Modeling the traffic flow evolution process after a network disruption. - He, Xiaozheng (My University, 2010)
Major disruption to a transportation network can disturb traffic flow patterns significantly. To deploy effective and efficient traffic restoration projects, a good prediction of the traffic flow pattern under network disruption is vital. Although traffic flow evolution processes have been modeled in various ways in the literature, very limited attention has been paid to the traffic flow evolution process after an unexpected network disruption. In fact, due to the lack of data, none of the existing day-to-day traffic assignment models have been compared against reality, and thus their quality has not yet been verified. There clearly exists a gap between day-to-day traffic flow evolution modeling and their practical applications, especially under network disruption scenarios that are of great interest to traffic management authorities. This doctoral research is dedicated to bridging that gap by developing and validating innovative new models for deterministic day-to-day traffic assignment problem. The first innovation is the development of a link-based traffic dynamic model for studying traffic evolution. Existing deterministic day-to-day traffic assignment models were all built upon path flow variables. Most path-based models, however, suffer two essential shortcomings. One is that their application requires a given initial path flow pattern, which is typically unidentifiable, i.e., mathematically nonunique and practically unobservable. In addition, different initial path flow patterns constituting the same link flow pattern generally gives different day-to-day link flow evolutions. The second shortcoming is the path overlapping problem, whereby the interdependence of paths is ignored, leading to unreasonable results for networks with overlapping paths. The proposed link-based day-to-day traffic dynamic model avoids the two shortcomings, and captures travelers' cost-minimization behavior in their path finding as well as their inertia. The stable point of the link-based dynamical system is rigorously proven to be the classic Wardrop user equilibrium. Its asymptotic stability is guaranteed under mild conditions. Our second innovation is the establishment of a "prediction-correction" framework for modeling traffic evolution after an unexpected network disruption. By studying actual behavioral changes of drivers after the collapse of the I-35W Mississippi River Bridge in Minneapolis, we found that most existing day-to-day traffic assignment models would not be suitable for modeling traffic evolution under network disruption, because they assume that drivers' travel cost perception depends solely on their experience from previous days. They do not recognize that, when a significant network change occurs unexpectedly, travelers' past experience on a traffic network may not be entirely useful if the disturbance to traffic patterns is extensive. To remedy this, this research proposes a "prediction-correction" model to describe the traffic equilibration process, in which travelers predict traffic patterns after network changes and gradually correct their predictions according to their new travel experience. We also prove rigorously that, under mild assumptions, the proposed "prediction-correction" process has the Wardrop user equilibrium flow pattern as a globally attractive point. Most importantly, this doctoral research verifies the proposed models against a real network disruption scenario. The proposed models are calibrated and validated with field data collected after the collapse of the I-35W Bridge. This study bridges the gap between theoretical modeling and practical applications of day-to-day traffic equilibration approaches and promotes a further understanding of traffic equilibration processes after an unexpected network disruption.
University of Minnesota Ph.D. dissertation. DEcember 2010. Major: Civil Engineering. Advisors: Dr. Henry Liu, Dr. David Levinson. 1 computer file (PDF); xi, 127 pages, appendix page 127. Ill. (some col.)
Keywords: Dynamical System; Network Disruption; Stability; Traffic Equilibration; User Equilibrium; Civil Engineering