Estimation methods for upper bounds of efficiency loss in traffic networks

In 2006, Huang H J, et al. discussed the relationship between user equilibrium and system optimum flow in traffic networks with fixed demands, and gave the formulae for computing the upper bounds for efficiency loss caused by user equilibrium behaviors. This paper uses a new rule for the parameter associated with the user equilibrium flow pattern, extend the application of the formulae for computing the upper bounds for efficiency loss, and give the new upper bounds for efficiency loss. Numerical examples show that the new formulae can give lower values of upper bounds than those reported in the literature.