Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T12:29:30.362Z Has data issue: false hasContentIssue false
  • English
  • Français

Quasi-stationary distributions and one-dimensional circuit-switched networks

Published online by Cambridge University Press:  14 July 2016

Ilze Ziedins
Ilze Ziedins*
Affiliation:
University of Cambridge
*
∗Postal address: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Riccarton, Edinburgh EH14 4A5, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss the quasi-stationary distribution obtained when a simple birth and death process is conditioned on never exceeding K. An application of this model to one-dimensional circuit-switched communication networks is described, and some special cases examined.

Keywords

BIRTH AND DEATH PROCESSESCOMMUNICATION NETWORKS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987 , pp. 965 - 977
Copyright
Copyright © Applied Probability Trust 1987 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Darroch, J. N. and Seneta, E. (1965) On quasi-stationary distributions in absorbing discrete-time finite Markov chains. J. Appl. Prob. 2, 88–100.Google Scholar
[2] Darroch, J. N. and Seneta, E. (1967) On quasi-stationary distributions in absorbing continuous-time finite Markov chains. J. Appl. Prob. 4, 192–196.Google Scholar
[3] Keilson, J. and Ramaswamy, R. (1984) Convergence of quasi-stationary distributions in birth-death processes. Stoch. Proc. Appl. 18, 301–312.Google Scholar
[4] Kelly, F. P. (1986) One-dimensional circuit-switched networks. Ann. Prob. 14,Google Scholar
[5] Lagarias, J. C., Odlyzko, A.M. and Zagier, D. B. (1985) Realizable traffic patterns and capacity of disjointly shared networks. Computer Networks. CrossRefGoogle Scholar
[6] Ledermann, W. and Reuter, G. E. (1954) Spectral theory for the differential equations of simple birth and death processes. Phil. Trans. R. Soc. London A 246, 321–369.Google Scholar
[7] Seneta, E. (1966) Quasi-stationary distributions and time-reversion in genetics. J. R. Statist. Soc. B 28, 253–277.Google Scholar
[8] Seneta, E. and Tweedie, R. L. (1985) Moments for stationary and quasi-stationary distributions of Markov chains. J. Appl. Prob. 22, 148–155.CrossRefGoogle Scholar