories across human- and automated-vehicle modes without relying on stationarity or backward-wave-speed estimation. It introduces Edie's generalized definitions applied to a time-variant scalene trapezoid area to compute instantaneous $k$, $q$, and $v$, followed by a simple bivariate aggregation over $k$ and $v$ across nine campaigns and five driver modes. The results show a clear triangular FD for autonomous modes, invariance to heterogeneity in platoon length, vehicle characteristics, and data accuracy, and substantial capacity gains for ACC with minimum headway, with CACC connectivity offering further improvements while human drivers display a broader near-capacity region; safety concerns arise due to high backward wave speeds in some ACC settings. The method's simplicity and accuracy support practical real-time traffic monitoring and control within modern intelligent transportation systems.

Abstract

We propose a simple and effective method to derive the Fundamental Diagram (FD) from platoon vehicle trajectories. Average traffic state variables are computed using Edie's generalized definitions within time-dependent trapezoidal space-time areas. To obtain a clear FD, we employ a bivariate data aggregation technique to eliminate scatter. Our findings are as follows: (i) The proposed method demonstrates a remarkably consistent relation between the traffic variables and a clear triangular shape for autonomously-driven vehicles. (ii) The FDs are invariant to several factors of heterogeneity such as the platoon length, vehicle characteristics, road particularities, and data acquisition accuracy. (iii) ACC-driven vehicle platoons with minimum headway setting achieve much higher capacity, roughly 90\% than those with a large headway setting. (iv) Connectivity might increase capacity. (v) Human drivers have a wider near-capacity operation area, showing different behaviors at high speeds than low ones, and (vi) Safety concerns might arise due to high values of backward wave speed for ACC-driven vehicles. Comparative analysis with the state-of-the-art confirms the validity of our approach. The proposed method stands out due to its simplicity and accuracy, which paves the way for practical applications in real-time traffic flow monitoring and control within modern intelligent transportation systems.

Figures (8)

• Figure 1: Schematic representation of an observed platoon and a dynamic area for instantaneous traffic state estimation.
• Figure 2: Schematic representation of the aggregation method. Blue dots correspond to instantaneous traffic state estimates for the same driver mode. Each dot corresponds to an observation without considering the experiment, platoon size, powertrain, etc. All estimates have instantaneous density withing the bin range, i.e., $k \in (n\delta_k, (n+1)\delta_k)$. The inferred fundamental traffic state for the corresponding bin is derived by averaging all observed instantaneous densities. Therefore each density bin corresponds to one flow value.
• Figure 3: Flow-Density plot with the proposed method and the measurement method proposed by laval_hysteresis_2011 after the application of the Shear transformation described in maiti_universality_2023 and the aggregation process described in this paper.
• Figure 4: Flow-Density plot for different platoon states. The plots refer to observed vehicle platoons driven with the ACC minimum setting.
• Figure 5: Bi-level plots with the proposed method after aggregation