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Curbing the computational difficulty of the logit equilibrium assignment model


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  • Leurent, Fabien M.
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    In the past, research in traffic assignment modeling has been directed primarily towards improving the deterministic model. Alternative, more behavioral principles were thought to be too demanding computationally. This paper presents two mathematical contributions that enable one to solve a logit assignment model with flow-dependent travel times at a reduced cost. First, a convergence test for Fisk's minimization program is introduced, based on a duality gap principle. Second, a new definition of Dial's STOCH fixedtime logit assignment procedure is given, in which the set of available paths is defined only once and the computations are re-interpreted. A numerical experiment indicates that these tools make the logit assignment model very competitive compared to the procedures conventionally used for solving the deterministic model.

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

    Volume (Year): 31 (1997)
    Issue (Month): 4 (August)
    Pages: 315-326

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    Handle: RePEc:eee:transb:v:31:y:1997:i:4:p:315-326

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    1. Leurent, Fabien, 1993. "Cost versus time equilibrium over a network," European Journal of Operational Research, Elsevier, vol. 71(2), pages 205-221, December.
    2. Fukushima, Masao, 1984. "On the dual approach to the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 18(3), pages 235-245, June.
    3. 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.
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    Cited by:
    1. Maher, Michael J. & Zhang, Xiaoyan & Vliet, Dirck Van, 2001. "A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows," Transportation Research Part B: Methodological, Elsevier, vol. 35(1), pages 23-40, January.
    2. 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.
    3. Paul Anderson & David Levinson & Pavithra Parthasarathi, 2011. "Accessibility Futures," Working Papers 000088, University of Minnesota: Nexus Research Group.
    4. Maher, Mike, 1998. "Algorithms for logit-based stochastic user equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 539-549, November.
    5. Bekhor, Shlomo & Toledo, Tomer, 2005. "Investigating path-based solution algorithms to the stochastic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 39(3), pages 279-295, March.
    6. Huang, Hai-Jun & Li, Zhi-Chun, 2007. "A multiclass, multicriteria logit-based traffic equilibrium assignment model under ATIS," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1464-1477, February.


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