Skip to main content
SpringerLink
Log in

Express Analysis and Aggregated Representation of the Set of Reachable Flows for a Multicommodity Network System

  • SYSTEMS ANALYSIS AND OPERATIONS RESEARCH
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

Within the formalism of the mathematical model of transferring a multicommodity flow, the reachability set of multiuser network systems is studied. A method is proposed for constructing an internal supporting frame based on the vectors of the maximum flows that can be transferred between all pairs of nodes in exclusive and limited exclusive modes of flow control. Using the obtained limit values, we construct a polyhedron of a simpler structure (frame) belonging to the set of reachable multi-flows and a cone of possible directions for the generation of boundary points. Methods for obtaining various multicriteria evaluations of the functional capabilities of a transmission network are considered. The developed approach can be used for the a priori analysis of the set of reachable multiflows, including quickly obtaining estimates and acceptable options for the fair distribution of the limited capacity of the transmission network.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.

Similar content being viewed by others

REFERENCES

  1. Yu. E. Malashenko, I. A. Nazarova, and N. M. Novikova, “One approach to the analysis of possible structural damage in multi-product network systems,” Comput. Math. Math. Phys. 59 (9), 1626–1638 (2019).

  2. A. A. Assad, “Multicommodity network flows: a survey,” Networks 8, 37–91 (1978).

    Article  MathSciNet  Google Scholar 

  3. A. V. Lotov and I. I. Pospelova, Multi-Criteria Decision Making Problems (MAKS Press, Moscow, 2008) [in Russian].

    Google Scholar 

  4. Yu. B. Germeier, Introduction to Operations Research Theory (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  5. P. A. Jensen and J. W. Barnes, Network Flow Programming (Wiley, New York, 1980).

    MATH  Google Scholar 

  6. D. Bertsekas and R. Gallager, Data Networks (Pearson, Englewood Cliffs, NJ, 1992).

    MATH  Google Scholar 

  7. W. Ogryczak, H. Luss, M. Pioro, D. Nace, and A. Tomaszewski, “Fair optimization and networks: a survey,” J. Appl. Math. 25, 1–25 (2014).

    MathSciNet  Google Scholar 

  8. J. Ros and W. K. Tsai, “A lexicographic optimization framework to the flow control problem,” IEEE Trans. Inform. Theory 56, 2875–2886 (2010).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Federal Research “Center Computer Science and Control”, Russian Academy of Sciences, 119333, Moscow, Russia

    Yu. E. Malashenko, I. A. Nazarova & N. M. Novikova

Authors
  1. Yu. E. Malashenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. A. Nazarova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. M. Novikova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to I. A. Nazarova or N. M. Novikova.

Additional information

Translated by I. Tselishcheva

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Malashenko, Y.E., Nazarova, I.A. & Novikova, N.M. Express Analysis and Aggregated Representation of the Set of Reachable Flows for a Multicommodity Network System. J. Comput. Syst. Sci. Int. 58, 889–897 (2019). https://doi.org/10.1134/S1064230719060133

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064230719060133

Search

Navigation