Transit Equilibrium Assignment: A Model and Solution Algorithms

Transportation SciencePublished 1 August 1994

Jia Wu, Michaël Florian, Patrice Marcotte

DOI10.1287/trsc.28.3.193

Source URL

Citations221

SJR quartileQ1

SJR score2.32

SNIP2.03

TL;DR

The behavior of the transit users is modeled by using the concept for hyperpaths on an appropriate network that is obtained from the road network and the transit lines by a transformation that makes explicit the walk, wait, in-vehicle, transfer, and alight arcs.

Abstract

In this paper we propose a model for the transit equilibrium assignment problem (TEAP) and develop two algorithms for its solution. The behavior of the transit users is modeled by using the concept of hyperpaths (strategies) on an appropriate network (general network) which is obtained from the road network and the transit lines by a transformation which makes explicit the walk, wait, in-vehicle, transfer and alight arcs. The waiting (generalized) cost is a function of both frequency of the transit lines and congestion effects due to queues at stops. The TEAP is stated and formulated as a variational inequality problem, in the space of hyperpath flows, and then solved by the linearized Jacobi method and the projection method. We prove the global convergence of these two algorithms for strongly monotone arc cost mappings. The implementation of the algorithms and computational experiments are presented as well.

Keywords

Social SciencesEngineering

Transportation Research Part B MethodologicalOptimal strategies: A new assignment model for transit networks

771 Citations1989Heinz Spiess, Michaël Florian

A model for the transit assignment problem with a fixed set of transit lines is described, formulated as a linear programming problem of a size that increases linearly with the network size that solves the latter problem in polynomial time.

Transportation ScienceAn Efficient Method for Computing Traffic Equilibria in Networks with Asymmetric Transportation Costs

431 Citations1984Sang Quang Nguyen, Clermont Dupuis

A new convex optimization formulation for the general traffic equilibrium problem is presented, and a simple iterative method for calculating traffic equilibria is proposed, which essentially involves postoptimizing a linear sub-problem at each iteration.

Mathematical ProgrammingAn iterative scheme for variational inequalities

278 Citations1983Stella Dafermos

A general iterative scheme for the numerical solution of finite dimensional variational inequalities that contains the projection, linear approximation and relaxation methods but also induces new algorithms and allows the possibility of adjusting the norm at each step of the algorithm.

Transportation Research Part B MethodologicalComparative tests of multimodal traffic equilibrium methods

105 Citations1984Anna B. Nagurney

This study tested the relative efficiencies of the two main computational techniques now available for calculating the traffic equilibrium in multimodal networks, namely, the relaxation and projection methods and found the Frank-Wolfe algorithm and the Dafermos-Sparrow algorithm to be the more efficient algorithm.

Transportation Research Part B MethodologicalThe convergence of diagonalization algorithms for asymmetric network equilibrium problems

99 Citations1982Michaël Florian, Heinz Spiess

Transportation ScienceAdaptation of a Modified Newton Method for Solving the Asymmetric Traffic Equilibrium Problem

33 Citations1988Patrice Marcotte, J Guelat

A restriction (simplicial decomposition) strategy is employed to efficiently implement a modified Newton method to solve the general asymmetric network equilibrium problem.