This Article 
 Bibliographic References 
 Add to: 
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.
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
Usage of this product signifies your acceptance of the Terms of Use.