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.