Peilin Zhao 赵沛霖

Peilin Zhao 赵沛霖

PhD Candidate @ NTU CEE

A platoon-centric approach to the capacity analysis of mixed traffic comprising connected and autonomous vehicles

Published in Transportation Research Part C: Emerging Technologies, 2025

Abstract

The study of mixed traffic capacity, involving both Connected and Autonomous Vehicles (CAVs) and Human-driven Vehicles (HVs), remains a critical area of research. Traditional models have typically focused on individual vehicles, while this research shifts the focus to platoons as the fundamental units of analysis to better capture the platooning characteristics of CAVs. Specifically, we introduce a new metric, the Inter-Platoon Platooning Intensity (IPI), to facilitate the analysis of mixed traffic capacity. Through both mathematical and numerical investigations, we evaluate the impact of the proposed IPI and Maximum Platoon Size (MPS) on mixed traffic dynamics. Our findings indicate that: (1) the IPI effectively measures the clustering of CAVs in a single-lane mixed traffic environment; (2) the calculated mixed traffic capacity closely matches the actual traffic capacity, showing only minor deviations; (3) the marginal analysis demonstrates the conditions under which mixed traffic capacity correlates monotonically with either MPS or IPI; and (4) an optimal MPS is determined that maximizes mixed traffic capacity. These insights contribute significantly to the existing literature on the effects of platoon size and platooning intensity on mixed traffic flow.

Highlights

  • A new metric, the Inter-Platoon Platooning Intensity (IPI), is introduced.

  • Impact of IPI and Maximum Platoon Size (MPS) is examined on mixed traffic dynamics.

  • IPI effectively measures the clustering strength of CAVs in mixed traffic.

  • Conditions where capacity rises monotonically with either MPS or IPI are derived.

  • The analysis is extended to the development of mixed traffic fundamental diagram.

Assumptions

  • The assumptions in this study follows the MPS constraint model in our previous study.

  • The primary objective of this study is to model the capacity of a single-lane road within a mixed traffic environment. Accordingly, each headway in this study represents the minimum headway between vehicles traveling at the design speed.

Platoon Centric Approach

  • This study considers the CAV platoon as the fundamental unit of analysis, where HVs (modeled as ‘0’) and CAV platoons (modeled as ‘1’) form the platoon sequence:

    1

  • Inter-platoon Platooning Intensity (IPI): For any platoon sequence \(\mathbb{M}: \{x_i\},\,i \in [1,\,M]\), based on the first-order unbiased ACF, the proposed IPI, denoted as \(\rho\), can be formulated as:

\[\begin{aligned} \rho &= \frac{\displaystyle \frac{1}{M-1} \sum_{i=1}^{\,M-1} (x_i - \bar{x})\,\bigl(x_{i+1} - \bar{x}\bigr)} {\displaystyle \frac{1}{M} \sum_{i=1}^{\,M} (x_i - \bar{x})^2}\\ \bar{x} &= \frac{\displaystyle \sum_{i=1}^{\,M} x_i}{M} \;=\; \frac{\displaystyle M\,q_{0}\cdot 0 \;+\; M\,q_{1}\cdot 1}{M} \;=\; q_{1} \end{aligned}\]

Where:

  • \(q_0\) denotes the proportion of HVs in a platoon sequence.
  • \(q_1\) denotes the proportion of CAV Platoons in a platoon sequence.

Capacity Analysis

  • Headway Types:

    2

  • Estimated Capacity:

\[\hat{C} \approx \frac{1}{h} \;=\; \frac{1} { \alpha_{\mathrm{HV\text{-}HV}} \;+\; \beta \, h_{\mathrm{plt\text{-}HV}} \;+\; \beta \, h_{\mathrm{HV\text{-}plt}} \;+\; \gamma \, h_{\mathrm{plt\text{-}plt}} \;+\; \delta \, h_{\mathrm{CAV\text{-}CAV}} }\] \[\begin{aligned} &\alpha = (1 - P_{\mathrm{CAV}})\,\bigl[\rho\,(1 - P_{0}) + P_{0}\bigr] \\[6pt] &\beta = (1 - P_{\mathrm{CAV}})\,(1 - P_{0})\,(1 - \rho) \\[6pt] &\gamma = \frac{\,1 - P_{\mathrm{CAV}}\,}{P_{0}}\;(1 - P_{0})\;\bigl(\rho\,P_{0} + 1 - P_{0}\bigr) \\[6pt] &\delta = 1 \;-\; \frac{\,1 - P_{\mathrm{CAV}}\,}{P_{0}} \\[6pt] &P_{0} = \frac{\,1 - P_{\mathrm{CAV}}^{\,L}\,}{\,1 - P_{\mathrm{CAV}}^{\,L} + P_{\mathrm{CAV}}\,} \end{aligned}\]

Where:

  • \(P_{\mathrm{CAV}}\) denotes the CAV penetration rate.

  • \(L\) denotes the maximum platoon size.

  • Model Accuracy:

    3

  • Marginal Analysis: Proposition 2 to Proposition 9 in the Orginal Paper.

Milestone

  • Nov 2023: Began research on estimating mixed traffic capacity using a platoon-centric approach.

  • Dec 2023: Formulated the capacity approximation model based on CAV platoons.

  • Jan 2024: Conducted marginal analysis based on the proposed capacity model.

  • Oct 2024: Developed fundamental diagram analysis from the capacity approximation.

  • May 2025: Published the article in Transportation Research Part C: Emerging Technologies.

DOI: 10.1016/j.trc.2025.105170

License: © 2025. This manuscript version is made available under the CC BY-NC-ND 4.0 license.

Recommended citation: Zhao, P., Wong, Y. D., & Zhu, F. (2025). A platoon-centric approach to the capacity analysis of mixed traffic comprising connected and autonomous vehicles. Transportation Research Part C: Emerging Technologies, 177, 105170.
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