Transformations on Channel Graphs

Miro Kraetzl; Charles J. Colbourn

doi:10.1109/26.225478

Transformations on Channel Graphs

Miro Kraetzl, Charles J. Colbourn

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A channel graph is a directed acyclic graph with a unique source vertex and a unique sink vertex, in which all edges are partitioned into stages according to their distance from the source. Edges cannot vertices in consecutive stages only. The blocking probability of a channel graph is the probability that every source to sink path is blocked. A general transformation is developed that never decreses the blocking probability. This transformation leads to a short proof of a generalization of a theorem of Takagi,and a theorem of Chung and Hwang, in the case of the binomial model.

Original language	English (US)
Pages (from-to)	664-666
Number of pages	3
Journal	IEEE Transactions on Communications
Volume	41
Issue number	5
DOIs	https://doi.org/10.1109/26.225478
State	Published - May 1993
Externally published	Yes

ASJC Scopus subject areas

Electrical and Electronic Engineering

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title = "Transformations on Channel Graphs",

abstract = "A channel graph is a directed acyclic graph with a unique source vertex and a unique sink vertex, in which all edges are partitioned into stages according to their distance from the source. Edges cannot vertices in consecutive stages only. The blocking probability of a channel graph is the probability that every source to sink path is blocked. A general transformation is developed that never decreses the blocking probability. This transformation leads to a short proof of a generalization of a theorem of Takagi,and a theorem of Chung and Hwang, in the case of the binomial model.",

author = "Miro Kraetzl and Colbourn, {Charles J.}",

note = "Funding Information: Paper approved by the Editor for Communications Switching of the IEEE Communications Society. Manuscript received January 13, 1991; revised May 27, 1991. This work was supported by NSERC Canada Grant A0579. The author are with the School of Mathematics and Statistics, Curtin University of Technology, Perth, Australia. IEEE Log Number 9209493.",

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N2 - A channel graph is a directed acyclic graph with a unique source vertex and a unique sink vertex, in which all edges are partitioned into stages according to their distance from the source. Edges cannot vertices in consecutive stages only. The blocking probability of a channel graph is the probability that every source to sink path is blocked. A general transformation is developed that never decreses the blocking probability. This transformation leads to a short proof of a generalization of a theorem of Takagi,and a theorem of Chung and Hwang, in the case of the binomial model.

AB - A channel graph is a directed acyclic graph with a unique source vertex and a unique sink vertex, in which all edges are partitioned into stages according to their distance from the source. Edges cannot vertices in consecutive stages only. The blocking probability of a channel graph is the probability that every source to sink path is blocked. A general transformation is developed that never decreses the blocking probability. This transformation leads to a short proof of a generalization of a theorem of Takagi,and a theorem of Chung and Hwang, in the case of the binomial model.

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Transformations on Channel Graphs

Abstract

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