Statistical metamodeling of dynamic network loading

Abstract

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.

Asymptotic approximations of transient behaviour for day-to-day traffic models

“…given the advances that have now been made in calculus for more complex dynamic network loading models (Shen et al 2007, Osorio et al 2011, Rinaldi et al 2016, Song et al 2018).…”

Simulation‐based dynamic traffic assignment: Meta‐heuristic solution methods with parallel computing

“…In other words, DTA models depend on a network performance module, which is called DNL. The DNL operator usually is not available in closed form because it severely complicates equilibrium calculation (Ngoduy, 2011;Song, Han, Wang, Friesz, & Del Castillo, 2017). Depending on the kind of simulator used to perform the network loading and determine travel times, the demand from origins to destinations can either be expressed as continuous flow or units of vehicles.…”

Simulation metamodeling approach to complex design of garment assembly lines

“…Kleijnen & Sargent [36] suggested ten (10) steps for developing the linear regression (including polynomial) metamodels for random simulation. The three main steps include: choosing a functional form for the metamodeling function based on the study goal, designing and executing the experiments to fit the metamodel, and model learning/fitting the metamodel and validating the quality of its fit [26,37]. Designing and execution of simulation experiments is one of the fundamental steps in regression metamodeling [38].…”