Transit assignment: Approach-based formulation, extragradient method, and paradox
operations - frequency, operations - performance, planning - network design
Frequency-based transit assignment, Approach proportion, Extragradient method, Variational inequality, Paradox
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.
Permission to publish the abstract has been given by Elsevier, copyright remains with them.
Szeto, W.Y., and Jiang, Y., (2014). Transit assignment: Approach-based formulation, extragradient method, and paradox. Transportation Research Part B: Methodological Volume 62, April 2014, Pages 51–76.