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Threshold channel graphs. (English) Zbl 0793.94006

Summary: A transformation that increases the blocking probability of the channel graphs arising in interconnection networks is developed. This provides the basis for efficiently computing a bound on the blocking probability by applying the transformation to reduce an arbitrary four-stage channel graph to a threshold challel 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.

MSC:

94C15 Applications of graph theory to circuits and networks
90B25 Reliability, availability, maintenance, inspection in operations research
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References:

[1] Colbourn, IEEE Transactions on Computers
[2] Lee, Bell System Technical Journal 34 pp 1287– (1955) · doi:10.1002/j.1538-7305.1955.tb03799.x
[3] DOI: 10.1002/net.3230130210 · Zbl 0569.68053 · doi:10.1002/net.3230130210
[4] Colbourn, The Combinatorics of Network Reliability (1987)
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