  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.
