Continuity of the Effective Delay Operator for Networks Based on the Link Delay Model
Continuity of the Effective Delay Operator for Networks Based on the Link Delay Model
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DOI：
10.1007/s11067-017-9379-5
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发表时间：
2017-12
影响因子：
2.4
通讯作者：
Ke Han;T. Friesz
中科院分区：
文献类型：
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作者：
Ke Han;T. Friesz
本文关注动态交通网络性能模型，称为动态网络负载（DNL），该模型经常用于分析动态用户均衡（DUE）的建模和计算。作为连续时间 DUE 模型的关键组成部分，DNL 旨在通过引入适当的动态来描述和预测流量传播、流量守恒和出行延误的动态，从而描述和预测与出行者既定路线和出发时间选择一致的网络上交通流的时空演化。 DNL 过程产生路径延迟算子，它将路径流向量（路径离开率）与相应的路径旅行成本相关联。在本文中，我们为通过链路延迟模型描述弧流的网络建立了路径延迟算子的强连续性（Friesz et al., Oper Res 41(1):80–91, 1993; Carey, Networks and Spatial Economics 1(3):349–375, 2001）。与 Zhu 和 Marcotte (Transp Sci 34(4):402–414, 2000) 建立的结果不同，我们的连续性证明是在不假设路径流的先验一致有界性的情况下构建的。这种更一般的连续性结果对于没有路径流的先验有界性的同时路线和出发时间 DUE 的存在以及任何允许严格分析收敛的数值算法有一些重要的影响。
This paper is concerned with a dynamic traffic network performance model, known asdynamic network loading(DNL), that is frequently employed in the modeling and computation of analyticaldynamic user equilibrium(DUE). As a key component of continuous-time DUE models, DNL aims at describing and predicting the spatial-temporal evolution of traffic flows on a network that is consistent with established route and departure time choices of travelers, by introducing appropriate dynamics to flow propagation, flow conservation, and travel delays. The DNL procedure gives rise to the path delay operator, which associates a vector of path flows (path departure rates) with the corresponding path travel costs. In this paper, we establish strong continuity of the path delay operator for networks whose arc flows are described by thelink delay model(Friesz et al., Oper Res 41(1):80–91, 1993; Carey, Networks and Spatial Economics 1(3):349–375, 2001). Unlike the result established in Zhu and Marcotte (Transp Sci 34(4):402–414, 2000), our continuity proof is constructed without assuminga prioriuniform boundedness of the path flows. Such a more general continuity result has a few important implications to the existence ofsimultaneous route-and-departure-timeDUE withouta prioriboundedness of path flows, and to any numerical algorithm that allows convergence to be rigorously analyzed.