Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2025-01-03T00:50:39.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Threshold Channel Graphs

Published online by Cambridge University Press:  12 September 2008

Miro Kraetzl  and
Charles J. Colbourn
Miro Kraetzl
Affiliation:
Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, CANADA N2L 3G1
Charles J. Colbourn
Affiliation:
Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, CANADA N2L 3G1
Get access Rights & Permissions [Opens in a new window]

Abstract

A transformation that increases the blocking probability of the channel graphs arising in interconnection networks is developed. This provides the basis for eminently computing a bound on the blocking probability by applying the transformation to reduce an arbitrary four-stage channel graph to a threshold channel graph. The four-stage channel graph that is most likely to block, given links that are equally likely to block, is characterized. Partial results are proved concerning the threshold channel graphs that are least likely to block.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 3 , September 1993 , pp. 337 - 349
Copyright
Copyright © Cambridge University Press 1993

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]Ball, M. O. and Provan, J. S. (1983) Calculating bounds on reachability and connectedness in stochastic networks. Networks 13 253–278.CrossRefGoogle Scholar
[2]Caccetta, L. and Kraetzl, M. (to appear) Blocking probabilities of certain classes of channel graphs. In: Kulli, V. R. (ed.) Recent Studies in Graph Theory.Google Scholar
[3]Colbourn, C. J. (1987) The Combinatorics of Network Reliability, Oxford University Press.Google Scholar
[4]Colbourn, C. J., Devitt, J. S., Harms, D. D. and Kraetzl, M. (to appear) Reliability of multistage interconnection networks. IEEE Transactions on Computers.Google Scholar
[5]Hwang, F. K. (1979) Superior channel graphs. Proceedings of 9th International Teletraffic Congress, Torremolino, Spain, paper no. 543.Google Scholar
[6]Lee, C. Y. (1955) Analysis of switching networks. Bell System Technical Journal 34 (6) 1287–1315.CrossRefGoogle Scholar