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Register a new userStabilizing Traffic via Autonomous Vehicles: A Continuum Mean Field Game Approach
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Added by
Kuang Huang
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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This paper presents scalable traffic stability analysis for both pure autonomous vehicle (AV) traffic and mixed traffic based on continuum traffic flow models. Human vehicles are modeled by a non-equilibrium traffic flow model, i.e., Aw-Rascle-Zhang (ARZ), which is unstable. AVs are modeled by the mean field game which assumes AVs are rational agents with anticipation capacities. It is shown from linear stability analysis and numerical experiments that AVs help stabilize the traffic. Further, we quantify the impact of AVs penetration rate and controller design on the traffic stability. The results may provide insights for AV manufacturers and city planners.
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This paper aims to answer the research question as to optimal design of decision-making processes for autonomous vehicles (AVs), including dynamical selection of driving velocity and route choices on a transportation network. Dynamic traffic assignment (DTA) has been widely used to model travelerss route choice or/and departure-time choice and predict dynamic traffic flow evolution in the short term. However, the existing DTA models do not explicitly describe ones selection of driving velocity on a road link. Driving velocity choice may not be crucial for modeling the movement of human drivers but it is a must-have control to maneuver AVs. In this paper, we aim to develop a game-theoretic model to solve for AVss optimal driving strategies of velocity control in the interior of a road link and route choice at a junction node. To this end, we will first reinterpret the DTA problem as an N-car differential game and show that this game can be tackled with a general mean field game-theoretic framework. The developed mean field game is challenging to solve because of the forward and backward structure for velocity control and the complementarity conditions for route choice. An efficient algorithm is developed to address these challenges. The model and the algorithm are illustrated on the Braess network and the OW network with a single destination. On the Braess network, we first compare the LWR based DTA model with the proposed game and find that the driving and routing control navigates AVs with overall lower costs. We then compare the total travel cost without and with the middle link and find that the Braess paradox may still arise under certain conditions. We also test our proposed model and solution algorithm on the OW network.
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.
We consider a mean field game (MFG) of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a FBSDE with possibly singular terminal condition on the backward component or, equivalently, in terms of a FBSDE with finite terminal value, yet singular driver. Extending the method of continuation to linear-quadratic FBSDE with singular driver we prove that the MFG has a unique solution. Our existence and uniqueness result allows to prove that the MFG with possibly singular terminal condition can be approximated by a sequence of MFGs with finite terminal values.
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