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首页> 外文期刊>Transportation research, Part B. Methodological >Kinematic wave models of lane-drop bottlenecks
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Kinematic wave models of lane-drop bottlenecks

机译：车道下降瓶颈的运动学波模型

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Lane-drop bottlenecks lead to both capacity reduction and capacity drop, but there are no systematic studies on traffic dynamics, especially the stationary traffic patterns when the upstream link is congested, at such critical bottlenecks within the framework of kinematic wave theory. In this paper, we study three kinematic wave models for both discontinuous and continuous lane-drop bottlenecks, where the number of lanes drops either suddenly or gradually. In the first two models, we apply the multilane LWR model (Lighthill and Whitham, 1955; Richards, 1956) for a discontinuous and continuous lane-drop bottleneck, respectively; in the third model, we assume that the standing wave is instantaneous inside a continuous lane-drop bottleneck. For the first model, we apply the kinematic wave theory developed in Jin et al. (2009) to solve the Riemann problem. In particular, we present an optimization formulation for the entropy condition, solve the stationary states and kinematic waves on both upstream and downstream links, and define instantaneous discontinuous standing waves connecting the upstream and downstream links' stationary states. For the second model, we define a generalized Riemann problem and show that the asymptotic stationary states and kinematic waves on both links are the same as those in the first model, but the asymptotic standing wave is continuous, comprising of stationary states inside the whole lane-drop zone. Assuming standing waves to be instantaneous as in the first model but continuous as in the second model, we present a new model of a continuous lane-drop bottleneck and a new theoretical framework to solve the generalized Riemann problem. Finally we develop three corresponding Cell Transmission Models and verify theoretical results, especially the presence and structure of continuous standing waves inside a continuous lane-drop zone, with numerical examples. We find that vehicles' acceleration rates across the standing waves can be infinite in the first model and unrealistically large in the other two and that there is no capacity drop in all of the models. The theoretical framework of the third model forms a basis for a follow-up study, (fin, 2017), in which we introduce bounded acceleration as an additional constraint on the instantaneous standing waves and present a behavioral model of capacity drop. (C) 2017 Elsevier Ltd. All rights reserved.
机译：车道下降瓶颈会导致容量减少和容量下降，但在运动波理论框架内，没有系统地研究交通动态，特别是上游链路拥堵时的静止交通模式。在本文中，我们研究了三种运动波模型，用于不连续和连续的车道下降瓶颈，其中车道数量突然或逐渐下降。在前两个模型中，我们应用了多车道轻水堆模型（Lighthill and Whitham， 1955;Richards，1956）分别表示不连续和连续的车道下降瓶颈;在第三个模型中，我们假设驻波在连续的车道下降瓶颈内是瞬时的。对于第一个模型，我们应用Jin等人（2009）开发的运动波理论来解决黎曼问题。特别是，我们提出了熵条件的优化公式，求解了上行和下行链路上的稳态和运动波，并定义了连接上行和下行链路稳态的瞬时不连续驻波。对于第二个模型，我们定义了一个广义黎曼问题，并表明两个链接上的渐近稳态和运动波与第一个模型相同，但渐近驻波是连续的，由整个车道下降区内的稳态组成。假设驻波在第一个模型中是瞬时的，但在第二个模型中是连续的，我们提出了一个连续的车道下降瓶颈的新模型和一个新的理论框架来解决广义黎曼问题。最后，我们建立了三个相应的小区传输模型，并通过数值算例验证了理论结果，特别是连续车道下降区内连续驻波的存在和结构。我们发现，在第一个模型中，车辆在驻波上的加速度可能是无限的，而在其他两个模型中则大得不切实际，并且所有模型的容量都没有下降。第三个模型的理论框架为后续研究奠定了基础（fin，2017），其中我们引入了有界加速度作为瞬时驻波的附加约束，并提出了容量下降的行为模型。（C） 2017 爱思唯尔有限公司保留所有权利。

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