Sensitivity analysis for the elastic-demand network equilibrium problem with applications

This paper presents a general framework and a rigorous approach for the quantitative analysis of the behaviour of equilibrium flows with elastic demand when the problem is subjected to perturbations in network characteristics. Explicit expressions of the derivatives of the equilibrium solutions with respect to a variety of parameters associated with the supply and demand functions are derived. The derivative information will be utilized to predict changes in the equilibrium flow pattern and various system performance measures when the demand and performance characteristics of the transportation networks are altered slightly. Three numerical examples drawn from network design, congestion pricing and traffic equilibrium paradoxes are presented to highlight the sensitivity analysis method and its applications.