[1] Wang Jian, Wu Dingxin, Deng Wei, et al. Sensitivity analysis for stochastic user equilibriumwith elastic demand assignment model [J]. Journal of Southeast University (English Edition), 2014, 30 (3): 363-367. [doi:10.3969/j.issn.1003-7985.2014.03.020]

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Sensitivity analysis for stochastic user equilibriumwith elastic demand assignment model()

弹性需求下随机用户均衡分配问题敏感性分析

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

30

Issue:

2014 3

Page:

363-367

Research Field:

Traffic and Transportation Engineering

Publishing date:

2014-09-30

Info

Title:

Sensitivity analysis for stochastic user equilibriumwith elastic demand assignment model

弹性需求下随机用户均衡分配问题敏感性分析

Author(s):

Wang Jian^{1, 2}, Wu Dingxin^{1, 3}, Deng Wei¹

¹School of Transportation, Southeast University, Nanjing 210096, China
²Lyles School of Civil Engineering, Purdue University, West Lafayette 47906, USA
³Faculty of Transportation Engineering, Huaiyin Institute of Technology, Huai’an 223001, China

王建^{1, 2}, 吴鼎新^{1, 3}, 邓卫¹

¹东南大学交通学院, 南京 210096; ²Lyles School of Civil Engineering, Purdue University, West Lafayette 47906, USA; ³淮阴工学院交通运输学院, 淮安 223001

Keywords:

network modeling;  stochastic user equilibrium;  elastic demand;  sensitivity analysis;  first-order approximation

网络建模;  随机用户均衡;  弹性需求;  敏感性分析;  一阶估计

PACS:

U491.1

DOI:

10.3969/j.issn.1003-7985.2014.03.020

Abstract:

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.

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.

References:

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[5] Ying J Q, Miyagi T. Sensitivity analysis for stochastic user equilibrium network flows—a dual approach[J]. Transportation Science, 2001, 35(2): 124-133.
[6] Dial R B. A probabilistic multipath traffic assignment model which obviates path enumeration[J]. Transportation Research Part B: Methodological, 1971, 5(2): 88-111.
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[8] Fiacco A V. Introduction to sensitivity and stability analysis in nonlinear programming[M]. New York: Academic Press, 1983.
[9] Maher M J, Hughes P C, Kim K S. New algorithms for the solution of the stochastic user equilibrium assignment problem with elastic demand[C]//Proceedings of the 14th International Symposium on Transportation and Traffic Theory. Jerusalem, Israel, 1999: 265-286.

Memo

Memo:

Biographies: Wang Jian(1988—), male, graduate; Deng Wei(corresponding author), male, doctor, professor, dengwei@seu.edu.cn.
Foundation items: The Scientific Innovation Research of College Graduates in Jiangsu Province(No.CXLX13_110), the Young Scientists Fund of National Natural Science Foundation of China(No.51408253), the Young Scientists Fund of Huaiyin Institute of Technology(No. 491713328).
Citation: Wang Jian, Wu Dingxin, Deng Wei. Sensitivity analysis for stochastic user equilibrium with elastic demand assignment model[J].Journal of Southeast University(English Edition), 2014, 30(3):363-367.[doi:10.3969/j.issn.1003-7985.2014.03.020]

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