Cyclic Diagnosability and Fault Diagnosis Algorithm of Data Center Network DCell

Data center DCell networks are particularly well-suited for large, reliability-critical data centers due to their scalability, fault tolerance, and efficient bandwidth utilization. The reliability and diagnosis of DCell networks are of paramount importance in ensuring smooth operation and continuous availability of data center services. Traditional fault diagnosis models, which focus on global fault detection, are more suited to simpler networks. In contrast, complex DCell networks require fault diagnosis under specific conditions to accommodate dynamic changes and constraints. This paper studies the cyclic diagnosability of DCell networks under different system-level diagnostic models, which is a novel fault diagnosis strategy. Cyclic diagnosability, denoted as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ct_{c}(G)$</tex-math> </inline-formula>, represents the maximum size of a set of fault vertices <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$D$</tex-math> </inline-formula> in a network <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$G$</tex-math> </inline-formula>, so that the self-diagnosis system can identify all vertices in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$D$</tex-math> </inline-formula> under the condition that at least two connected components of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$G-D$</tex-math> </inline-formula> contain a cycle. We show that for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-dimensional DCell with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$</tex-math> </inline-formula>-port switches <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$DCell_{k,n}$</tex-math> </inline-formula>, when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k \geq 2$</tex-math> </inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3 \leq n \leq 5$</tex-math> </inline-formula>, or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k \geq \frac {n}{2} + 1$</tex-math> </inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n \geq 6$</tex-math> </inline-formula>, the cyclic diagnosability is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4k+2n-5$</tex-math> </inline-formula> under the PMC and MM* models based on the indistinguishability of the constructed set and the linear multiple fault analysis technology. Additionally, we propose two practical cyclic fault diagnosis algorithms with low time complexity: PMC-Based Cyclic Fault Diagnosis (PMCCFD) and MM*-Based Cyclic Fault Diagnosis (MMCFD) for the PMC and MM* models to improve fault detection and recovery in large-scale DCell networks. We also implement the PMCCFD and MMCFD algorithms on both synthetic and real data. Furthermore, we verify the availability/efficiency of algorithms PMCCFD and MMCFD in terms of accuracy rate, recall, false negative rate, negative predictive value, and F1Score.