Nash流随时间的变化及溢出和运动波
Nash Flows over Time with Spillback and Kinematic Waves
摘要：
道路网络中的交通建模是一个广泛研究但具有挑战性的问题，特别是在假设驾驶员自私行为的情况下。一种常见的方法是确定性排队模型，在过去的几年中，动态平衡的结构已被广泛研究。其基本思想是通过一个连续的流量，通过网络，其中弧被赋予过境时间和能力的时间旅行模型。当流速超过容量时，流动颗粒就会形成一个队列。到目前为止，它是不可能的，以代表在这个模型中的溢出或运动波。通过引入存储容量，弧可以变满，并且因此可能阻塞前面的弧，即，会发生溢出。此外，我们模拟运动波的上游移动流量随着时间的推移，代表车辆之间的差距。我们将原模型的主要结果推广到我们的推广中，即，我们通过特定静态流的序列来描述纳什流随时间的变化，即所谓的溢出细流。此外，我们给出了一个建设性的证明的存在性的动态平衡，这表明其计算的算法。这解决了[13]中提出的一个开放问题。
英文摘要：
Modeling traffic in road networks is a widely studied but challenging problem, especially under the assumption that drivers act selfishly. A common approach is the deterministic queuing model, for which the structure of dynamic equilibria has been studied extensively in the last couple of years. The basic idea is to model traffic by a continuous flow that travels over time through a network, in which the arcs are endowed with transit times and capacities. Whenever the flow rate exceeds the capacity the flow particles build up a queue. So far it was not possible to represent spillback or kinematic waves in this model. By introducing a storage capacity arcs can become full, and thus, might block preceding arcs, i.e., spillback occurs. Furthermore, we model kinematic waves by upstream moving flows over time representing the gaps between vehicles. We carry over the main results of the original model to our generalization, i.e., we characterize Nash flows over time by sequences of particular static flows, so-called spillback thin flows. Furthermore, we give a constructive proof for the existence of dynamic equilibria, which suggests an algorithm for their computation. This solves an open problem stated by [13].
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