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Matematicheskoe modelirovanie, 2014, Volume 26, Number 6, Pages 34–70 (Mi mm3488)  

This article is cited in 13 scientific papers (total in 13 papers)

On the three-stage version of stable dynamic model

A. Gasnikov, Yu. Dorn, Yu. Nesterov, S. Shpirko

MIPT, Laboratory for Structural Methods of Data Analysis in Predictive Modeling
References:
Abstract: In this paper we propose a new model of the traffic assignment problem. This model joints the entropy model, flow decomposition and the Stable Dynamic model. All parameters in use have a direct physical meaning and interpretations. We show that this model reduces to a non-smooth convex optimization problem that admits natural primal-dual formulation. For completeness, we present and criticize the standard static traffic assignment models. In particular, we prove that the Beckmann model reduces to the Stable Dynamic Model as a result of some limiting process.
Keywords: traffic assignment, original-destination matrix, entropy-linear programming, flow decomposition, large-scale convex optimization, primal-dual method, bounded variation of subgradient.
Received: 25.02.2013
Document Type: Article
Language: Russian
Citation: A. Gasnikov, Yu. Dorn, Yu. Nesterov, S. Shpirko, “On the three-stage version of stable dynamic model”, Matem. Mod., 26:6 (2014), 34–70
Citation in format AMSBIB
\Bibitem{GasDorNes14}
\by A.~Gasnikov, Yu.~Dorn, Yu.~Nesterov, S.~Shpirko
\paper On the three-stage version of stable dynamic model
\jour Matem. Mod.
\yr 2014
\vol 26
\issue 6
\pages 34--70
\mathnet{http://mi.mathnet.ru/mm3488}
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  • https://www.mathnet.ru/eng/mm3488
  • https://www.mathnet.ru/eng/mm/v26/i6/p34
  • This publication is cited in the following 13 articles:
    1. Yu. V. Dorn, O. M. Shitikov, “Identifikatsiya paradoksa Braessa v modeli stabilnoi dinamiki”, Kompyuternye issledovaniya i modelirovanie, 16:1 (2024), 35–51  mathnet  crossref
    2. I. V. Podlipnova, Yu. V. Dorn, I. A. Sklonin, “Oblachnaya interpretatsiya entropiinoi modeli rascheta matritsy korrespondentsii”, Kompyuternye issledovaniya i modelirovanie, 16:1 (2024), 89–103  mathnet  crossref
    3. Y. S. Popkov, “Oscillations in Dynamic Systems with an Entropy Operator”, Rus. J. Nonlin. Dyn., 19:1 (2023), 125–135  mathnet  crossref  mathscinet
    4. Evgeniya V. Gasnikova, Aleksandr V. Gasnikov, Demyan V. Yarmoshik, Meruza B. Kubentaeva, Mikhail I. Persiyanov, Irina V. Podlipnova, Ekaterina V. Kotlyarova, Ilya A. Sklonin, Elena D. Podobnaya, Vladislav V. Matyukhin, “O mnogostadiinoi transportnoi modeli i dostatochnykh usloviyakh ee potentsialnosti”, MTIP, 15:2 (2023), 3–17  mathnet
    5. E. V. Kotlyarova, A. V. Gasnikov, E. V. Gasnikova, D. V. Yarmoshik, “Poisk ravnovesii v dvukhstadiinykh modelyakh raspredeleniya transportnykh potokov po seti”, Kompyuternye issledovaniya i modelirovanie, 13:2 (2021), 365–379  mathnet  crossref
    6. D. R. Baymurzina, A. V. Gasnikov, E. V. Gasnikova, P. E. Dvurechenskii, E. I. Ershov, M. B. Kubentayeva, A. A. Lagunovskaya, “Universal method of searching for equilibria and stochastic equilibria in transportation networks”, Comput. Math. Math. Phys., 59:1 (2019), 19–33  mathnet  crossref  crossref  isi  elib
    7. M. V. Goremyko, I. R. Pleve, V. V. Makarov, A. E. Khramov, “Modelirovanie sotsialnoi sistemy «abiturienty tekhnicheskogo universiteta» s ispolzovaniem apparata slozhnykh setei”, Matem. modelirovanie, 30:1 (2018), 63–75  mathnet  elib
    8. A. V. Gasnikov, M. B. Kubentaeva, “Poisk stokhasticheskikh ravnovesii v transportnykh setyakh s pomoschyu universalnogo pryamo-dvoistvennogo gradientnogo metoda”, Kompyuternye issledovaniya i modelirovanie, 10:3 (2018), 335–345  mathnet  crossref
    9. A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, “Dual methods for finding equilibriums in mixed models of flow distribution in large transportation networks”, Comput. Math. Math. Phys., 58:9 (2018), 1395–1403  mathnet  crossref  crossref  isi  elib
    10. A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, A. V. Chernov, “Efficient numerical methods for entropy-linear programming problems”, Comput. Math. Math. Phys., 56:4 (2016), 514–524  mathnet  crossref  crossref  mathscinet  isi  elib
    11. A. V. Gasnikov, P. E. Dvurechenskii, Yu. V. Dorn, Yu. V. Maksimov, “Chislennye metody poiska ravnovesnogo raspredeleniya potokov v modeli Bekmana i v modeli stabilnoi dinamiki”, Matem. modelirovanie, 28:10 (2016), 40–64  mathnet  elib
    12. A. V. Gasnikov, Yu. E. Nesterov, V. G. Spokoiny, “On the efficiency of a randomized mirror descent algorithm in online optimization problems”, Comput. Math. Math. Phys., 55:4 (2015), 580–596  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. A. V. Gasnikov, “Ob effektivnoi vychislimosti konkurentnykh ravnovesii v transportno-ekonomicheskikh modelyakh”, Matem. modelirovanie, 27:12 (2015), 121–136  mathnet  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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