Highlights • A link-to-link segment-based Kriging metamodel of dynamic network loading. • Spatial and temporal proximity and segments’ cross dependency through routes are incorporated. • The segment-based metamodel offers substantial dimension reduction compared to its route-based counterpart. • A furthest point active sampling algorithm is proposed for the training datapoint selection. • The metamodel is tested in the Nguyen-Dupuis and Sioux Falls networks against MATSim and neural network models.

Abstract Dynamic network loading (DNL) is a core part of simulation-based dynamic traffic assignment (DTA) models, which describes how traffic propagates on a transportation network and usually maps a set of route departure rates to a set of route travel times. Due to the incorporation of different intra- and inter-link dynamics such as queuing, spillback, etc., DNL becomes complex, resulting in models with undesirable analytical properties (e.g., discontinuity, non-differentiability, and lack of closed-form) and requiring intensive computational efforts. Moreover, as DNL is applied repeatedly in simulation-based DTA algorithms, it often is the computational bottleneck of large-scale traffic assignment and related optimization problems. In this research, we address these problems by proposing a link-to-link segment-based Kriging metamodel for dynamic network loading. The proposed Kriging model calculates route travel time, link travel time, and link flow. It systematically approximates the traditional DNL model while being faster and maintaining some desirable analytical properties. Both temporal and spatial proximity information and the route segment incidence information are incorporated in the metamodel formulation. The models are trained using maximum likelihood estimation with different dataset sizes. In the experiments, the proposed Kriging metamodels performed better than a state-of-the-art neural network model, achieving an average error of 1.64% and 5.32% in the Nguyen Dupuis (ND) network and the Sioux Falls (SF) network, respectively, along with at least 43 times, sometimes as high as over 1300 times, improvement in computational speed. The results, however, suggest a tradeoff between efficiency and accuracy and the size of the training dataset. With balanced route demand, the model’s performance was reasonable even under congested traffic conditions. The MAPE values were at most 3% and 18% in the ND network and the SF network, respectively, for different level of congestion demonstrating the effectiveness of the proposed model.