Stochastic Decentralized Routing of Unsplittable Vehicle Flows Using Constraint Optimization

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 217)

Abstract

A decentralized solution to the unsplittable flow problem (UFP) in a transport network is considered, where each flow uses only one route from source to sink and the flows cannot be separated into parts in intermediate nodes. The flow costs in each edge depend on the combination of the assigned flows as well as on external random variables. The distributions of the random variables are unknown, only samples are available. In order to use the information available in the samples more effectively, several resamples are constructed from the original samples. The nodes agree on the resamples in a decentralized way using a cooperative resampling scheme. A decentralized asynchronous solution algorithm for the flow routing problem in these conditions is proposed, which is based on the ADOPT algorithm for asynchronous distributed constraint optimization (DCOP). An example illustrating the proposed approach is presented.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Englewood Cliffs (1993)MATHGoogle Scholar
  2. 2.
    Andronov, A., Fiosina, J., Fiosins, M.: Statistical estimation for a failure model with damage accumulation in a case of small samples. J. of Stat. Planning and Inf. 139, 1685–1692 (2009)CrossRefMATHGoogle Scholar
  3. 3.
    Andronov, A., Fiosins, M.: Applications of resampling approach to statistical problems of logical systems. Acta et Comm. Univ. Tartuensis de Mathematica 8, 63–72 (2004)Google Scholar
  4. 4.
    Atlas, J., Decker, K.: Task scheduling using constraint optimization with uncertainty. In: Proc. of CAPS 2007, pp. 25–27 (2007)Google Scholar
  5. 5.
    Azar, Y., Regev, O.: Strongly polynomial algorithms for the unsplittable flow problem. In: Aardal, K., Gerards, B. (eds.) IPCO 2001. LNCS, vol. 2081, pp. 15–29. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Fiosins, M., Fiosina, J., Müller, J.P.: Change point analysis for intelligent agents in city traffic. In: Cao, L., Bazzan, A.L.C., Symeonidis, A.L., Gorodetsky, V.I., Weiss, G., Yu, P.S. (eds.) ADMI 2011. LNCS (LNAI), vol. 7103, pp. 195–210. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Fiosins, M., Fiosina, J., Müller, J.P., Görmer, J.: Reconciling strategic and tactical decision making in agent-oriented simulation of vehicles in urban traffic. In: Proc. of the 4th Int. ICST Conf. Simulation Tools and Techniques, pp. 144–151. ACM Digital Library (2011)Google Scholar
  8. 8.
    Ford, L., Fulkerson, D.: Flows in Networks. Princeton University Press (1962)Google Scholar
  9. 9.
    Glockner, G., Nemhauser, G.: A dynamic network flow problem with uncertain arc capacities: Formulation and problem structure. Operations Research 48(2), 233–242 (2000)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Goldberg, A.V., Grigoriadis, M.D., Tarjan, R.E.: Use of dynamic trees in a network simplex algorithm for the maximum flow problem. Mathematical Programming 50, 277–290 (1991)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Karakostas, G.: Faster approximation schemes for fractional multicommodity flow problems. ACM Trans. Algorithms 4(1), 13:1–13:17 (2008)Google Scholar
  12. 12.
    Léauté, T., Faltings, B.: E[DPOP]: Distributed Constraint Optimization under Stochastic Uncertainty using Collaborative Sampling. In: Proc. of the IJCAI 2009, pp. 87–101 (2009)Google Scholar
  13. 13.
    Modi, P.J., Shen, W., Tambe, M., Yokoo, M.: Adopt: Asynchronous distributed constraint optimization with quality guarantees. Artificial Intelligence Journal 161, 149–180 (2005)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Ottens, B., Faltings, B.: Coordinating agent plans through distributed constraint optimization. In: Proc. of MASPLAN 2008 (2008)Google Scholar
  15. 15.
    Petcu, A., Faltings, B.: Dpop: A scalable method for multiagent constraint optimization. In: Proc. of the 19th Int. Joint Conf. on Artificial Intelligence, pp. 266–271 (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Clausthal University of TechnologyClausthal-ZellerfeldGermany

Personalised recommendations