Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment (DTA), in which road travelers engage in a non-cooperative Nash-like
game with departure time and route choices. DUE models describe and predict the
time-varying traffic flows on a network consistent with traffic flow theory and travel
behavior. This paper documents theoretical and numerical advances in synthesizing traffic flow theory and DUE modeling, by presenting a holistic computational
theory of DUE, which is numerically implemented in a MATLAB package. In particular, the dynamic network loading (DNL) sub-problem is formulated as a system
of differential algebraic equations based on the Lighthill-Whitham-Richards fluid
dynamic model, which captures the formation, propagation and dissipation of physical queues as well as vehicle spillback on networks. Then, the fixed-point algorithm
is employed to solve the DUE problems with simultaneous route and departure time
choices on several large-scale networks. We make openly available the MATLAB
package, which can be used to solve DUE problems on user-defined networks, aiming
to not only facilitate benchmarking a wide range of DUE algorithms and solutions,
but also offer researchers a platform to further develop their own models and applications. The MATLAB package and computational examples are available online.
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Statistical Metamodeling of Dynamic Network Loading
Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses 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 (or costs). 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, nondifferentiability, nonmonotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult issue, 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 such as those based on the link transmission model). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, with closed-form Jacobians. We provide in-depth discussions on the implications of these properties to DTA research and model applications.
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- Award ID(s):
- 1662968
- NSF-PAR ID:
- 10122278
- Date Published:
- Journal Name:
- Transportation research. Part B, Methodological
- Volume:
- 117
- ISSN:
- 1879-2367
- Page Range / eLocation ID:
- 740-756
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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