Sensitivity Analysis of User Equilibrium Flows Revisited

Byung Do Chung, Hsun-Jung Cho, Terry L. Friesz, Henh Huang, Tao Yao*

*Corresponding author for this work

Research output: Contribution to journalArticle

9 Scopus citations


This paper addresses certain misconceptions regarding what is known and what may be expected when performing sensitivity analyses of network user equilibrium flow patterns. Our presentation relies on a simple observation: any given user equilibrium sensitivity analysis technique should be employed only when the regularity conditions on which it is based are satisfied. Violating regularity, as we show through previously published numerical examples, as well as new examples presented here for the first time, may well lead to incorrect results when the Tobin-Friesz sensitivity analysis method is applied. This is especially so when the most critical regularity assumption of the Tobin-Friesz method, namely that the unperturbed solution must be a nondegenerate extreme point, is violated. We also illustrate how a degenerate unperturbed solution may sometimes be modified to obtain an appropriate nondegenerate solution, thereby allowing the Tobin-Friesz method to be applied.

Original languageEnglish
Pages (from-to)183-207
Number of pages25
JournalNetworks and Spatial Economics
Issue number2
StatePublished - 1 Jan 2014


  • Network user equilibrium
  • Regularity condition
  • Sensitivity analysis

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    Chung, B. D., Cho, H-J., Friesz, T. L., Huang, H., & Yao, T. (2014). Sensitivity Analysis of User Equilibrium Flows Revisited. Networks and Spatial Economics, 14(2), 183-207.