Skip to main content
  • 595 Accesses

Abstract

The problems described here are concerned with a stochastic model of a communication network. The model represents the interactions between the random demands placed on a network, and the aim is to understand its stationary behavior. In particular, we are interested in any clues that the network may exhibit instabilities, with perhaps various distinct modes of behavior possible.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. M. Ya. Kelbert and Yu. M. Suhov, “Conditions for Existence and Uniqueness of the Full Random Field Describing a State of a Switching Network,” Probl. Pered. Inform., 19, pp. 50–71 (1983).

    Google Scholar 

  2. F.P. Kelly, “Stochastic Models of Computer Communication Systems,” J. Roy. Statist. Soc., B47, pp. 379–395 (1985).

    Google Scholar 

  3. F.P. Kelly, “Blocking Probabilities in Large Circuit-Switched Networks,” Adv. Appl. Prob., 18, pp. 473–505 (1986).

    Article  MATH  Google Scholar 

  4. R. Kinderman and J.L. Snell, “Markov Random Fields and Their Applications,” Contemporary Mathematics, Vol. I, American Mathematical Society, Providence, R.I., 1980.

    Google Scholar 

  5. T.M. Liggett, Interacting Particle Systems, Springer-Verlag, New York, 1985.

    MATH  Google Scholar 

  6. V.V. Marbukh, “Asymptotic Investigation of a Complete Communications Network with a Large Number of Points and Bypass Routes,” Probl. Pered. Inform., 17, pp. 89–95 (1981).

    MathSciNet  Google Scholar 

  7. F. Spitzer, “Markov Random Fields on an Infinite Tree,” Ann. Prob., 3, pp. 387–398 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  8. Yu.M. Suhov, “Full Random Field Describing States of a Switching Network,” Fundamentals of Teletraffic Theory, Proceedings of the Third International Seminar on Teletraffic Theory, 1984. Institute for Problems of Information Transmission of the USSR Academy of Sciences, pp. 410–415.

    Google Scholar 

  9. I. Ziedins, “Quasi-Stationary Distributions and One-Dimensional Circuit-Switched Networks,” J. Appl. Prob., 23 (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Kelly, F.P. (1987). Instability in a Communication Network. In: Cover, T.M., Gopinath, B. (eds) Open Problems in Communication and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4808-8_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4808-8_15

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9162-6

  • Online ISBN: 978-1-4612-4808-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics