  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 travelers' 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
one's 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 AVs' 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 in on Braess
networks. 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.
