We consider a dynamic model of traffic that has received a lot of attention in the past few years. Users control infinitesimal flow particles aiming to travel from an origin to a destination as quickly as possible. Flow patterns vary over time, and congestion effects are modeled via queues, which form whenever the inflow into a link exceeds its capacity. Despite lots of interest, some very basic questions remain open in this model. We resolve a number of them: - We show uniqueness of journey times in equilibria. - We show continuity of equilibria: small perturbations to the instance or to the traffic situation at some moment cannot lead to wildly different equilibrium evolutions. - We demonstrate that, assuming constant inflow into the network at the source, equilibria always settle down into a "steady state" in which the behavior extends forever in a linear fashion. One of our main conceptual contributions is to show that the answer to the first two questions, on uniqueness and continuity, are intimately connected to the third. To resolve the third question, we substantially extend the approach of Cominetti et al., who show a steady-state result in the regime where the input flow rate is smaller than the network capacity.

翻译：我们考虑一个近年来备受关注的动态交通模型。用户控制无穷小流量粒子，力求以最快速度从出发地到达目的地。流量模式随时间变化，拥堵效应通过排队来建模——当进入路段的流入量超过其通行能力时，排队即会发生。尽管该模型引起了广泛兴趣，但一些基本问题仍未解决。我们解决了其中若干问题：- 证明了均衡状态下出行时间的唯一性。- 证明了均衡的连续性：对实例或某时刻交通状况的微小扰动，不会导致均衡演化产生剧烈差异。- 我们证明，假设网络源头流入量恒定，均衡总会趋于一种"稳态"，其中行为以线性方式无限延伸。我们的一项主要概念贡献在于，表明前两个问题（唯一性和连续性）的答案与第三个问题密切相关。为解决第三个问题，我们大幅扩展了Cominetti等人的方法——他们证明了在输入流量率小于网络通行能力情形下的稳态结果。