System optimum (SO) routing, wherein the total travel time of all users is minimized, is a holy grail for transportation authorities. However, SO routing may discriminate against users who incur much larger travel times than others to achieve high system efficiency, i.e., low total travel times. To address the inherent unfairness of SO routing, we study the $\beta$-fair SO problem whose goal is to minimize the total travel time while guaranteeing a $\beta\geq 1$ level of unfairness, which specifies the maximal ratio between the travel times of different users with shared origins and destinations. To obtain feasible solutions to the $\beta$-fair SO problem while achieving high system efficiency, we develop a new convex program, the Interpolated Traffic Assignment Problem (I-TAP), which interpolates between a fair and an efficient traffic-assignment objective. We then leverage the structure of I-TAP to develop two pricing mechanisms to collectively enforce the I-TAP solution in the presence of selfish homogeneous and heterogeneous users, respectively, that independently choose routes to minimize their own travel costs. We mention that this is the first study of pricing in the context of fair routing. Finally, we use origin-destination demand data for a range of transportation networks to numerically evaluate the performance of I-TAP as compared to a state-of-the-art algorithm. The numerical results indicate that our approach is faster by several orders of magnitude, while achieving higher system efficiency for most levels of unfairness.
翻译:最优(SO) 系统最优(SO) 路由问题,即将所有用户的旅行时间全部减少到最低,是运输当局的一个神圣的弱点。然而,对于旅行时间比其他用户多得多的用户来说,为了实现系统效率,也即旅行时间总数少,因此路由路线可能歧视旅行时间比其他用户多得多的用户。为了解决路由路线本身固有的不公平问题,我们研究了美元-美元-公平(SO)问题,其目标是尽量减少总旅行时间,同时保证1美元/贝塔/geq 1美元的不公待遇,具体规定不同用户旅行时间的最大比重。为了在达到较高的系统效率的同时找到解决美元-美元-公平(SO)问题的可行办法,我们制定了一个新的康韦克斯方案,即国际间交通分配问题(I-TAP),它是一个公平而高效的交通目标。然后我们利用I-TAP的结构来制定两个定价机制,在自私的用户面前,分别独立选择更高的路线来尽量减少他们自己的旅行费用。我们提到,这是在最公平的运输水平上,我们用一个数字序列来比较的网络来评估。