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Efficient Placement of Parity and Data to Tolerate Two Disk Failures in Disk Array Systems
November 1995 (vol. 6 no. 11)
pp. 1177-1184

Abstract—In this paper, we deal with the data/parity placement problem which is described as follows: how to place data and parity evenly across disks in order to tolerate two disk failures, given the number of disks N and the redundancy rate p which represents the amount of disk spaces to store parity information. To begin with, we transform the data/parity placement problem into the problem of constructing an N×N matrix such that the matrix will correspond to a solution to the problem. The method to construct a matrix has been proposed and we have shown how our method works through several illustrative examples. It is also shown that any matrix constructed by our proposed method can be mapped into a solution to the placement problem if a certain condition holds between N and p where N is the number of disks and p is a redundancy rate.

[1] P.C. Dibble,“A Parallel interleaved file system,” Computer Science, Tech. Report 334, Univ. of Rochester, Mar. 1990.
[2] S. Frey,“DATACUBE distributed system,” IBM Los Angeles Scientific Center, Mar. 1991.
[3] G.A. Gibson, L. Hellerstein, R.M. Karp, R.H. Katz, and D.A. Patterson, Coding Techniques for Hhandling Failures in Large Disk Arrays, csd-88-477 technical report, Univ. of California Berkley, 1988.
[4] G.A. Gibson, “Redundant Disk Arrays: Reliable, Parallel Secondary Storage,” PhD thesis, University of California at Berkley, Dec. 1990.
[5] R.H. Katz,G.A. Gibson,, and D.A. Patterson,“Disk system architectures for high performance computing,” Proc. IEEE, vol. 77, no. 12, pp. 1,842-1,858, Dec. 1989.
[6] M.Y. Kim, "Synchronized Disk Interleaving," IEEE Trans. Computers, vol. 35, no. 11, pp. 978-988, Nov. 1986.
[7] H.T. Kung, “Memory Requirements for Balanced Computer Architectures,” Proc. Int'l Symp. Computer Architecture, ISCA, pp. 49-54, 1986.
[8] E.K. Lee and R.H. Katz, "Performance Consequences of Parity Placement in Disk Arrays," Proc. Fourth Int'l Conf. Architectural Support for Programming Languages and OS, pp. 190-199, Apr. 1991.
[9] E.K. Lee and R.H. Katz, “The Performance of Parity Placements in Disk Arrays,” IEEE Trans. Computers, vol. 42, no. 6, pp. 651-664, June 1993.
[10] S.W. Ng,“Sparing for a redundant disk array,” IBM Research Report RJ 7621, 1990.
[11] C.-I. Park,“Comparison of MTTF of various coding techniques in disk arrays,” internal memo, System Software Lab., Dept. of Computer Science,POSTECH, 1992.
[12] A.M. Patel,“Error and failure-control procedure for a large-size bubble memory,” IEEE Trans. Magnetics, vol. 18, no. 6, pp. 1,319-1,321, 1982.
[13] D.A. Patterson, G. Gibson, and R.H. Katz, “A Case for Redundant Arrays of Inexpensive Disks (RAID),” Proc. ACM SIGMOD Conf., pp. 109–116, 1988.
[14] D.A. Patterson, et al.,“Introduction to redundant arrays of inexpensive disks (RAID),” Computer Science Report CSD88-479, Univ. of Calif. Berkeley, 1988.
[15] W.W. Peterson and E.J. Weldon Jr.,Error-Correcting Codes, MIT Press, 1972.
[16] A. Reddy and P. Banerjee, “Evaluation of Multiple-Disk I/O Systems,” IEEE Trans. Computers, vol. 38, pp. 1,680–1,690, Dec. 1989.
[17] A.L. Narasimha Reddy and P. Banerjee, "Gracefully Degradable Disk Arrays," Proc. 21st Int'l Symp. Fault Tolerant Computing Systems, pp. 401-408,Montreal, Canada, June 1991.
[18] K. Salem and H. Garcia-Molina, Disk Striping Proc. Data Eng. '86, pp. 336-342, 1986.

Index Terms:
Data protection, disk array, disk failures, I/O performance, parity placement.
Chan-Ik Park, "Efficient Placement of Parity and Data to Tolerate Two Disk Failures in Disk Array Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 11, pp. 1177-1184, Nov. 1995, doi:10.1109/71.476189
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