  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's
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's 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.
