Strong Regularity and the Sensitivity Analysis of Traffic Equilibria: A Comment
Transportation Science
Strong Regularity and the Sensitivity Analysis of Traffic Equilibria: A Comment
Transportation Science
Comparative tests of solution methods for signal-controlled road networks
Information Sciences: an International Journal
Sensitivity of Wardrop Equilibria
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Optimization of a nonlinear area traffic control system with elastic demand
Automatica (Journal of IFAC)
Column generation algorithms for nonlinear optimization, II: Numerical investigations
Computers and Operations Research
A Midpoint Method for Generalized Equations Under Mild Differentiability Condition
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Hi-index | 0.00 |
The contribution of the paper is a complete analysis of the sensitivity of elastic demand traffic (Wardrop) equilibria. The existence of a directional derivative of the equilibrium solution (link flow, least travel cost, demand) in any direction is given a characterization, and the same is done for its gradient. The gradient, if it exists, is further interpreted as a limiting case of the gradient of the logit-based SUE solution, as the dispersion parameter tends to infinity. In the absence of the gradient, we show how to compute a subgradient. All these computations (directional derivative, (sub)gradient) are performed by solving similar traffic equilibrium problems with affine link cost and demand functions, and they can be performed by the same tool as (or one similar to) the one used for the original traffic equilibrium model; this fact is of clear advantage when applying sensitivity analysis within a bilevel (or mathematical program with equilibrium constraints, MPEC) application, such as for congestion pricing, OD estimation, or network design. A small example illustrates the possible nonexistence of a gradient and the computation of a subgradient.