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 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.

本文旨在回答有关自动驾驶汽车（AV）决策过程的最佳设计的研究问题，包括在交通网络上动态选择行驶速度和选择路线。动态交通分配（DTA）已被广泛用于对旅行者的路线选择或/和出发时间选择进行建模，并在短期内预测动态交通流的演变。但是，现有的DTA模型没有明确描述人们在道路上的行驶速度选择。驾驶速度的选择对于模拟驾驶员的动作可能不是至关重要的，但它是操纵AV的必备控件。在本文中，我们旨在开发一种博弈论模型，以解决AV在道路连接内部的速度控制和交叉路口路线选择的最佳驱动策略。为此，ñ汽车差分游戏，并证明该游戏可以使用一般的平均场博弈理论框架解决。由于速度控制的前向和后向结构以及路线选择的互补条件，因此开发的平均场博弈具有挑战性。开发了一种有效的算法来应对这些挑战。该模型和算法在具有单个目标的Braess网络和OW网络上进行了说明。在Braess网络上，我们首先将基于LWR的DTA模型与建议的游戏进行比较，发现驱动和路由控制以较低的总体成本导航AV。然后，我们比较不使用中间链接和使用中间链接的总旅行成本，发现Braess悖论在某些情况下仍可能出现。我们还在OW网络上测试了我们提出的模型和解决方案算法。