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On the convergence of Bell's logit assignment formulation

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  • Wong, S. C.

Abstract

In Bell M.G.H. (1995. Transportation Research B 29, 287-295), a new logit assignment formulation was developed, which considered all possible paths in the network while still retaining the absence of a need for path enumeration. In his formulation, it presumes that the sum of a geometric series of the weights matrix always converges and hence can be computed as the inversion of a matrix. In this paper, we investigate the convergence properties of this geometric series by means of an eigensystem interpretation which states that the series converges if and only if all the eigenvalues associated with the weights matrix fall into the unit circle in a complex plane. It is found that the geometric series converges unconditionally for acyclic networks, but not necessarily does so for general networks.

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  • Wong, S. C., 1999. "On the convergence of Bell's logit assignment formulation," Transportation Research Part B: Methodological, Elsevier, vol. 33(8), pages 609-616, November.
    • Handle: RePEc:eee:transb:v:33:y:1999:i:8:p:609-616
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    References listed on IDEAS

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    1. Warren B. Powell & Yosef Sheffi, 1982. "The Convergence of Equilibrium Algorithms with Predetermined Step Sizes," Transportation Science, INFORMS, vol. 16(1), pages 45-55, February.
    2. Huang, Hai-Jun & Bell, Michael G. H., 1998. "A study on logit assignment which excludes all cyclic flows," Transportation Research Part B: Methodological, Elsevier, vol. 32(6), pages 401-412, August.
    3. Van Vliet, Dirck, 1981. "Selected node-pair analysis in dial's assignment algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 15(1), pages 65-68, February.
    4. Akamatsu, Takashi, 1996. "Cyclic flows, Markov process and stochastic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 369-386, October.
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    Cited by:

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    2. Tan, Heqing & Xu, Xiangdong & Chen, Anthony, 2024. "On endogenously distinguishing inactive paths in stochastic user equilibrium: A convex programming approach with a truncated path choice model," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).

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