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Speed | Acceleration rate |
Traditional | First-order (e.g., LWR) | Higher-order (e.g., PW/ARZ) |
Game-theoretic | First-order MFGs | Higher-order MFGs |
This paper proposes an efficient computational framework for longitudinal velocity control of a large number of autonomous vehicles (AVs) and develops a traffic flow theory for AVs. Instead of hypothesizing explicitly how AVs drive, our goal is to design future AVs as rational, utility-optimizing agents that continuously select optimal velocity over a period of planning horizon. With a large number of interacting AVs, this design problem can become computationally intractable. This paper aims to tackle such a challenge by employing mean field approximation and deriving a mean field game (MFG) as the limiting differential game with an infinite number of agents. The proposed micro-macro model allows one to define individuals on a microscopic level as utility-optimizing agents while translating rich microscopic behaviors to macroscopic models. Different from existing studies on the application of MFG to traffic flow models, the present study offers a systematic framework to apply MFG to autonomous vehicle velocity control. The MFG-based AV controller is shown to mitigate traffic jam faster than the LWR-based controller. MFG also embodies classical traffic flow models with behavioral interpretation, thereby providing a new traffic flow theory for AVs.
Citation: |
Figure 2. From an $ N $-car differential game to MFG (adapted from [39])
Table 1. Classification of macroscopic traffic flow models
![]() |
Speed | Acceleration rate |
Traditional | First-order (e.g., LWR) | Higher-order (e.g., PW/ARZ) |
Game-theoretic | First-order MFGs | Higher-order MFGs |
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From Micro to Macroscopic Traffic Flow Models
From an
Connections between MFG and LWR
[MFG-LWR]
Density Evolution of [MFG-NonSeparable] and [MFG-Separable]
Fundamental diagram of [MFG-NonSeparable]
Density, speed and optimal cost profiles for [MFG-NonSeparable] and [MFG-Separable] at
Convergence of solution algorithm in
MFE-constructed control cost v.s. best response strategy cost,
Accuracy v.s. Number of cars