Upper bounds of efficiency loss for user equilibrium behavior in traffic networks

Determining the upper bounds of efficiency loss for user equilibrium behavior in traffic networks has become a hot topic. The relationship between user equilibrium and system optimum flow patterns was explored in traffic networks with fixed demands. New formulae for computing the upper bounds of efficiency loss caused by user equilibrium behavior were derived through introducing a parameter associated with the user equilibrium flow pattern. Numerical examples show that the new formulae can give lower values of the upper bounds than those reported in literature. It is also concluded that finding more accurate upper bounds has to be connected with all characteristics of the studied networks, including the link cost functions, the network configurations and the travel demands.