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A reduction method for local sensitivity analyses of network equilibrium arc flows

Author

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  • Cho, Hsun-Jung
  • Smith, Tony E.
  • Friesz, Terry L.

Abstract

A reduction method is proposed which allows standard sensitivity techniques for variational inequalities to applied to equilibrium network flow problems without additional assumptions on either the underlying network or the numbers of active paths. In particular it is shown that under mild regularity conditions, small perturbations of equilibria can be given an explicit arc-flow representation which is free of path-flow variables. It is also shown that this reduced form allows the differentiability of perturbations to be studied by standard methods. These results are illustrated by a small numerical example.

Suggested Citation

  • Cho, Hsun-Jung & Smith, Tony E. & Friesz, Terry L., 2000. "A reduction method for local sensitivity analyses of network equilibrium arc flows," Transportation Research Part B: Methodological, Elsevier, vol. 34(1), pages 31-51, January.
    • Handle: RePEc:eee:transb:v:34:y:2000:i:1:p:31-51
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    Cited by:

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    4. Lu, Shu & (Marco) Nie, Yu, 2010. "Stability of user-equilibrium route flow solutions for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 609-617, May.
    5. Jafari, Ehsan & Boyles, Stephen D., 2016. "Improved bush-based methods for network contraction," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 298-313.
    6. Sheu, Jiuh-Biing, 2006. "A composite traffic flow modeling approach for incident-responsive network traffic assignment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 461-478.
    7. Michael Patriksson & R. Tyrrell Rockafellar, 2002. "A Mathematical Model and Descent Algorithm for Bilevel Traffic Management," Transportation Science, INFORMS, vol. 36(3), pages 271-291, August.
    8. Shu Lu, 2008. "Sensitivity of Static Traffic User Equilibria with Perturbations in Arc Cost Function and Travel Demand," Transportation Science, INFORMS, vol. 42(1), pages 105-123, February.
    9. Takebayashi, Mikio & Kanafani, Adib, 2005. "Network Competition in Air Transportation Markets: Bi-Level Approach," Research in Transportation Economics, Elsevier, vol. 13(1), pages 101-119, January.
    10. Byung Chung & Hsun-Jung Cho & Terry Friesz & Henh Huang & Tao Yao, 2014. "Sensitivity Analysis of User Equilibrium Flows Revisited," Networks and Spatial Economics, Springer, vol. 14(2), pages 183-207, June.
    11. Michael Patriksson, 2004. "Sensitivity Analysis of Traffic Equilibria," Transportation Science, INFORMS, vol. 38(3), pages 258-281, August.
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    13. Clark, Stephen D. & Watling, David P., 2006. "Applications of sensitivity analysis for probit stochastic network equilibrium," European Journal of Operational Research, Elsevier, vol. 175(2), pages 894-911, December.

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