An Approach to Avoid the Unreal High Flows on Congested Links and Investigates the Evolution of Congestion over Network

TL;DR

This paper introduces a novel traffic assignment model that accurately captures the evolution of congestion over time by addressing unreal high flows caused by traditional static models, using a branch-and-bound algorithm.

Contribution

The paper develops a new traffic assignment approach that models congestion evolution and eliminates unreal high flows by linking the fundamental diagram with a non-convex user equilibrium model.

Findings

Effectively reproduces congestion evolution over time.

Eliminates unreal high flows in traffic assignment.

Demonstrates improved reliability over traditional models.

Abstract

The unreal high flows may appear on the actually congested links in the result when a monotonically increasing link travel time function of flow volume is adopted in traffic assignment. The fixed link flow results of a static traffic assignment model (TAM) make it nearly impossible to investigate and make use of the actual evolution of congested zones over the network during the predetermined observation time period. Many methods, such as TAMs with side-constraints on link flow capacity and the pseudo dynamic traffic assignment based on day-by-day traffic, have been proposed to improve the reliability of the results of TAM, but cannot eliminate the problem. To resolve the above problems, we first uncover the origin of problem by analyzing the connection between the link travel time function and the fundamental diagram of traffic flow theory. According to the above connection a mapping is formulated to reflect the two branches of the fundamental diagram. Then with the assumption that the link flow states are given, new traffic assignment models are presented. To resolve the obtained non-convex user equilibrium model, a branch-and-bound algorithm is designed based on linearizing the nonlinear part of the objective function. At last, by repeatedly resolving the corresponding traffic assignment model with the renewed initial flow states of links, the evolution of congested zones during the observation time period can be reproduced and investigated. The numerical examples demonstrate the effectiveness of the new approach.