Statistical learning of dynamic transportation models
Open Access
- Author:
- Song, Wenjing
- Graduate Program:
- Industrial Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- July 20, 2020
- Committee Members:
- Terry Lee Friesz, Dissertation Advisor/Co-Advisor
Terry Lee Friesz, Committee Chair/Co-Chair
Enrique Del Castillo, Committee Member
Runze Li, Committee Member
Vikash V. Gayah, Outside Member
Steven James Landry, Program Head/Chair
Vinayak Uday Shanbhag, Committee Member - Keywords:
- Statistical learning
Kriging
Dynamic traffic assignment
Dynamic network loading
Dynamic user equilibrium
Big data - Abstract:
- Statistical learning (machine learning) and big data are among the most rapidly growing fields in the 21st century. Big-data based technologies emerge fast to provide business insight, push the boundaries of traditional communication, support informed decisions, and improve healthcare services. Statistical models are developed, revised, and applied every day to cope with the challenges big data brings. In the big data era, well-developed statistical models are crucial to meeting the needs involved in studying transportation systems and the associated management challenges that accompany vehicular traffic operations. Modern traffic management emphasizes smart signal controls, automated driving, tolling, congestion relief, and emergency support during critical events of a public health and/or security nature. These traffic management tasks are intrinsically dynamic. In the field of transportation research, statistical learning methods are being increasingly applied to aid traffic management and forecasting. However, existing application of statistical learning to transportation modeling neither overcomes the need to mathematically articulate models nor resolves the curse of dimensionality that plagues all large-scale models. Rather, these studies provide alternative ways to make predictions based on already established models; those alternatives reduce the burden of finding new solutions when fundamental parameters change or data is insufficient. In this dissertation, we conduct original statistical learning studies on some of the most difficult traffic modeling problems with the aim of enhancing both computational efficiency and analytical simplicity. We present surrogate models, coupled to established traffic assignment and path finding procedures, that provide a family of new statistics-assisted dynamic transportation modeling methods. The new framework that incorporates statistical models into DTA constitutes a paradigm shift. By taking a statistics-oriented direction, existing dynamic traffic assignment (DTA) models can be upgraded following our new framework without fundamental difficulty. This includes dynamic network loading (DNL), dynamic user equilibrium (DUE), and bi-level models for transportation network design and control. DTA models rely on a network performance module known as dynamic network loading (DNL), which expresses flow propagation, flow conservation, and travel delay on a network level. DNL determines the so-called network delay operator, which maps a set of path departure rates to a set of path travel times or costs (delays). It is well 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, nonmonotonicity, and computational inefficiency. Given the theoretical and computational limitations of the conventional way of exploring the delay operator, we first propose a fresh take on this classic problem from the novel perspective of statistical metamodeling. Development of a DNL metamodel is the main focus of the first part of this dissertation, and the core technique on which the subsequent studies are built. In the DNL metamodeling part, our goal is to provide a class of surrogate DNL models that approximate the exact ones, with considerable benefits, including closed-form representation, improved regularity, and superior computational efficiency, at the expense of minor yet controllable approximation errors. Successful metamodeling of the DNL submodel opens a pathway to a family of new network performance models with a level of tractability not generally seen in conventional DNL; the result is a tool for improving the analytical and computational experience associated with various classes of dynamic transportation problems. Any model that involves evaluating travel time on a network whose agents behave in an intrinsically dynamic way would benefit from the paradigm presented in this dissertation. Furthermore, we propose to apply our DNL metamodel to a group of classical dynamic transportation problems that require a delay operator, taking advantage of the closed form representation and analytical properties of the metamodel over conventional non-closed form DNL procedures. These applications include the reformulation of an approximate DUE with a closed-form delay operator and bi-level optimization problems with DUE embedded in its lower level. We also introduce network aggregation through clustering and provide alternative covariance functions. These developments enable several extensions on the statistical metamodeling framework to help it accommodate a wider range of traffic models, including large-scale network models and bi-level DTA. Moreover, these extensions still enjoy all the desirable properties of the original model. We provide in-depth discussions on the implications of these properties in DTA research. This dissertation contains eight chapters. In Chapter 1-3 we review dynamic transportation models and Kriging/metamodeling. In Chapter 4 we present the novel approach to build surrogate models for DNL using statistical metamodeling. Chapter 5 contains extensions of the notions of a distance metric, covariance function and modeling framework. Chapter 6 and Chapter 7 discusses applications to large-scale networks and bi-level problems. In the final chapter, we summarize the new statistical models presented for handling the challenges brought by big data in conjunction with DTA and suggest future research directions.