In this work we propose a macroscopic model for studying routing on networks shared between human-driven and autonomous vehicles that captures the effects of autonomous vehicles forming platoons. We use this to study inefficiency due to selfish routing and bound the Price of Anarchy (PoA), the maximum ratio between total delay experienced by selfish users and the minimum possible total delay. To do so, we establish two road capacity models, each corresponding to an assumption regarding the platooning capabilities of autonomous vehicles. Using these we develop a class of road delay functions, parameterized by the road capacity, that are polynomial with respect to vehicle flow. We then bound the PoA and the bicriteria, another measure of the inefficiency due to selfish routing. We find these bounds depend on: 1) the degree of the polynomial in the road cost function and 2) the degree of asymmetry, the difference in how human-driven and autonomous traffic affect congestion. We demonstrate that these bounds recover the classical bounds when no asymmetry exists. We show the bounds are tight in certain cases and that the PoA bound is order-optimal with respect to the degree of asymmetry.

中文翻译：

---

混合自治的交通网络路由

在这项工作中，我们提出了一个宏观模型，用于研究人类驾驶和自动驾驶车辆之间共享的网络上的路由，该模型捕捉自动驾驶车辆形成排的影响。我们使用它来研究由于自私路由导致的低效率，并限制了无政府状态的价格（PoA），即自私用户经历的总延迟与最小可能总延迟之间的最大比率。为此，我们建立了两个道路容量模型，每个模型都对应于关于自动驾驶汽车的排队能力的假设。使用这些，我们开发了一类道路延迟函数，由道路通行能力参数化，是关于车辆流量的多项式。然后我们绑定了 PoA 和双标准，这是衡量自私路由导致的低效率的另一种衡量标准。我们发现这些界限取决于：1) 道路成本函数中多项式的程度和 2) 不对称程度，人类驾驶和自主交通如何影响拥堵的差异。我们证明，当不存在不对称性时，这些边界恢复了经典边界。我们表明在某些情况下边界很紧，并且 PoA 边界在不对称程度方面是顺序最优的。