Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
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 -