The Price of Anarchy for Transportation Networks with Mixed Autonomy

Abstract

We study routing behavior in transportation networks with mixed autonomy, that is, networks in which a fraction of the vehicles on each road are equipped with autonomous capabilities such as adaptive cruise control that enable reduced headways and increased road capacity. Motivated by capacity models developed for such roads with mixed autonomy, we consider transportation networks in which the delay on each road or link is an affine function of two quantities: the number of vehicles with autonomous capabilities on the link and the number of regular vehicles on the link. We particularly study the price of anarchy for such networks, that is, the ratio of the total delay experienced by selfish routing to the socially optimal routing policy. Unlike the case when all vehicles are of the same type, for which the price of anarchy is known to be bounded, we first show that the price of anarchy can be arbitrarily large for such mixed autonomous networks. Next, we define a notion of asymmetry equal to the maximum possible travel time improvement due to the presence of autonomous vehicles. We show that when the degree of asymmetry of all links in the network is bounded by a factor less than 4, the price of anarchy is bounded. We also bound the bicriteria, which is a bound on the cost of selfishly routing traffic compared to the cost of optimally routing additional traffic. These bounds depend on the degree of asymmetry and recover classical bounds on the price of anarchy and bicriteria in the case when no asymmetry exists. Further, we show with examples that these bound are tight in particular cases.

Pricing Traffic Networks with Mixed Vehicle Autonomy

“…where a l and γ l are positive link parameters, β l is a positive integer, m l is the capacity of link l when all vehicles are human-driven, and M l is the capacity of link l when all vehicles are autonomous. Following [11], for each link l ∈ L, we define…”

“…Inefficiency of equilibria is commonly measured via the price of anarchy [10]. In [11], the price of anarchy of traffic networks with mixed vehicle autonomy was computed, and it was shown that the price of anarchy of networks with mixed vehicle autonomy is larger than that of networks with no autonomy. This implies that although the optimal overall delay of networks with mixed autonomy is lower (due to the capacity increase of autonomous vehicles), at equilibrium, the overall delay of networks with mixed autonomy is further from its optimum.…”

Capacity modeling and routing for traffic networks with mixed autonomy

“…This choice of cost functions implies that road delay is separable, meaning that the congestion on one road does not affect that on another. In the conference version of this paper [15], we bound the price of anarchy and bicriteria for some nonseparable affine cost functions.…”

Coordinated management and control of autonomous traffic systems

“…Mehr和Horowitz [33] 通过算 例说明了系统最优的道路收费方案需要对自动车和常 规车区别对待. Roughgarden和Tardos [34] 证明了非自动 驾驶下最差均衡效率(price of anarchy, PoA)是有界的, 而Lazar等人 [35] 通过算例说明了混合交通环境下PoA可 能是无界的, 并给出PoA有界的一个充分条件. 假定自 动车和常规车分别只能在各自所规划的区域行驶, 而 双模式车不受区域限制, Beirigo等人 [36] 定量研究了混 合交通环境对出行服务水平的影响.…”