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Submission to the DTA2012 Special Issue: Approximating Time Delays in Solving Continuous-Time Dynamic User Equilibria

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  • Rui Ma
  • Xuegang Ban
  • Jong-Shi Pang
  • Henry Liu

Abstract

We develop an approximation scheme, called “pseudo-derivative (PD)” to solving the dynamic user equilibrium (DUE) problem. The PD approximation can convert time-varying, state dependent delays usually involved in DUE to a constant time delay. We study the properties of the proposed PD and the resulting approximate DUE (ADUE) problem after applying the approximation. Some issues of the ADUE, such as the possible violation of the flow conservation at network nodes are also discussed and resolved. It turns out that the original DUE problem can be solved iteratively with an ADUE solved in each iteration. Numerical results are shown on a small test network and the Sioux Falls network. The results show that the iterative algorithm can converge to some reasonable solution, although a formal convergence proof result is not established in the paper. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Rui Ma & Xuegang Ban & Jong-Shi Pang & Henry Liu, 2015. "Submission to the DTA2012 Special Issue: Approximating Time Delays in Solving Continuous-Time Dynamic User Equilibria," Networks and Spatial Economics, Springer, vol. 15(3), pages 443-463, September.
    • Handle: RePEc:kap:netspa:v:15:y:2015:i:3:p:443-463
    DOI: 10.1007/s11067-014-9240-z
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    References listed on IDEAS

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    1. Friesz, Terry L. & Mookherjee, Reetabrata, 2006. "Solving the dynamic network user equilibrium problem with state-dependent time shifts," Transportation Research Part B: Methodological, Elsevier, vol. 40(3), pages 207-229, March.
    2. Friesz, Terry L. & Kim, Taeil & Kwon, Changhyun & Rigdon, Matthew A., 2011. "Approximate network loading and dual-time-scale dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 176-207, January.
    3. Ban, Xuegang (Jeff) & Pang, Jong-Shi & Liu, Henry X. & Ma, Rui, 2012. "Continuous-time point-queue models in dynamic network loading," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 360-380.
    4. Terry L. Friesz, 2010. "Dynamic Optimization and Differential Games," International Series in Operations Research and Management Science, Springer, number 978-0-387-72778-3, December.
    5. Soulaymane Kachani & Georgia Perakis, 2009. "A Dynamic Travel Time Model for Spillback," Networks and Spatial Economics, Springer, vol. 9(4), pages 595-618, December.
    6. Terry L. Friesz, 2010. "Dynamic User Equilibrium," International Series in Operations Research & Management Science, in: Dynamic Optimization and Differential Games, chapter 0, pages 411-456, Springer.
    7. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    8. Malachy Carey & Y. Ge, 2012. "Comparison of Methods for Path Flow Reassignment for Dynamic User Equilibrium," Networks and Spatial Economics, Springer, vol. 12(3), pages 337-376, September.
    9. Ban, Xuegang (Jeff) & Liu, Henry X. & Ferris, Michael C. & Ran, Bin, 2008. "A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 823-842, November.
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    Cited by:

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