SCIENCE CHINA Information Sciences, Volume 61, Issue 10: 100303(2018) https://doi.org/10.1007/s11432-018-9499-0

Storage and repair bandwidth tradeoff for distributed storage systems with clusters and separate nodes$^\dagger$

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  • ReceivedMar 10, 2018
  • AcceptedJun 19, 2018
  • PublishedAug 20, 2018


The optimal tradeoff between node storage and repair bandwidth is an important issue for distributed storage systems (DSSs). For realistic DSSs with clusters, while repairing a failed node, downloading more data from intra-cluster nodes than from cross-cluster nodes is effective. Therefore, differentiating the repair bandwidth from intra-cluster and cross-cluster is useful. For cluster DSSs, the tradeoff is considered with special repair assumptions where all alive nodes are used for repairing a failed node. In this paper, we investigate the optimal tradeoff for the cluster DSSs under more general storage/repair parameters. Furthermore, we propose a regenerating code construction strategy that achieves the points in the optimal tradeoff curve for the cluster DSSs with specific parameters as a numerical example. Moreover, we consider the influence of separate nodes for the tradeoff for the DSSs with clusters and separated nodes.


[1] Hu Y C, Li X L, Zhang M. Optimal repair layering for erasure-coded data centers. ACM Trans Storage, 2017, 13: 1-24 CrossRef Google Scholar

[2] Zhang H Y, Li H, Li R S. Repair tree: fast repair for single failure in erasure-coded distributed storage systems. IEEE Trans Parallel Distrib Syst, 2017, 28: 1728-1739 CrossRef Google Scholar

[3] Huang C, Chen M H, Li J. Pyramid codes: flexible schemes to trade space for access efficiency in reliable data storage systems. In: Proceedings of the 6th IEEE International Symposium on Network Computing and Applications, Cambridge, 2007. Google Scholar

[4] Dimakis A G, Godfrey P B, Wu Y N. Network coding for distributed storage systems. IEEE Trans Inf Theory, 2010, 56: 4539-4551 CrossRef Google Scholar

[5] Ernvall T, Rouayheb S E, Hollanti C. Capacity and security of heterogeneous distributed storage systems. IEEE J Sel Areas Commun, 2013, 31: 2701-2709 CrossRef Google Scholar

[6] Yu Q, Shum K W, Sung C W. Tradeoff between storage cost and repair cost in heterogeneous distributed storage systems. Trans Emerg Telecommun Technol, 2015, 26: 1201-1211 CrossRef Google Scholar

[7] Akhlaghi S, Kiani A, Ghanavati M R. Cost-bandwidth tradeoff in distributed storage systems. Comput Commun, 2010, 33: 2105-2115 CrossRef Google Scholar

[8] Ford D, Labelle F, Popovici F I, et al. Availability in globally distributed storage systems. In: Proceedings of the 9th USENIX Conference on Operating Systems Design and Implementation, Vancouver, 2010. Google Scholar

[9] Hu Y C, Lee P P C, Zhang X Y. Double regenerating codes for hierarchical data centers. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), Barcelona, 2016. 245--249. Google Scholar

[10] Hou H X, Lee P P C, Shum K W, et al. Rack-aware regenerating codes for data centers. 2018,. arXiv Google Scholar

[11] Prakash N, Abdrashitov V, Médard M. The storage vs repair-bandwidth trade-off for clustered storage systems. IEEE Trans Inf Theory, 2017,. arXiv Google Scholar

[12] Pernas J, Yuen C, Gastón B, et al. Non-homogeneous two-rack model for distributed storage systems. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), Istanbul, 2013. 1237--1241. Google Scholar

[13] Sohn J Y, Choi B, Yoon S W, et al. Capacity of clustered distributed storage. In: Proceedings of IEEE International Conference on Communications (ICC), Paris, 2017. Google Scholar

[14] Kubiatowicz J, Weimer W, Wells C. OceanStore: an architecture for global-scale persistent storage. SIGPLAN Notice, 2000, 35: 190-201 CrossRef Google Scholar

[15] Dimakis A G, Ramchandran K, Yunnan Wu K. A survey on network codes for distributed storage. Proc IEEE, 2011, 99: 476-489 CrossRef Google Scholar

[16] Rashmi K V, Shah N B, Kumar P V. Optimal exact-regenerating codes for distributed storage at the MSR and MBR points via a product-matrix construction. IEEE Trans Inf Theory, 2011, 57: 5227-5239 CrossRef Google Scholar

[17] Li S Y R, Yeung R W, Ning Cai R W. Linear network coding. IEEE Trans Inf Theory, 2003, 49: 371-381 CrossRef Google Scholar

[18] Ahlswede R, Cai N, Li R S. Network information flow. IEEE Trans Inf Theory, 2000, 46: 1204-1216 CrossRef Google Scholar

[19] Smith D K, Ahuja R K, Magnanti T L. Network flows: theory, algorithms, and applications. J Oper Res Soc, 1994, 45: 1340 CrossRef Google Scholar

[20] Goparaju S, Fazeli A, Vardy A. Minimum storage regenerating codes for all parameters. IEEE Trans Inf Theory, 2017, 63: 6318-6328 CrossRef Google Scholar

  • Figure 1

    System model for CSN-DSS.

  • Figure 2

    The IFGs of DSS with one cluster and separate nodes. (a) One node in cluster 1 and one separate node have failed; (b) two nodes in cluster 1 have failed.

  • Figure 5

    (Color online) The numbered nodes are selected nodes. There are two cluster orders $\boldsymbol{\pi}^*$ and $\boldsymbol{\pi}$ for a selected node distribution ${\boldsymbol~s}=(0,4,3,1)$. (a) $\boldsymbol{\pi}^*={(1,2,3,1,2,1,2,1)}$; (b) $\boldsymbol{\pi}={(1,2,1,2,1,2,1,3)}$.


    Algorithm 1 Vertical-order algorithm

    Require:${\boldsymbol~s}=(s_0,s_1,\ldots,s_L).$ Initial cluster label $j~\leftarrow~1$.


    for $i=1$ to $k$

    if textthe $i$-th selected node is a separate node then

    $\pi^*_i\gets~0;$ continue;

    end if

    if $s_j=0$ then



    $\pi_i^*\gets~j$; $s_j\gets~s_j-1$; $j\gets~(j~{\rm~mod}~L)+1$;

    end if

    end for

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