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This article addresses sensitivity analysis of logit-based stochastic user equilibrium (SUE) network ﬂows on transportation networks with entry–exit toll schemes. These schemes have a technical challenge that the generalized travel time including tolls on a path is nonadditive. First, it shows that the perturbed logit-based network ﬂows—link and entry–exit ﬂows—are implicit but continuously differentiable functions with respect to the perturbation parameters arising from link travel time functions, origin–destination demands, and entry–exit tolls. Second, this article derives elegant analytical expressions of gradients of perturbed logit-based SUE network ﬂows, and elaborates that these gradients can be calculated by the two-stage stochastic network loading algorithm, which obviates the need for path enumeration. Finally, two numerical examples are presented to demonstrate the calculation process and computational capability.

@article{meng_sensitivity_2008, title = {Sensitivity {Analysis} of {Logit}-{Based} {Stochastic} {User} {Equilibrium} {Network} {Flows} with {Entry}-{Exit} {Toll} {Schemes}: {Sensitivity} analysis of logit-based stochastic user equilibrium network flows}, volume = {23}, issn = {10939687}, shorttitle = {Sensitivity {Analysis} of {Logit}-{Based} {Stochastic} {User} {Equilibrium} {Network} {Flows} with {Entry}-{Exit} {Toll} {Schemes}}, url = {http://doi.wiley.com/10.1111/j.1467-8667.2007.00530.x}, doi = {10.1111/j.1467-8667.2007.00530.x}, abstract = {This article addresses sensitivity analysis of logit-based stochastic user equilibrium (SUE) network ﬂows on transportation networks with entry–exit toll schemes. These schemes have a technical challenge that the generalized travel time including tolls on a path is nonadditive. First, it shows that the perturbed logit-based network ﬂows—link and entry–exit ﬂows—are implicit but continuously differentiable functions with respect to the perturbation parameters arising from link travel time functions, origin–destination demands, and entry–exit tolls. Second, this article derives elegant analytical expressions of gradients of perturbed logit-based SUE network ﬂows, and elaborates that these gradients can be calculated by the two-stage stochastic network loading algorithm, which obviates the need for path enumeration. Finally, two numerical examples are presented to demonstrate the calculation process and computational capability.}, language = {en}, number = {2}, urldate = {2018-08-23}, journal = {Computer-Aided Civil and Infrastructure Engineering}, author = {Meng, Qiang and Wang, Xiubin}, month = jan, year = {2008}, pages = {138--156} }

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