A dual approximation framework for dynamic network analysis: congestion pricing, traffic assignment calibration and network design problem
Dynamic Traffic Assignment (DTA) is gaining wider acceptance among agencies and practitioners because it serves as a more realistic representation of real-world traffic phenomena than static traffic assignment. Many metropolitan planning organizations and transportation departments are beginning to utilize DTA to predict traffic flows within their networks when conducting traffic analysis or evaluating management measures. To analyze DTA-based optimization applications, it is critical to obtain the dual (or gradient) information as dual information can typically be employed as a search direction in algorithmic design. However, very limited number of approaches can be used to estimate network-wide dual information while maintaining the potential to scale. This dissertation investigates the theoretical/practical aspects of DTA-based dual approximation techniques and explores DTA applications in the context of various transportation models, such as transportation network design, off-line DTA capacity calibration and dynamic congestion pricing. Each of the later entities is formulated as bi-level programs. Transportation Network Design Problem (NDP) aims to determine the optimal network expansion policy under a given budget constraint. NDP is bi-level by nature and can be considered a static case of a Stackelberg game, in which transportation planners (leaders) attempt to optimize the overall transportation system while road users (followers) attempt to achieve their own maximal benefit. The first part of this dissertation attempts to study NDP by combining a decomposition-based algorithmic structure with dual variable approximation techniques derived from linear programming theory. One of the critical elements in considering any real-time traffic management strategy requires assessing network traffic dynamics. Traffic is inherently dynamic, since it features congestion patterns that evolve over time and queues that form and dissipate over a planning horizon. It is therefore imperative to calibrate the DTA model such that it can accurately reproduce field observations and avoid erroneous flow predictions when evaluating traffic management strategies. Satisfactory calibration of the DTA model is an onerous task due to the large number of variables that can be modified and the intensive computational resources required. In this dissertation, the off-line DTA capacity calibration problem is studied in an attempt to devise a systematic approach for effective model calibration. Congestion pricing has increasingly been seen as a powerful tool for both managing congestion and generating revenue for infrastructure maintenance and sustainable development. By carefully levying tolls on roadways, a more efficient and optimal network flow pattern can be generated. Furthermore, congestion pricing acts as an effective travel demand management strategy that reduces peak period vehicle trips by encouraging people to shift to more efficient modes such as transit. Recently, with the increase in the number of highway Build-Operate-Transfer (B-O-T) projects, tolling has been interpreted as an effective way to generate revenue to offset the construction and maintenance costs of infrastructure. To maximize the benefits of congestion pricing, a careful analysis based on dynamic traffic conditions has to be conducted before determining tolls, since sub-optimal tolls can significantly worsen the system performance. Combining a network-wide time-varying toll analysis together with an efficient solution-building approach will be one of the main contributions of this dissertation. The problems mentioned above are typically framed as bi-level programs, which pose considerable challenges in theory and as well as in application. Due to the non-convex solution space and inherent NP-complete complexity, a majority of recent research efforts have focused on tackling bi-level programs using meta-heuristics. These approaches allow for the efficient exploration of complex solution spaces and the identification of potential global optima. Accordingly, this dissertation also attempts to present and compare several meta-heuristics through extensive numerical experiments to determine the most effective and efficient meta-heuristic, as a means of better investigating realistic network scenarios.
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