Traffic Equilibrium with Responsive Traffic Control
Traffic Equilibrium with Responsive Traffic Control
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DOI：
10.1287/trsc.27.2.118
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发表时间：
1993-05
期刊：
影响因子：
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通讯作者：
Mike Smith;T. Vuren
中科院分区：
文献类型：
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作者：
Mike Smith;T. Vuren
本文提出了一种包含响应式信号控制策略的交通平衡理论，该理论以对称的方式处理驾驶员的路径选择和控制策略对绿色时间的选择。本文的中心思想是迭代优化指派算法。该算法可以被认为是计算与给定的响应控制策略相一致的平衡的一种手段。但是，它也可以被视为一个高度理想化的模型的日常动态驾驶员的路线选择时，一个响应信号设置政策;在“第1天”，信号保持固定并且驾驶员稳定到平衡流模式，在“第2天”，流模式保持固定并且根据用于固定流模式的控制策略更新信号，在“第3天”，信号保持固定，驾驶员稳定到“平衡流模式”。我们国家的自然，但强有力的条件下，保证该算法必然会收敛到一个凸集的流量，控制对，使i的流量是一个用户的平衡和ii的控制参数满足响应控制策略，我们给出了一个收敛的证明，在这些条件下，我们不寻求最小化总旅行成本。我们的条件涉及的延迟或成本公式使用的BPR成本公式，修改以自然的方式，允许绿色时间，传统的政策选择控制参数，最大限度地减少所观察到的交通模式的延迟完全满足这些条件。然而，与韦伯斯特的延迟公式传统的控制策略是一个漫长的路要走，从满足我们的条件，并寻求满足他们与此延迟公式导致我们两个新的控制策略。我们假设整个需求是由一个固定的OD矩阵，给出每个OD对的稳定总流量。我们还假设网络特性不变，因此不考虑事件，例如饱和流是恒定的。
This paper presents a theory of traffic equilibrium which involves responsive signal control policies; in this theory drivers' route choices and the control policy's choice of green times are treated in a symmetrical manner. The central theme of the paper is the iterative optimization assignment algorithm. This algorithm may be considered as a means of calculating equilibria which are consistent with a given responsive control policy. But it may also be regarded as a highly idealized model of the day to day dynamics of drivers' route choices when a responsive signal setting policy is employed; on "day" 1 the signals are held fixed and drivers settle down to an equilibrium flow pattern, on "day 2" the flow pattern is held fixed and the signals are updated according to the control policy for the fixed flow pattern, on "day" 3 the signals are held fixed and drivers settle down to an equilibrium flow pattern'. We state natural but strong conditions on the responsive control policy which guarantee that this algorithm is bound to converge to a convex set of flow, control pairs such that i the flow is a user equilibrium and ii the control parameters satisfy the responsive control policy; and we give a proof of convergence under these conditions-we do not seek to minimize total travel cost. Our conditions involve the delay or cost formula used; with the BPR cost formula, modified in a natural way to allow for green times, the traditional policy of choosing control parameters which minimize delay for the observed traffic pattern does satisfy these conditions in full. However, with Webster's delay formula traditional control policies are a long way from satisfying our conditions; and seeking to satisfy them with this delay formula leads us to two novel control policies. We assume throughout that demand is determined by a fixed OD matrix, giving the steady total flow rates for each OD pair. We also suppose that network characteristics do not change; so that incidents are not considered and saturation flows, for example, are constant.