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Characteristic functions of directed graphs and applications to stochastic equilibrium problems

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  • NESTEROV, Yu.

Abstract

In this paper we introduce the notions of characteristic and potential functions of directed graphs and study their properties. The main motivation for our research is the stochastic equilibrium traffic assignment problem, in which the drivers choose their routes with some probabilities. Since the number of the strategies in this game is very big, we need to find an efficient way of computation of the expected arc flows in the network. We show that the characteristic functions of the graphs are very useful in this respect. Using this technique we can form and solve numerically the equilibrium traffic assignment problem in a reasonable computational time. As a byproduct of our results we show that the spectral radius of a matrix with non-negative elements admits a convex parametrization as a function of its entries.

Suggested Citation

  • NESTEROV, Yu., 2003. "Characteristic functions of directed graphs and applications to stochastic equilibrium problems," LIDAM Discussion Papers CORE 2003013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2003013
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2003.html
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    References listed on IDEAS

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    1. NESTEROV, Yu & de PALMA, André, 2000. "Stable dynamics in transportation systems," LIDAM Discussion Papers CORE 2000027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. NESTEROV, Yurii, 1999. "Stable flows in transportation networks," LIDAM Discussion Papers CORE 1999007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. NESTEROV, Yu, 2004. "Fast Fourier Transform and its applications to integer knapsack problems," LIDAM Discussion Papers CORE 2004064, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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