Statistical metamodeling of dynamic network loading
Statistical metamodeling of dynamic network loading
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DOI：
10.1016/j.trpro.2017.05.016
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发表时间：
2018-11
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影响因子：
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通讯作者：
Wenjing Song;Ke Han;Yiou Wang;T. Friesz;Enrique del Castillo
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文献类型：
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作者：
Wenjing Song;Ke Han;Yiou Wang;T. Friesz;Enrique del Castillo
动态流量分配模型依赖于称为动态网络负载（DNL）的网络性能模块，它表达了网络级别的流量传播、流量守恒和行程延迟的动态。 DNL定义了所谓的网络延迟算子，它将一组路径离开率映射到一组路径旅行时间。众所周知，延迟算子不能以封闭形式提供，并且具有使 DTA 分析和计算严重复杂化的不良特性，例如不连续性、不可微性、非单调性和计算效率低下。本文通过提供一类基于统计学习方法（称为克里金法）的代理 DNL 模型，对这个重要且困难的问题提出了新的看法。我们提出了一个元建模框架，该框架系统地近似 DNL 模型，并且在允许建模者在模型粒度、复杂性和准确性之间进行权衡的意义上是灵活的。结果表明，此类替代 DNL 模型可产生高度准确的近似值（误差低于 8%）和卓越的计算效率（比传统 DNL 程序快 9 至 455 倍）。此外，这些近似 DNL 模型允许闭式和解析延迟算子，这些算子是 Lipschitz 连续且无限可微的，同时具有闭式雅可比行列式。深入讨论了这些理想特性对 DTA 研究和模型应用的影响。
Dynamic traffic assignment models rely on a network performance module known asdynamic network loading(DNL), which expresses the dynamics of flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called networkdelay operator,which maps a set of path departure rates to a set of path travel times. It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, non-differentiability, non-monotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult problem, by providing a class of surrogate DNL models based on a statistical learning method known asKriging.We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, while possessing closed-form Jacobians. The implications of these desirable properties for DTA research and model applications are discussed in depth.