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Transit assignment: approach-based formulation, extragradient method, and paradox

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Transit assignment: approach-based formulation, extragradient method, and paradox. / Szeto, W. Y.; Jiang, Y.
In: Transportation Research Part B: Methodological, Vol. 62, 04.2014, p. 51-76.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Szeto WY, Jiang Y. Transit assignment: approach-based formulation, extragradient method, and paradox. Transportation Research Part B: Methodological. 2014 Apr;62:51-76. Epub 2014 Mar 5. doi: 10.1016/j.trb.2014.01.010

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Szeto, W. Y. ; Jiang, Y. / Transit assignment : approach-based formulation, extragradient method, and paradox. In: Transportation Research Part B: Methodological. 2014 ; Vol. 62. pp. 51-76.

Bibtex

@article{6c2b9352d75e4b5ba1db417690098cb6,
title = "Transit assignment: approach-based formulation, extragradient method, and paradox",
abstract = "This paper uses the concept of approach proportion to propose a novel variational inequality (VI) formulation of the frequency-based transit assignment problem. The approach proportion is defined as the proportion of passengers leaving a node through its outgoing link. To solve the VI problem, an extragradient method with adaptive stepsizes is developed. Unlike the existing methods for solving the frequency-based transit assignment problem, the convergence of our method requires only the pseudomonotone and Lipschitz continuous properties of the mapping function in VI, and it is not necessary for the Lipschitz constant to be known in advance. A Braess-like paradox in transit assignment is also discussed, where providing new lines to a transit network or increasing the frequency of an existing line may not improve the system performance in terms of expected total system travel cost. Various numerical examples are given to illustrate some paradox phenomena and to test the performance of our proposed algorithm. (C) 2014 Elsevier Ltd. All rights reserved.",
keywords = "Frequency-based transit assignment, Approach proportion, Extragradient method, Variational inequality, Paradox, PSEUDOMONOTONE VARIATIONAL-INEQUALITIES, TRAFFIC ASSIGNMENT, TRANSPORT NETWORK, CAPACITY CONSTRAINTS, EQUILIBRIUM PROBLEM, ROAD NETWORK, MODEL, DESIGN, FREQUENCY, STRATEGIES",
author = "Szeto, {W. Y.} and Y. Jiang",
year = "2014",
month = apr,
doi = "10.1016/j.trb.2014.01.010",
language = "English",
volume = "62",
pages = "51--76",
journal = "Transportation Research Part B: Methodological",
issn = "0191-2615",
publisher = "PERGAMON-ELSEVIER SCIENCE LTD",

}

RIS

TY - JOUR

T1 - Transit assignment

T2 - approach-based formulation, extragradient method, and paradox

AU - Szeto, W. Y.

AU - Jiang, Y.

PY - 2014/4

Y1 - 2014/4

N2 - This paper uses the concept of approach proportion to propose a novel variational inequality (VI) formulation of the frequency-based transit assignment problem. The approach proportion is defined as the proportion of passengers leaving a node through its outgoing link. To solve the VI problem, an extragradient method with adaptive stepsizes is developed. Unlike the existing methods for solving the frequency-based transit assignment problem, the convergence of our method requires only the pseudomonotone and Lipschitz continuous properties of the mapping function in VI, and it is not necessary for the Lipschitz constant to be known in advance. A Braess-like paradox in transit assignment is also discussed, where providing new lines to a transit network or increasing the frequency of an existing line may not improve the system performance in terms of expected total system travel cost. Various numerical examples are given to illustrate some paradox phenomena and to test the performance of our proposed algorithm. (C) 2014 Elsevier Ltd. All rights reserved.

AB - This paper uses the concept of approach proportion to propose a novel variational inequality (VI) formulation of the frequency-based transit assignment problem. The approach proportion is defined as the proportion of passengers leaving a node through its outgoing link. To solve the VI problem, an extragradient method with adaptive stepsizes is developed. Unlike the existing methods for solving the frequency-based transit assignment problem, the convergence of our method requires only the pseudomonotone and Lipschitz continuous properties of the mapping function in VI, and it is not necessary for the Lipschitz constant to be known in advance. A Braess-like paradox in transit assignment is also discussed, where providing new lines to a transit network or increasing the frequency of an existing line may not improve the system performance in terms of expected total system travel cost. Various numerical examples are given to illustrate some paradox phenomena and to test the performance of our proposed algorithm. (C) 2014 Elsevier Ltd. All rights reserved.

KW - Frequency-based transit assignment

KW - Approach proportion

KW - Extragradient method

KW - Variational inequality

KW - Paradox

KW - PSEUDOMONOTONE VARIATIONAL-INEQUALITIES

KW - TRAFFIC ASSIGNMENT

KW - TRANSPORT NETWORK

KW - CAPACITY CONSTRAINTS

KW - EQUILIBRIUM PROBLEM

KW - ROAD NETWORK

KW - MODEL

KW - DESIGN

KW - FREQUENCY

KW - STRATEGIES

U2 - 10.1016/j.trb.2014.01.010

DO - 10.1016/j.trb.2014.01.010

M3 - Journal article

VL - 62

SP - 51

EP - 76

JO - Transportation Research Part B: Methodological

JF - Transportation Research Part B: Methodological

SN - 0191-2615

ER -