Skip to main content
SpringerLink
Log in

Multi-access system with many users: Stability and metastability

  • Communication Network Theory
  • Published:
Problems of Information Transmission Aims and scope Submit manuscript

Abstract

A model of random multi-access system with an ALOHA-type protocol is analyzed when the number N of users is large and the system is overloaded. In the limit as N → ∞, the behavior of the system is described by a nonrandom dynamical system. We give a condition for the dynamical system to have an attractive fixed point and outline cases of several fixed points. The presence of several fixed points indicates that the finite system may exhibit a metastability phenomenon.

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. Vvedenskaya, N.D., Dobrushin, R.L., and Karpelevich, F.I., Queueing System with Selection of the Shortest of Two Queues: An Asymptotic Approach, Probl. Peredachi Inf., 1996, vol. 32, no. 1, pp. 20–34 [Probl. Inf. Trans. (Engl. Transl.), 1996, vol. 32, no. 1, pp. 15–27].

    MathSciNet  Google Scholar 

  2. Martin, J.B. and Suhov, Yu.M., Fast Jackson Networks, Ann. Appl. Probab., 1999, vol. 9, no. 3, pp. 854–870.

    Article  MATH  MathSciNet  Google Scholar 

  3. Karpelevich, F.I. and Rybko, A.N., Asymptotic Behavior of the Thermodynamical Limit for Symmetric Closed Queueing Networks, Probl. Peredachi Inf., 2000, vol. 36, no. 2, pp. 69–95 [Probl. Inf. Trans. (Engl. Transl.), 2000, vol. 36, no. 2, pp. 154–179].

    MathSciNet  Google Scholar 

  4. Rybko, A.N. and Shlosman, S.B., Poisson Hypothesis for Information Networks. I, II, Mosc. Math. J., 2005, vol. 5, no. 3, pp. 679–704; no. 4, pp. 927–959.

    MATH  MathSciNet  Google Scholar 

  5. Mikhailov, V.A., Geometrical Analysis of the Stability of Markov Chains in ℝ n+ and Its Application to Throughput Evaluation of the Adaptive Random Multiple Access Algorithm, Probl. Peredachi Inf., 1988, vol. 24, no. 1, pp. 61–73 [Probl. Inf. Trans. (Engl. Transl.), 1988, vol. 24, no. 1, pp. 47–56].

    Google Scholar 

  6. Kuznetsov, D.Yu. and Nazarov, A.A., Non-Markovian Models of Communication Networks with Adaptive Random Multiple Access Protocols, Avtomat. Telemekh., 2001, vol. 62, no. 5, pp. 124–146 [Automat. Remote Control (Engl. Transl.), 2001, vol. 62, no. 5, pp. 789–808].

    MathSciNet  Google Scholar 

  7. Sharma, G., Ganesh, A., and Key, P., Performance Analysis of Contention Based Medium Access Control Protocols, in Prov. IEEE Infocom, Barcelona, April 2006. Available at http://research.microsoft.com/:_peterkey/Papers/IEEE_MAC_DIFFUSION.pdf.

  8. Ethier, S.N. and Kurtz, T.G., Markov Processes: Characterization and Convergence, New York: Wiley, 1986.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia

    N. D. Vvedenskaya

  2. Kharkevich Institute for Information Transmission Problems, RAS, Russia

    Yu. M. Suhov

  3. Moscow Statistical Laboratory, Centre for Mathematical Sciences, Cambridge University, UK

    Yu. M. Suhov

Authors
  1. N. D. Vvedenskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. M. Suhov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. D. Vvedenskaya.

Additional information

Original Russian Text © N.D. Vvedenskaya, Yu.M. Suhov, 2007, published in Problemy Peredachi Informatsii, 2007, Vol. 43, No. 3, pp. 105–111.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vvedenskaya, N.D., Suhov, Y.M. Multi-access system with many users: Stability and metastability. Probl Inf Transm 43, 263–269 (2007). https://doi.org/10.1134/S0032946007030088

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0032946007030088

Keywords

Search

Navigation