Novel Reliability Indicators From the Perspective of Data Center Networks

Modern large-scale computing systems always demand better connectivity indicators for reliability evaluation. However, as more processing units have been rapidly incorporated into emerging computing systems, existing indicators (e.g., <inline-formula><tex-math notation="LaTeX">...

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Bibliographic Details
Published in:IEEE transactions on reliability Vol. 74; no. 1; pp. 2459 - 2472
Main Authors: Zhuang, Hongbin, Li, Xiao-Yan, Lin, Cheng-Kuan, Liu, Ximeng, Jia, Xiaohua
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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Algorithms
conditional matroidal connectivity
Connectivity
Data centers
Fault tolerance
Fault tolerant systems
Indicators
matroidal connectivity
Multiprocessor interconnection
Network reliability
Partitions (mathematics)
Reliability analysis
Servers
Simulation
Switches
Topology
ISSN:0018-9529, 1558-1721
Online Access:Get full text
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Summary:Modern large-scale computing systems always demand better connectivity indicators for reliability evaluation. However, as more processing units have been rapidly incorporated into emerging computing systems, existing indicators (e.g., <inline-formula><tex-math notation="LaTeX">\ell</tex-math></inline-formula>-component edge connectivity and <inline-formula><tex-math notation="LaTeX">\ell</tex-math></inline-formula>-extra edge connectivity) have gradually failed to provide the required fault tolerance. In addition, these indicators require, for example, that the faulty network should have at least <inline-formula><tex-math notation="LaTeX">\ell</tex-math></inline-formula> components (or that each component should have at least <inline-formula><tex-math notation="LaTeX">\ell</tex-math></inline-formula> nodes). These fault assumptions are not flexible enough to deal with diversified structural demands in practice circumstances. In order to address these challenges simultaneously, this article proposes two novel indicators for network reliability by utilizing the partition matroid technique, named matroidal connectivity and conditional matroidal connectivity. We first investigate the accurate values of (conditional) matroidal connectivity of <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-ary <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula>-cube <inline-formula><tex-math notation="LaTeX">Q_{n}^{k}</tex-math></inline-formula>, which is an appealing option as the underlying topology for modern parallel computing systems. Moreover, we propose an <inline-formula><tex-math notation="LaTeX">O(k^{n-1})</tex-math></inline-formula> algorithm for determining structural features of minimum edge sets whose cardinality is the conditional matroidal connectivity of <inline-formula><tex-math notation="LaTeX">Q_{n}^{k}</tex-math></inline-formula>. Simulation results are presented to verify our algorithm's correctness and further investigate the distribution pattern of edge sets subject to the restriction of partition matroid. We also present comparative analyses illustrating the superior edge fault tolerance of our findings in relation to prior research, which even exhibits an exponential enhancement when <inline-formula><tex-math notation="LaTeX">k\geq 4</tex-math></inline-formula>.
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ISSN:0018-9529
1558-1721
DOI:10.1109/TR.2024.3393133