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Investigating path-based solution algorithms to the stochastic user equilibrium problem

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  • Bekhor, Shlomo
  • Toledo, Tomer
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    Abstract

    This paper focuses on path-based solution algorithms to the stochastic user equilibrium (SUE) and investigates their convergence properties. Two general optimization methods are adapted to solve the logit SUE problem. First, a method that closely follows the Gradient Projection (GP) algorithm developed for the deterministic problem is derived. While this method is very efficient for the deterministic user equilibrium problem, we use a simple example to illustrate why it is not suitable for the SUE problem. Next, a different variant of gradient projection, which exploits special characteristics of the SUE solution, is presented. In this method the projection is on the linear manifold of active constraints. The algorithms are applied to solve simple networks. The examples are used to compare the convergence properties of the algorithms with a path-based variant of the Method of Successive Averages (MSA) and with the Disaggregate Simplicial Decomposition (DSD) algorithm.

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    Bibliographic Info

    Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

    Volume (Year): 39 (2005)
    Issue (Month): 3 (March)
    Pages: 279-295

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    Handle: RePEc:eee:transb:v:39:y:2005:i:3:p:279-295

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    References

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    1. Akamatsu, Takashi, 1996. "Cyclic flows, Markov process and stochastic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 369-386, October.
    2. Damberg, Olof & Lundgren, Jan T. & Patriksson, Michael, 1996. "An algorithm for the stochastic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 30(2), pages 115-131, April.
    3. Fisk, Caroline, 1980. "Some developments in equilibrium traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 243-255, September.
    4. Mingyuan Chen & Attahiru Sule Alfa, 1991. "Algorithms for solving fisk's stochastic traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 25(6), pages 405-412, December.
    5. Leurent, Fabien M., 1997. "Curbing the computational difficulty of the logit equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 315-326, August.
    6. Maher, Mike, 1998. "Algorithms for logit-based stochastic user equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 539-549, November.
    7. Jayakrishnan, R. & Tsai, Wei T. & Prashker, Joseph N. & Rajadhyaksha, Subodh, 1994. "A Faster Path-Based Algorithm for Traffic Assignment," University of California Transportation Center, Working Papers qt2hf4541x, University of California Transportation Center.
    8. Chen, Anthony & Lee, Der-Horng & Jayakrishnan, R., 2002. "Computational study of state-of-the-art path-based traffic assignment algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(6), pages 509-518.
    9. Prashker, Joseph N. & Bekhor, Shlomo, 2000. "Some observations on stochastic user equilibrium and system optimum of traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 34(4), pages 277-291, May.
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    Cited by:
    1. Chen, Anthony & Pravinvongvuth, Surachet & Xu, Xiangdong & Ryu, Seungkyu & Chootinan, Piya, 2012. "Examining the scaling effect and overlapping problem in logit-based stochastic user equilibrium models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1343-1358.

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