An empirical comparison of equilibrium and non-equilibrium transit assignment models

摘要

We present a comparitive analysis of different transit assignment models based on the concept of 'transit route'. Firstly, we define some basic concepts related to transit networks and then we introduce the mathematical formulation of the models: (a) an all-or-nothing assignment model to minimal routes between zone centroids; (b) a multi-route assignment model between zone centroids with all-or-nothing assignment between access nodes; and (c) a user equilibrium assignment model. Secondly, we briefly describe the solution algorithms. The first two are tree-building algorithms applied over a virtual network where the arcs are access links and travel links, representing a set of 'attractive lines', while the solution method of the equilibrium assignment model (formulated as a variational inequality with a convex set of feasible solutions) is based on a diagonlisation procedure which solves, at each iteration, a non-linear problem. The empirical part of the paper is devoted to test the computational implementation of the solution methods mentioned above with a real-size transit system (Santiago, Chile) and to compare their most important results. Finally, some comments and conclusions about these models and the potentiality of the transit equilibrium models are given.