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arXiv 2304.04705eess.SYcs.SY
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基于弧段的交通分配:均衡刻画与学习

Arc-based Traffic Assignment: Equilibrium Characterization and Learning

Chih-Yuan Chiu, Chinmay Maheshwari, Pan-Yang Su, Shankar Sastry

AI总结:

针对基于弧段的交通分配易产生环路且难支持双向网络的问题,本文提出CoDAG表示,证明其均衡唯一且可由严格凸优化刻画,并设计收敛到均衡邻域的离散学习适应机制。

摘要:

基于弧段的交通分配模型(TAM)是一种常用框架,用于建模由自利出行者在网络上根据其感知延迟依次选择弧段而产生的交通网络拥堵。然而,现有的基于弧段的TAM要么会将出行者分配到含环路径,要么无法扩展到节点之间具有双向弧段(或边)的网络。为克服这些困难,我们提出了一种用于随机基于弧段的TAM的新建模框架。给定一个具有双向弧段的交通网络,我们复制其弧段和节点以构建一个有向无环图(DAG),并将其称为Condensed DAG(CoDAG)表示。自利出行者在CoDAG表示上依次选择弧段以到达目的地。我们证明,相关的均衡流(我们称之为Condensed DAG均衡)存在、唯一,并且可以被刻画为一个严格凸优化问题。此外,我们提出了一个离散时间动力系统,用以描述自利出行者为了解网络上涌现的拥堵而采用的自然适应规则。我们证明,由该适应规则生成的弧段流会收敛到Condensed DAG均衡的一个邻域。据我们所知,我们的工作首次研究了基于弧段的TAM中的学习与适应。最后,我们给出了数值结果,以印证我们的理论结果。

英文摘要:

Arc-based traffic assignment models (TAMs) are a popular framework for modeling traffic network congestion generated by self-interested travelers who sequentially select arcs based on their perceived latency on the network. However, existing arc-based TAMs either assign travelers to cyclic paths, or do not extend to networks with bi-directional arcs (or edges) between nodes. To overcome these difficulties, we propose a new modeling framework for stochastic arc-based TAMs. Given a traffic network with bidirectional arcs, we replicate its arcs and nodes to construct a directed acyclic graph (DAG), which we call the Condensed DAG (CoDAG) representation. Self-interested travelers sequentially select arcs on the CoDAG representation to reach their destination. We show that the associated equilibrium flow, which we call the Condensed DAG equilibrium, exists, is unique, and can be characterized as a strictly convex optimization problem. Moreover, we propose a discrete-time dynamical system that captures a natural adaptation rule employed by self-interested travelers to learn about the emergent congestion on the network. We show that the arc flows generated by this adaptation rule converges to a neighborhood of Condensed DAG equilibrium. To our knowledge, our work is the first to study learning and adaptation in an arc-based TAM. Finally, we present numerical results that corroborate our theoretical results.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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