Detecting Braess Paradox Based on Stable Dynamics in General Congested Transportation Networks

Abstract

This study examined the detection of the Braess Paradox by stable dynamics in general congested transportation networks. Stable dynamics, suggested by Nesterov and de Palma (2003), is a new model which describes and provides a stable state of congestion in urban transportation networks. In comparison with the user equilibrium model, which is based on the arc travel time function in analyzing transportation networks, stable dynamics requires few parameters and is coincident with intuitions and observations on congestion. It is therefore expected to be a useful analysis tool for transportation planners. The phenomenon whereby increasing network capacity, for example creating new routes, known as arcs, may decrease its performance is called the Braess Paradox. It has been studied intensively under user equilibrium models with the arc travel time function since it was first demonstrated by Braess (1968). However, the development of a general model to detect the Braess Paradox under stable dynamics models remains an open problem. In this study, we suggest a model to detect the paradox in general networks under stable dynamics. In our model, we decide whether the Braess Paradox will occur in a given network, detect Braess arcs or Braess crosses if the network permits the paradox, and present a numerical example of the application of the model to a given network.