Abstract
Recently, the reliability evaluation of data center network (DCN) is important to the design and operation of DCNs. Extra connectivity determination and faulty networks structure analysis are two significant aspects for the reliability evaluation of DCNs. The DCell network is suitable for a massive data centers with high network capacity by only using cheap switches. A k-dimensional DCell built with n-port switches, denoted by \(D_{k,n}\), is an \((n+k-1)\)-regular graph. In this paper, we firstly prove that the extra-h connectivity of \(D_{k,n}\) for \(n \ge 2\), \(\kappa _h(D_{k,n}) = (k-1)(h+1) + n\) if \(k \ge 2\) and \(0 \le h \le n-1\), and \(\kappa _h(D_{k,n}) = (k-1)(h+1) + 2n - 2\) if \(k \ge n + 1\) and \(n \le h \le 2n-1\), respectively. What’s more, for any faulty node set \(F \subseteq V(D_{k,n})\) with \(|F| \le \kappa _h(D_{k,n}) - 1\), we obtain that there contains a large connected component in \(D_{k,n} - F\), and the rest of small connected components have not more than h nodes in total if \(k \ge 2\) and \(0 \le h \le n-1\) (resp. \(k \ge n+1\) and \(n \le h \le 2n-1\)). Our result can provide a proper measure for the reliability evaluation of the DCell network when it is used to model the topological structure of a large-scale DCN.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dean, J., Ghemawat, S.: MapReduce: simplified data processing on large clusters. Commun. ACM 51(1), 107–113 (2008)
Ghemawat, S., Gobioff, H., Leung, S.: The Google file system. In: Symposium on Operating Systems Principles (SIGOPS), pp. 29–43 (2003)
Anthony, S.: Microsoft now has one million servers (2013). http://www.extremetech.com/extreme/161772-microsoft-now-has-one-million-servers-less-than-google-but-more-than-amazon-says-ballmer
Guo, C., Wu, H., Tan, K., Shi, L., Zhang, Y., Lu, S.: DCell: a scalable and fault-tolerant network structure for data centers. In: Special Interest Group on Data Communication (SIGCOMM), pp. 75–86 (2008)
Zhu, Q., Wang, X.K., Cheng, G.: Reliability evaluation of BC networks. IEEE Trans. Comput. 62(11), 2337–2340 (2013)
Harary, F.: Conditional connectivity. Networks 13(3), 347–357 (1983)
Fàbrega, J., Fiol, M.A.: Extraconnectivity of graphs with large girth. Discrete Math. 127(1), 163–170 (1994)
Fàbrega, J., Fiol, M.A.: On the extraconnectivity of graphs. Discrete Math. 155(1), 49–57 (1996)
Zhu, Q., Wang, X., Ren, J.: Extra connectivity measures of 3-ary \(n\)-cubes. Computing Research Repository (2011). arxiv.org/pdf/1105.0991v1
Gu, M., Hao, R.: 3-extra connectivity of 3-ary \(n\)-cube networks. Inf. Process. Lett. 114(9), 486–491 (2014)
Lin, L., Zhou, S., Xu, L., Wang, D.: The extra connectivity and conditional diagnosability of alternating group networks. IEEE Trans. Parallel Distrib. Syst. 26(8), 2352–2362 (2015)
Chang, N.W., Tsai, C.Y., Hsieh, S.Y.: On 3-extra connectivity and 3-extra edge connectivity of folded hypercubes. IEEE Trans. Comput. 63(6), 1594–1600 (2014)
Yang, W., Lin, H.: Reliability evaluation of BC networks in terms of the extra vertex-and edge-connectivity. IEEE Trans. Comput. 63(10), 2540–2548 (2014)
Lin, L., Xu, L., Zhou, S., Hsieh, S.Y.: The extra, restricted connectivity and conditional diagnosability of split-star networks. IEEE Trans. Parallel Distrib. Syst. 27(2), 533–545 (2016)
Lin, L., Xu, L., Zhou, S.: Relating the extra connectivity and the conditional diagnosability of regular graphs under the comparison model. Theor. Comput. Sci. 618, 21–29 (2016)
Guo, J., Lu, M.: The extra connectivity of bubble-sort star graphs. Theor. Comput. Sci. 645, 91–99 (2016)
Li, D., Guo, C., Wu, H., Tan, K., Zhang, Y., Lu, S.: FiConn: using backup port for server interconnection in data centers. In: International Conference on Computer Communications (INFOCOM), pp. 2276–2285 (2009)
Guo, C., Lu, G., Li, D., Wu, H., Zhang, X., Shi, Y., Tian, C., Zhang, Y., Lu, S.: BCube: a high performance, server-centric network architecture for modular data centers. In: Special Interest Group on Data Communication (SIGCOMM), pp. 63–74 (2009)
Libdeh, H., Costa, P., Rowstron, A., O’Shea, G., Donnelly, A.: Symbiotic routing in future data centers. In: Special Interest Group on Data Communication (SIGCOMM), pp. 51–62 (2010)
Kliegl, M., Lee, J., Li, J., Zhang, X., Guo, C., Rincon, D.: Generalized DCell structure for load-balanced data center networks. In: International Conference on Computer Communications (INFOCOM), pp. 1–5 (2010)
Wang, X., Fan, J., Zhou, J., Lin, C.K.: The restricted \(h\)-connectivity of the data center network DCell. Discrete Appl. Math. 203, 144–157 (2016)
Wang, X., Fan, J., Lin, C.K., Jia, X.: Vertex-disjoint paths in DCell networks. J. Parallel Distrib. Comput. 96, 38–44 (2016)
Wang, X., Fan, J., Jia, X., Lin, C.K.: An efficient algorithm to construct disjoint path covers of DCell networks. Theoret. Comput. Sci. 609(1), 197–210 (2016)
Wang, X., Erickson, A., Fan, J., Jia, X.: Hamiltonian properties of DCell networks. Comput. J. 58(11), 2944–2955 (2015)
Acknowledgment
This paper is supported by National Natural Science Foundation of China (Nos. 61702351 and 61602333), China Postdoctoral Science Foundation (No. 172985), and Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Nos. 17KJB520036 and 16KJB520050).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Wang, X., He, F., Han, Y., You, L. (2018). Reliability Evaluation of DCell Networks. In: Sun, G., Liu, S. (eds) Advanced Hybrid Information Processing. ADHIP 2017. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 219. Springer, Cham. https://doi.org/10.1007/978-3-319-73317-3_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-73317-3_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73316-6
Online ISBN: 978-3-319-73317-3
eBook Packages: Computer ScienceComputer Science (R0)