Maximin Headway Control of Automated Vehicles for System Optimal Dynamic Traffic Assignment in General Networks

TL;DR

This work develops a headway-aware framework for Automated Vehicles to achieve System Optimal Dynamic Traffic Assignment ($SO$-$DTA$) across general networks by introducing a headway-dependent fundamental diagram ($HFD$) and a headway-dependent double queue ($HDQ$) to capture how AV headway alters traffic dynamics. It proves that the minimum headway on each link guarantees $SO$-$DTA$ but that optimal headways are not unique, motivating the novel maximin headway concept—the largest headway that still attains $TTT^{*}$. An exact, efficient algorithm is then proposed to compute the maximin headway in the discretized network, with both small-network and Hong Kong-scale numerical experiments validating the theory and highlighting safety margins as headway increases. The results show substantial safety margins are feasible under $SO$-$DTA$ and demonstrate the framework’s scalability and potential for real-time implementation via online algorithms. These insights offer a practical approach to leverage AV headway control to balance efficiency and safety in automated traffic networks, and they point to future work in mixed-traffic, stochastic demand, and partial deployment scenarios.

Abstract

This study develops the headway control framework in a fully automated road network, as we believe headway of Automated Vehicles (AVs) is another influencing factor to traffic dynamics in addition to conventional vehicle behaviors (e.g. route and departure time choices). Specifically, we aim to search for the optimal time headway between AVs on each link that achieves the network-wide system optimal dynamic traffic assignment (SO-DTA). To this end, the headway-dependent fundamental diagram (HFD) and headway-dependent double queue model (HDQ) are developed to model the effect of dynamic headway on roads, and a dynamic network model is built. It is rigorously proved that the minimum headway could always achieve SO-DTA, yet the optimal headway is non-unique. Motivated by these two findings, this study defines a novel concept of maximin headway, which is the largest headway that still achieves SO-DTA in the network. Mathematical properties regarding maximin headway are analyzed and an efficient solution algorithm is developed. Numerical experiments on both a small and large network verify the effectiveness of the maximin headway control framework as well as the properties of maximin headway. This study sheds light on deriving the desired solution among the non-unique solutions in SO-DTA and provides implications regarding the safety margin of AVs under SO-DTA.

Figures (15)

• Figure 1: Illustration of headway control around an intersection.
• Figure 2: Illustrative relationship between the probability of accident and headway.
• Figure 3: Illustration of the maximin headway for SO-DTA.
• Figure 4: Fundamental diagram of AVs with different headway.
• Figure 5: Flow area and buffer area in a link.

Theorems & Definitions (21)

• Definition 1: Maximin Headway - Layman's version
• Proposition 1: Reduction of HDQ to DQ
• proof
• Proposition 2: Headway-dependent flow rate bounds
• proof
• Proposition 3: Feasibility
• Definition 2
• Proposition 4: Minimum headway achieves SO-DTA
• Proposition 5: Non-uniqueness
• proof