Solutions to Sensitivity Analysis for the Equilibrium Network Flow
用户均衡网络中的敏感度分析方法

The equilibrium network flow problem is formulated in its general form as a mathematical programming, and sensitivity analysis are developed for the mathematical programming. The sensitivity analysis is to calculate the derivatives of the equilibrium link flows with respect to perturbations, which are of the cost functions, of the origin-destination matrix and of the link capacities. At the same time, a path-based gradient projection with variable step is proposed, and adopted in the sensitivity. The numerical example illustrates the applications of sensitivity analysis in traffic planning, construction and operations.