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Title: Probit-based stochastic user equilibrium problems and their applications in congestion pricing
Keywords: stochastic user equilibrium, traffic assignment, congestion pricing, distributed computing, elastic demand
Issue Date: 7-Jun-2011
Citation: LIU ZHIYUAN (2011-06-07). Probit-based stochastic user equilibrium problems and their applications in congestion pricing. ScholarBank@NUS Repository.
Abstract: When compared to other user equilibrium principles for traffic assignment, the probit-based stochastic user equilibrium (SUE) is known to have properties well suited for practical conditions. However, theoretical studies and practical implementations of probit-based SUE are largely limited due to the difficulties of solving such a problem. Thus, a primary objective of this dissertation is to inherently reduce the computational time of solving the probit-based SUE problem. To further improve its suitability to practical conditions, the following extensions are further taken into consideration for the traffic assignment problem (a) elastic demand, (b) asymmetric link travel time functions, termed as probit-based asymmetric SUE problem with elastic demand (PA-SUEED). Although it converges sub-linearly, the cost averaging (CA) method is the only known convergent algorithm for PA-SUEED in the literature. This dissertation accelerates the computation of PA-SUEED from two aspects: firstly, it proposes two projection-type prediction-correction (PC) algorithms with linear convergent speed. As validated by numerical experiments, the two PC algorithms can accelerate the computational speed for five to ten times, when compared with CA method; secondly, note that the solution algorithms for SUE problems need to calculate the stochastic network loading (SNL) problem in each iteration, and solution algorithm for the SNL in the context of PA-SUEED is still an open question. A link-based two-stage Monte Carlo simulation method is proposed for the SNL problem, wherein each trial of this Monte Carlo simulation method is independent with identical tasks, thus it has a superior parallelism. Therefore, this dissertation further improves the computational speed of solving PA-SUEED by proposing three distributed (parallel) computing approaches for its SNL problem. Based on a comprehensive numerical experiment, it shows that the distributed computing approaches can further improve the computational speed for over fifty times. Link capacity constraints are recognized to be a logical extension of standard traffic assignment problems. However, studies for SUE problem with link capacity constraints are fairly scarce, due to the difficulties in formulating and solving this problem. In the context of PA-SUEED, this problem becomes even more complicated and challenging. This dissertation thus investigates about formulating and solving the PA-SUEED with link capacity constraints, which is a highly mathematical topic with considerable theoretical contributions. A VI model is proposed and the monotonicity and Lipschitz-continuity of this VI model are rigorously proven. Based on these properties of the VI model, convergence of a PC algorithm thus can be guaranteed to solve the VI model. The proposed methodology is finally validated by a numerical example. The un-cooperative travel behavior of drivers would usually lead to traffic congestions, especially in the dense urban areas. Thereby, the network authorities intend to encourage them to use uncongested road segments. Congesting pricing is one of the few instruments for this purpose, thus it is a good complement for the studies of traffic assignment. Note that the drivers? value-of-time (VOT) is necessitated for the analysis of congestion pricing. In this study, VOT is assumed to be continuously distributed, to cover the vast diversity of drivers? income levels. On the other hand, the drivers? diversity of perception errors on travel times should also be considered, which gives rise to SUE principles. Thus, another objective of this dissertation is to investigate about the congestion pricing problem with PA-SUEED constraints.
Appears in Collections:Ph.D Theses (Open)

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