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首页> 外文期刊>Transportation Research Part B: Methodological >Macroscopic relations of urban traffic variables: Bifurcations, multivaluedness and instability
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Macroscopic relations of urban traffic variables: Bifurcations, multivaluedness and instability

机译：城市交通变量的宏观关系：分叉，多值性和不稳定性

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摘要

Recent experimental work has shown that the average flow and average density within certain urban networks are related by a unique, reproducible curve known as the Macroscopic Fundamental Diagram (MFD). For networks consisting of a single route this MFD can be predicted analytically; but when the networks consist of multiple overlapping routes experience shows that the flows observed in congestion for a given density are less than those one would predict if the routes were homogeneously congested and did not overlap. These types of networks also tend to jam at densities that are only a fraction of their routes' average jam density. This paper provides an explanation for these phenomena. It shows that, even for perfectly homogeneous networks with spatially uniform travel patterns, symmetric equilibrium patterns with equal flows and densities across all links are unstable if the average network density is sufficiently high. Instead, the stable equilibrium patterns are asymmetric. For this reason the networks jam at lower densities and exhibit lower flows than one would predict if traffic was evenly distributed. Analysis of small idealized networks that can be treated as simple dynamical systems shows that these networks undergo a bifurcation at a network-specific critical density such that for lower densities the MFDs have predictably high flows and are univalued, and for higher densities the order breaks down. Microsimulations show that this bifurcation also manifests itself in large symmetric networks. In this case though, the bifurcation is more pernicious: once the network density exceeds the critical value, the stable state is one of complete gridlock with zero flow. It is therefore important to ensure in real-world applications that a network's density never be allowed to approach this critical value. Fortunately, analysis shows that the bifurcation's critical density increases considerably if some of the drivers choose their routes adaptively in response to traffic conditions. So far, for networks with adaptive drivers, bifurcations have only been observed in simulations, but not (yet) in real life. This could be because real drivers are more adaptive than simulated drivers and/or because the observed real networks were not sufficiently congested.
机译：最近的实验工作表明，某些城市网络中的平均流量和平均密度与被称为宏观基本图（MFD）的独特，可复制的曲线有关。对于由单个路由组成的网络，可以通过分析来预测该MFD；但是，当网络由多个重叠的路线组成时，经验表明，对于给定的密度，在拥塞中观察到的流量要小于那些预测的流量是否均匀拥塞且没有重叠的流量。这些类型的网络还倾向于以仅是其路由平均阻塞密度的一小部分的密度进行阻塞。本文为这些现象提供了解释。它表明，即使对于平均均质的网络，其空间分布均具有均匀的旅行模式，但如果平均网络密度足够高，则在所有链路上具有相等流量和密度的对称平衡模式也是不稳定的。相反，稳定的平衡模式是不对称的。由于这个原因，网络阻塞的密度较低，并且流量低于人们预测流量是否均匀分布的流量。对可以视为简单动力系统的小型理想网络的分析表明，这些网络在特定于网络的临界密度下经历了分叉，因此对于较低的密度，MFD具有可预测的高流量和单值，而对于较高的密度，该阶分解。微观仿真表明，这种分歧也表现在大型对称网络中。但是，在这种情况下，分叉会更加有害：一旦网络密度超过临界值，稳定状态便是零流量的完全僵局之一。因此，重要的是要确保在实际应用中，不允许网络的密度接近该临界值。幸运的是，分析表明，如果一些驾驶员根据交通情况自适应地选择路线，则分叉的临界密度会大大提高。到目前为止，对于具有自适应驱动器的网络，只在仿真中观察到分叉，而在现实生活中尚未观察到。这可能是因为实际的驱动程序比模拟的驱动程序更具适应性，并且/或者因为观察到的实际网络没有足够的拥塞。

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