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Mirrored Disk Organization Reliability Analysis
December 2006 (vol. 55 no. 12)
pp. 1640-1644
Disk mirroring or RAID level 1 (RAID1) is a popular paradigm to achieve fault tolerance and a higher disk access bandwidth for read requests. We consider four RAID1 organizations: basic mirroring, group rotate declustering, interleaved declustering, and chained declustering, where the last three organizations attain a more balanced load than basic mirroring when disk failures occur. We first obtain the number of configurations, A(n, i), which do not result in data loss when i out of n disks have failed. The probability of no data loss in this case is A(n,i)/{n \choose i}. The reliability of each RAID1 organization is the summation over 1 \leq i \leq n/2 of A(n, i) r^{n-i}(1-r)^{i}, where r denotes the reliability of each disk. A closed-form expression for A(n,i) is obtained easily for the first three organizations. We present a relatively simple derivation of the expression for A(n,i) for the chained declustering method, which includes a correctness proof. We also discuss the routing of read requests to balance disk loads, especially when there are disk failures, to maximize the attainable throughput.

[1] D. Bitton and J. Gray, “Disk Shadowing,” Proc. 14th Int'l Conf. Very Large Data Bases (VLDB), pp. 331-338, Aug. 1998.
[2] M. Blaum, J. Brady, J. Bruck, and J. Menon, “EVENODD: An Optimal Scheme for Tolerating Double Disk Failures in RAID Architectures,” IEEE Trans. Computers, vol. 44, no. 2, pp. 192-202, Feb. 1995.
[3] P.M. Chen, E.K. Lee, G.A. Gibson, R.H. Katz, and D.A. Patterson, “RAID: High-Performance, Reliable Secondary Storage,” ACM Computing Surveys, vol. 26, no. 2, pp. 145-185, June 1994.
[4] S.-Z. Chen and D. Towsley, “A Performance Evaluation of RAID Architectures,” IEEE Trans. Computers, vol. 45, no. 10, pp. 1116-1130, Oct. 1996.
[5] G.A. Gibson, Redundant Disk Arrays: Reliable, Parallel Secondary Storage. MIT Press, 1992.
[6] J. Gray, “Greetings from a Filesystem User,” Proc. Fourth USENIX Conf. File and Storage Technologies (FAST '02), Dec. 2005.
[7] H.-I. Hsiao and D.J. DeWitt, “A Performance Study of Three High Availability Data Replication Strategies,” J. Distributed and Parallel Databases, vol. 1, no. 1, pp. 53-80, Jan. 1993.
[8] S.W. Ng, “Reliability, Availability, and Performability Analysis of Duplex Disk Systems,” Reliability and Quality Control, M.H. Hamza, ed., pp. 5-9, ACTA Press, 1987.
[9] D.A. Patterson, G.A. Gibson, and R.H. Katz, “A Case for Redundant Arrays of Inexpensive Disks (RAID),” Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 109-116, June 1988.
[10] Tandem Corp. “Nonstop SQL: A Distributed, High-Performance, High-Reliability Implementation of SQL,” Performance Transaction Systems, D. Gawlick et al., eds., pp. 60-103, Springer-Verlag, 1987.
[11] Teradata Corp. Teradata DBC/1012 Database Computer System Manual, Teradata Corp., Nov. 1985.
[12] A. Thomasian and J. Menon, “RAID5 Performance with Distributed Sparing,” IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 6, pp.640-657, June 1997.
[13] A. Thomasian, “Mirrored Disk Routing and Scheduling,” Cluster Computing9, 2006.
[14] A. Thomasian, “Shortcut Method for Reliability Comparisons in RAID,” J.Systems and Software (JSS), 2006.
[15] A. Thomasian and J. Xu, “Reliability and Performance of Mirrored Disk Organizations,” The Computer J., submitted Mar. 2006.
[16] K.S. Trivedi, Probability and Statistics with Reliability, Queueing, and Computer Science Applications, second ed. Wiley, 2002.

Index Terms:
Disk mirroring, RAID level 1, reliability modeling, interleaved declustering, chained declustering, group rotate declustering.
Citation:
Alexander Thomasian, Mario Blaum, "Mirrored Disk Organization Reliability Analysis," IEEE Transactions on Computers, vol. 55, no. 12, pp. 1640-1644, Dec. 2006, doi:10.1109/TC.2006.201
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