Pricing Traffic Networks with Mixed Vehicle Autonomy

Abstract

In a traffic network, vehicles normally select their routes selfishly. Consequently, traffic networks normally operate at an equilibrium characterized by Wardrop conditions. However, it is well known that equilibria are inefficient in general. In addition to the intrinsic inefficiency of equilibria, the authors recently showed that, in mixed-autonomy networks in which autonomous vehicles maintain a shorter headway than human-driven cars, increasing the fraction of autonomous vehicles in the network may increase the inefficiency of equilibria. In this work, we study the possibility of obviating the inefficiency of equilibria in mixed-autonomy traffic networks via pricing mechanisms. In particular, we study assigning prices to network links such that the overall or social delay of the resulting equilibria is minimum. First, we study the possibility of inducing such optimal equilibria by imposing a set of undifferentiated prices, i.e. a set of prices that treat both humandriven and autonomous vehicles similarly at each link. We provide an example which demonstrates that undifferentiated pricing is not sufficient for achieving minimum social delay. Then, we study differentiated pricing where the price of traversing each link may depend on whether vehicles are human-driven or autonomous. Under differentiated pricing, we prove that link prices obtained from the marginal cost taxation of links will induce equilibria with minimum social delay if the degree of road capacity asymmetry (i.e. the ratio between the road capacity when all vehicles are human-driven and the road capacity when all vehicles are autonomous) is homogeneous among network links.

Optimal Tolling for Heterogeneous Traffic Networks with Mixed Autonomy

“…Can such a tolling scheme yield a unique socially-optimal equilibrium? Previous work has answered this question negatively -in [24], the authors show an example of a network with multiple source destination pairs in which undifferentiated tolls fail to minimize social cost in equilibrium. In this section we extend these results and show a simple two-road network in which undifferentiated tolls fail.…”

“…Remark 1: These optimal tolls are the same as the edge tolls in [7], though in that work the proof of optimality is limited to when the social cost is a convex function, which in our setting it is not. The optimality of these same tolls has been proven in the mixed autonomy setting when there are two vehicle types [8], but it is restricted to the case in which the asymmetry in the congestion effects of the vehicle types is constant across roads, though they prove this for polynomial latency functions. Since they consider only two vehicle types, this assumption means that a 1 i /a 2 i = k for some constant k for all roads i in the set of roads [n].…”

“…Specifically, [7] assumes that the Jacobians of the latency functions are positive definite; the latency function derived in (3) in Section II violate this assumption. This is addressed in [24]; there the authors show by example that in multicommodity networks (networks with multiple source-destination pairs), if autonomous vehicles and human drivers experience the same tolls, it is not always possible to create an equilibrium that minimizes social cost. However, they have positive results for a homogeneous network; a network in which all roads see the same multiplicative increase in capacity from the presence of autonomous vehicles.…”

Coordinated management and control of autonomous traffic systems

“…Mehr 和Horowitz [32] 也提出随着自动驾驶车辆渗透率的增加, 系统总阻抗并不单调递减. 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.…”

Pricing of Connected and Autonomous Vehicles in Mixed-Traffic Networks

“…Simoni et al ( 8 ) evaluate the impacts on travelers’ choices of different pricing strategies, including marginal cost pricing, using agent-based modeling. Mehr and Horowitz ( 9 ) consider marginal cost pricing at network level with both HDVs and CAVs taxed under undifferentiated and differentiated (between the two vehicle classes) schemes. Boffa et al ( 10 ) investigate marginal cost pricing in a stylized case of a connection with two lanes.…”