TY - JOUR
T1 - Statistical metamodeling of dynamic network loading
AU - Song, Wenjing
AU - Han, Ke
AU - Wang, Yiou
AU - Friesz, Terry
AU - Del Castillo, Enrique
N1 - Publisher Copyright:
© 2017 The Authors. Elsevier B.V. All rights reserved.
PY - 2017
Y1 - 2017
N2 - Dynamic traffic assignment models rely on a network performance module known as dynamic 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 network delay 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 as Kriging. 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.
AB - Dynamic traffic assignment models rely on a network performance module known as dynamic 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 network delay 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 as Kriging. 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.
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U2 - 10.1016/j.trpro.2017.05.016
DO - 10.1016/j.trpro.2017.05.016
M3 - Article
AN - SCOPUS:85020516663
SN - 2352-1457
VL - 23
SP - 263
EP - 282
JO - Transportation Research Procedia
JF - Transportation Research Procedia
ER -