Traffic Networks: Wardrop Equilibrium and Braess’ Paradox

The well-known Braess’ paradox illustrates situations when adding a new link to a transport network might lead to an equilibrium state in which travel times of users will increase. Here, Braess’ paradox and the equilibrium state are analysed in the classical network configuration introduced by Braess in 1968. This network configuration 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. Moreover, the probability of Braess’ paradox occurring in the classical network configuration will be studied, with particular emphasis on the Erlang distribution of parameters of the travel time function. This distribution is important in the context of traffic networks. However, other distributions will be analysed as well because Braess’ paradox can be observed in various applied contexts such as telecommunication networks and power transmission networks.

A Transportation Network Paradox: Consideration of Travel Time and Health Damage due to Pollution

In cities with serious air pollution, travel time and health damage significantly affect route choice by travelers (e.g., motorcycle and scooter drivers). Consequently, the classical Braess paradox is no longer realistic because it only considers the traveler’s value of time (VOT). In the current study, we describe a new transportation network paradox that considers both the VOT and the traveler’s perception of pollution damage. To examine the conditions that create the new paradox, we developed a novel method to compute a total comprehensive cost that combines the VOT with health damage. We analyzed the conditions for the new paradox and the system’s performance using a user equilibrium model and system optimization. Furthermore, an improved model is used to analyze how different transport modes influence the Braess paradox. We found that whether the new paradox occurs and the potential improvement of the system’s performance depend on whether the total travel demand falls within critical ranges. The bounds of these ranges depend on the values of the parameters in the function that describes the health damage and the link travel time function. In addition, high health damage significantly affects route choices and traffic flow distribution. This paper presents a new perspective for decision-making by transportation planners and for route choices in cities with serious air pollution.