Research On Fault Diagnosis Of K-Ary N Cube Networks

The increase of network system size will increase the risk of network node failure in the system,so it is necessary to evaluate the fault tolerance of the network system and repair or replace the failed nodes.The indicators to evaluate the fault tolerance of network system include classical connectivity,additional connectivity,connectivity branch fault diagnosis,fault block connectivity and so on.To repair or replace the fault node,we must first find the fault node in the network system.The strategies for fault diagnosis include t-diagnosis strategy,t/s-diagnosis strategy,t/t-diagnosis strategy and t/k-diagnosis strategy and so on.In addition,it is also important to select a specific diagnosis model to identify the fault node.Among many diagnosis models,two models are used more:PMC model and MM*model.Based on the above aspects,this paper mainly studies the fault tolerance and fault diagnosis of k-ary n cube network from the following aspects.Firstly,this paper analyzes the topology of k-ary n cube networks,calculates the maximum upper bound of the sum of the number of nodes of all components including the upper limit number of nodes after removing some network nodes,and calculates the connected distribution of the remaining nodes according to the obtained maximum upper bound.Secondly,according to the definition and judgment conditions of t/sdiagnosable strategy,the diagnostic degree under t/s-diagnosis strategy is obtained,and it is proved that the 3-ary n cube networks is η/η+h-1diagnosable under PMC and MM*model,where n≥2,1 ≤h≤n-1 and 2hn-3(h-1)-(h-1)(h-2)/2-1<η2(h+1)n-3h-h(h-1)/2-1;kary n cube networks is η/η+h-1-diagnosable under PMC and MM*model,where k≥4,n≥2,1 ≤h ≤n-1 and 2hn-2(h-1)-(h-1)(h-2)/21<η ≤2(h+1)n-2h-h(h-1)-1.Thirdly,according to the definition of component fault diagnosis,this paper proves that under PMC and MM*model,for k(k≥ 3)-ary n(n≥5)cube networks,the g-component fault diagnosis degree ctg(Qnk)=2gn-gg(g-1)/2+1(1≤g≤n-1).