Date of Award:

5-2013

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Civil and Environmental Engineering

Committee Chair(s)

Anthony Chen

Committee

Anthony Chen

Committee

Yong Seog Kim

Committee

Gilberto E. Urroz

Committee

Gary P. Merkley

Committee

Kevin P. Heaslip

Abstract

Traffic assignment problem is an important component of the transportation planning model. State-of-the-practice traffic assignment models adopt the equilibrium principle to equilibrate the travel demand with the travel supply (e.g., highway and transit networks) under congestion. These models give the transportation network performance measures to compare among transportation alternatives for supporting the decision-making processes. The deterministic user equilibrium (DUE) principle is perhaps the most widely used in the traffic assignment problem. In this principle, all travelers are assumed to minimize their individual travel cost, such that only the lowest-cost route is used at equilibrium. However, this perfect knowledge assumption is unrealistic. Travelers do not know the exact travel costs of all possible routes in the transportation network, and some travelers do not always use the minimum travel cost criterion for their route selection.

To relax this restrictive perfect knowledge assumption, the stochastic user equilibrium (SUE) principle was suggested. A random error term is incorporated in the route cost function to simulate travelers’ imperfect perceptions of network travel costs, such that they do not always end up selecting only the minimum cost route. In the literature, two widely used random error terms are Gumbel and Normal distributions, corresponding to the multinomial logit (MNL) and multinomial probit (MNP) route choice models, respectively. The MNL model has a closed-form probability expression, and the MNL-SUE model can be formulated as an equivalent mathematical programming (MP) formulation under congestion. Several efficient algorithms can be applied to solve this MNL-SUE model in a real-size network. The two major drawbacks of this model are: (1) inability to handle route overlapping (or correlation) among routes, and (2) inability to account for heterogeneous perception variance with respect to different trip lengths. These two drawbacks stem from the underlying assumption of an independently and identically distributed (IID) Gumbel variate. The multinomial probit (MNP) model, on the other hand, does not have such drawbacks. This route choice model uses the Normal distribution to allow the covariance between random error terms for pairs of routes; however, due to the lack of a closed-form solution, the MNP-SUE model is computationally burdensome when the choice set contains more than a handful of routes.

In this study, we provide a new SUE model using the Weibull random error terms as an alternative to overcome the drawbacks of these two classical SUE models. A pathsize weibit (PSW) model is developed to handle both route overlapping among routes and heterogeneous perception variance with respect to different trip lenghts, while retaining an analytical closed-form solution. Specifically, the PSW route choice model handles the route overlapping through the path-size factor and handles the route-specific perception variance through the Weibull distributed random error terms. Both constrained and unconstrained equivalent MP formulations for the PSW-SUE model are provided. In addition, model extensions to consider the demand elasticity and combined travel choice of the PSW-SUE model are also provided. Unlike the logit-based model, these model extensions incorporate the logarithmic expected perceived travel cost as the network level of service to determine the demand elasticity and travel choice. Qualitative properties of these minimization programs are given to establish equivalency and uniqueness conditions. Both path-based and link-based algorithms are developed for solving the proposed MP formulations. Numerical examples show that the proposed models can produce a compatible traffic flow pattern compared to the MNP-SUE model, and these models can be implemented in a real-world transportation network.

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