平衡车辆交通的同步流和宽移动堵塞
Synchronized flow and wide moving jams from balanced vehicular traffic
摘要：
最近，我们提出了一个扩展的Aw，Rascle和Greenberg的流量模型。扩展的交通模型可以写成一个双曲线系统的平衡定律和数值再现的反向$λ$形状的基本图的交通流。在目前的工作中，我们分析了新模型的稳态解及其稳定性。除了平衡流动曲线之外，平凡的稳态解在流动-密度图中形成另外两个分支。我们发现，特征结构排除这些分支的部分，从而导致反向$λ$形状的流量密度关系。上分支是亚稳态的同步流的形成为中等密度和不稳定的高密度，而下分支是不稳定的中等密度和亚稳态的高密度。此外，该模型可以再现宽移动堵塞下游前缘的典型速度。它进一步再现了一个恒定的流出广泛移动堵塞，这是远远低于最大自由流。应用该模型来模拟交通流的瓶颈，我们观察到一个一般的模式与广泛的移动堵塞旅行通过瓶颈。
英文摘要：
Recently we proposed an extension to the traffic model of Aw, Rascle and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse $λ$ shape of the fundamental diagram of traffic flow. In the current work we analyze the steady state solutions of the new model and their stability properties. In addition to the equilibrium flow curve the trivial steady state solutions form two additional branches in the flow-density diagram. We show that the characteristic structure excludes parts of these branches resulting in the reverse $λ$ shape of the flow-density relation. The upper branch is metastable against the formation of synchronized flow for intermediate densities and unstable for high densities, whereas the lower branch is unstable for intermediate densities and metastable for high densities. Moreover, the model can reproduce the typical speed of the downstream front of wide moving jams. It further reproduces a constant outflow from wide moving jams, which is far below the maximum free flow. Applying the model to simulate traffic flow at a bottleneck we observe a general pattern with wide moving jams traveling through the bottleneck.
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