Skip to main content
SpringerLink
Log in

Asymmetric resource networks. III. A study of limit states

  • System Analysis and Operations Research
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

This work is devoted to methods of computing the limit state and the limit flow in a resource network for large values of the resource. To do so, we study resource distribution processes in families of networks with various bandwidth matrices corresponding to the same stochastic matrix. The threshold value of the resource T such that the network operates differently on both sides of this value and the coordinates of the limit state vector for vertices that are not attractors are expressed via parameters of the bandwidth matrix and the limit transitions matrix for the Markov chain corresponding to the stochastic matrix in question. If the network has several potential attractors, the limit amount of resource in them depends on the initial state.

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

Similar content being viewed by others

References

  1. Kuznetsov, O.P., Uniform Resource Networks I. Complete Graphs, Autom. Remote Control, 2009, vol. 70, no. 11, pp. 1889–1900.

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhilyakova, L.Yu., Asymmetrical Resource Networks. I. Stabilization Processes for Low Resources, Autom. Remote Control, 2011, vol. 72, no. 4, pp. 798–807.

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhilyakova, L.Yu., Asymmetrical Resource Networks. II. Flows for Large Resources and Their Stabilization, Autom. Remote Control, 2012, vol. 73, no. 6, pp. 1016–1028.

    Article  Google Scholar 

  4. Ford, L.R., Jr. and Fulkerson, D.R., Flows in Networks, Princeton: Princeton Univ. Press, 1962. Translated under the title Potoki v setyakh, Moscow: Mir, 1966.

    MATH  Google Scholar 

  5. Ahuja, R.K., Magnati, T.L., and Orlin, J.B., Network Flows: Theory, Algorithms and Applications, New Jersey: Prentice Hall, 1993.

    MATH  Google Scholar 

  6. Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Fizmatlit, 2004.

    Google Scholar 

  7. Kemeny, J. and Snell, J., Finite Markov Chains, Princeton: Van Nostrand, 1960. Translated under the title Konechnye tsepi Markova, Moscow: Nauka, 1970.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    L. Yu. Zhilyakova

Authors
  1. L. Yu. Zhilyakova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © L.Yu. Zhilyakova, 2012, published in Avtomatika i Telemekhanika, 2012, No. 7, pp. 67–77.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhilyakova, L.Y. Asymmetric resource networks. III. A study of limit states. Autom Remote Control 73, 1165–1172 (2012). https://doi.org/10.1134/S0005117912070065

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117912070065

Keywords

Search

Navigation