CAJ | 학술논문

提出了一种对弹性需求下随机用户均衡（ SUEED）分配问题进行敏感性分析的方法。首先，证明了SUEED模型在均衡解处输出变量对扰动参数的可导性。其次，通过采用对一般非线性规划问题进行敏感性分析的梯度下降法，建立了SUEED模型中设计变量在均衡流量解处对扰动参数的计算公式。这些公式不仅可以对logit型SUEED问题进行敏感性分析，而且同样适用于probit型SUEED问题。算例路网的应用研究发现，所提出的方法可有效估计logit型SUEED问题和probit型SUEED问题中输入变量扰动后的均衡流量解。
제출료일충대탄성수구하수궤용호균형（ SUEED）분배문제진행민감성분석적방법。수선，증명료SUEED모형재균형해처수출변량대우동삼수적가도성。기차，통과채용대일반비선성규화문제진행민감성분석적제도하강법，건립료SUEED모형중설계변량재균형류량해처대우동삼수적계산공식。저사공식불부가이대logit형SUEED문제진행민감성분석，이차동양괄용우probit형SUEED문제。산례로망적응용연구발현，소제출적방법가유효고계logit형SUEED문제화probit형SUEED문제중수입변량우동후적균형류량해。
This paper puts forward a rigorous approach for a sensitivity analysis of stochastic user equilibrium with the elastic demand SUEED model.First proof is given for the existence of derivatives of output variables with respect to the perturbation parameters for the SUEED model.Then by taking advantage of the gradient-based method for sensitivity analysis of a general nonlinear program detailed formulae are developed for calculating the derivatives of designed variables with respect to perturbation parameters at the equilibrium state of the SUEED model.This method is not only applicable for a sensitivity analysis of the logit-type SUEED problem but also for the probit-type SUEED problem.The application of the proposed method in a numerical example shows that the proposed method can be used to approximate the equilibrium link flow solutions for both logit-type SUEED and probit-type SUEED problems when small perturbations are introduced in the input parameters.