Research on(t,k)-diagnosability for exchanged hypercube network
Fault diagnosis was an important part in the processing of network system repair.PMC was a diagnosis model which was simple and easy to be understood.Through analysis of the structure of exchanged hypercube,a generalization measure of fault diagnosis for the network system was provided,called (t,k)-...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | zho |
| Published: |
Editorial Department of Journal on Communications
2016-03-01
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| Series: | Tongxin xuebao |
| Subjects: | |
| Online Access: | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2016067/ |
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| Summary: | Fault diagnosis was an important part in the processing of network system repair.PMC was a diagnosis model which was simple and easy to be understood.Through analysis of the structure of exchanged hypercube,a generalization measure of fault diagnosis for the network system was provided,called (t,k)-fault diagnosis method.By computing,it is shown that EH(s,p) is <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mo>( </mo> <mrow> <msup> <mn>2 </mn> <mrow> <mfrac> <mrow> <mi>s </mi> <mo>+ </mo> <mi>p </mi> <mo>− </mo> <mn>1 </mn> </mrow> <mn>2 </mn> </mfrac> </mrow> </msup> <mo>,</mo> <mi>s </mi> <mo>+ </mo> <mn>1 </mn> </mrow> <mo>) </mo> </mrow> </math>-diagnosable and conditional <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mo>( </mo> <mrow> <mfrac> <mrow> <msup> <mn>2 </mn> <mrow> <mi>s </mi> <mo>+ </mo> <mi>p </mi> <mo>+ </mo> <mn>1 </mn> </mrow> </msup> <mo>− </mo> <mn>2 </mn> <mi>s </mi> </mrow> <mrow> <mi>p </mi> <mo>+ </mo> <mn>1 </mn> </mrow> </mfrac> <mo>,</mo> <mn>2 </mn> <mi>s </mi> </mrow> <mo>) </mo> </mrow> </math> -diagnosable,where 1≤s≤p.The result shows that the(t,k)-diagnosability of EH(s,p) is <math xmlns="http://www.w3.org/1998/Math/MathML"> <msup> <mn>2 </mn> <mrow> <mfrac> <mrow> <mi>s </mi> <mo>+ </mo> <mi>p </mi> <mo>− </mo> <mn>1 </mn> </mrow> <mn>2 </mn> </mfrac> </mrow> </msup> </math> ,which is bigger than its ordinary diagnosability s+1,and the conditional (t,k)-diagnosability is <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfrac> <mrow> <msup> <mn>2 </mn> <mrow> <mi>s </mi> <mo>+ </mo> <mi>p </mi> <mo>+ </mo> <mn>1 </mn> </mrow> </msup> <mo>− </mo> <mn>2 </mn> <mi>s </mi> </mrow> <mrow> <mi>p </mi> <mo>+ </mo> <mn>1 </mn> </mrow> </mfrac> </mrow> </math>,which is bigger than its ordinary conditional diagnosability 4s-3.Above results present the important theory basis for fault diagnosis of exchanged hypercube network. |
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| ISSN: | 1000-436X |