Braess' Paradox in a Generalised Traffic Network

TL;DR

This paper generalizes Braess' network to arbitrary volume-delay functions, establishing conditions for the paradox's occurrence in more realistic, asymmetric traffic networks beyond the classical symmetric case.

Contribution

It introduces a generalized network model and formulates conditions for Braess' paradox without assuming symmetry in volume-delay functions.

Findings

Conditions for Braess' paradox in general networks derived

Extension beyond symmetric volume-delay functions

Applicable to real-world asymmetric traffic networks

Abstract

The classical network configuration introduced by Braess in 1968 is of fundamental significance because Valiant and Roughgarden showed in 2006 that `the "global" behaviour of an equilibrium flow in a large random network is similar to that in Braess' original four-node example'. In this paper, a natural generalisation of Braess' network is introduced and conditions for the occurrence of Braess' paradox are formulated for the generalised network. The Braess' paradox has been studied mainly in the context of the classical problem introduced by Braess and his colleagues, assuming a certain type of networks. Specifically, two pairs of links in those networks are assumed to have the same volume-delay functions. The occurrence of Braess' paradox for this specific case of network symmetry was investigated by Pas and Principio in 1997. Such a symmetry is not common in real-life networks because the parameters of volume-delay functions are associated with roads physical and functional characteristics, which typically differ from one link to another (e.g. roads in networks are of different length). Our research provides an extension of previous studies on Braess' paradox by considering arbitrary volume-delay functions, i.e. symmetry properties are not assumed for any of the network's links and the occurrence of Braess' paradox is studied for a general configuration.