A link-based user equilibrium traffic assignment for urban transportation networks - Varameth Vichiensan; Fujiwara, Okitsugu; Nakatsuji, Takashi; Do, Ba Khang; Nguyen Luong Bach; Royal Thai Government (Bangkok : Asian Institute of Technology, 1998)
This study shows that the user equilibrium assignment can be represented as an optimization problem with only link variables, i.e., link-based user equilibrium problem. Such a formulation does not require to enumerate the possible paths, so it seems feasible to obtain the exact solution compared with the solution from classical algorithms. This study concentrates on the problem formulations with only link-based variables rather than developing algorithms or testing the solution convergence speed. The equivalence of route-based and link-based user equilibrium problem is theoretically derived; the optimality conditions of link-based program must satisfy that of the route-based program and vice versa. And from this equivalency, the same set of solution can be obtained by solving either models. The relation between link flow and route flow is also investigated for the uniqueness conditions. The computation trade-offs between two models are discussed. The size of two problems are compared as well as some issues relating to the dynamic user equilibrium (DUE) problem are mentioned. Since the solution is not unique in terms of path flow, the most likely path flow pattern is then determined. Next, the concept of link-based user equilibrium is extended to analyze some of the typical transportation planning problems in a way parallel to Sheffi (1985). Next, the link-based user equilibrium concept is applied to Bell (1995)'s model which presented the equilibrium assignment with queues. Finally, the stochastic user equilibrium is analyzed based on link variables, and various models are discussed. In this study only small network problems are numerically solved to validate the model formulated.
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Civil Engineering
Thesis (M.Eng.) - Asian Institute of Technology, 1998
Keywords: Urban transportation -- Mathematical models