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Analytic Modeling and Comparisons of Striping Strategies for Replicated Disk Arrays
March 1995 (vol. 44 no. 3)
pp. 419-433

Abstract—Data replication has been widely used as a means of increasing the data availability for critical applications in the event of disk failure. There are different ways of organizing the two copies of the data across a disk array. This paper compares strategies for striping data of the two copies in the context of database applications. By keeping both copies active, we explore strategies that can take advantage of the additional copy to improve not only availability, but also performance during both normal and failure modes. We consider the effects of small and large stripe sizes on the performance of disk arrays with two active copies of data under a mixed workload of queries and transactions with a skewed access pattern. We propose a dual (hybrid) striping strategy which uses different stripe sizes for the two copies and a disk queuing policy designed to exploit this organization for optimal performance. An analytical model is devised for this scheme, by treating the individual disks as independent, and applying an M/G/1 queuing model. Disks on which a large query scan is running are modeled by a variation of the queue with permanent customers, which leads to an iterative functional equation for the query scan delay distribution. A solution for this equation is given. The results are validated against simulations and are shown to match well. Comparison with uniform striping strategies show that the dual striping scheme yields the most stable performance in a variety of workloads, out-performing the uniform striping strategy using either mirrored or chained declustering under both normal and failure mode operations.

[1] J.A. Katzman,“A fault-tolerant computer system,” Proc. 11th Hawaii Conf. on System Sciences, Jan. 1978.
[2] Teradata Corp., DBC/1012 Database Computer System Manual Release 2.0, Doc. No. C10-0001-02, Nov. 1985.
[3] Tandem database group, “A distributed, high-performance, high reliability implementation of SQL,” Workshop On High Performance Transaction Systems, Asilomar, Calif., Sept., 1987.
[4] H. Hsiao and D.J. DeWitt, “Chained Declustering: A New Availability Strategy for Multiprocessor Database Machines,” Proc. Data Eng., pp. 456–465, 1990.
[5] 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.
[6] J. Gray, B. Horst, and M. Walker, "Parity Striping of Disk Arrays: Low Cost Reliable Storage with Acceptable Throughput," Proc. 16th Int'l VLDB Conf., p. 152, 1990.
[7] M. Stonebraker and G.A. Schloss, “Distributed RAID—A New Multiple Copy Algorithm,” Proc. Sixth Int'l Conf. Data Eng., pp. 430-437, Feb. 1990.
[8] R.R. Muntz and J.C.S. Lui, "Performance Analysis of Disk Arrays Under Failure," Proc. 16th Int'l Conf. Very Large Data Bases, pp. 162-173,Brisbane, Australia, Aug. 1990.
[9] M.Y. Kim, "Synchronized Disk Interleaving," IEEE Trans. Computers, vol. 35, no. 11, pp. 978-988, Nov. 1986.
[10] D. Bitton and J. Gray, “Disk Shadowing,” Very Large Data Bases, pp. 331–338, 1988.
[11] B. Meyer, Reusable Software: The Base Object-Oriented Component Libraries, Prentice Hall, 1994.
[12] P.S. Yu,M.-S. Chen,H. Heiss,, and S.H. Lee,“On workload characterization of relational database environments,” IEEE Trans on Software Engineering, vol. 18, no. 4, pp. 347-355, Apr. 1992.
[13] A. Reddy and P. Banerjee, “Evaluation of Multiple-Disk I/O Systems,” IEEE Trans. Computers, vol. 38, pp. 1,680–1,690, Dec. 1989.
[14] A. Merchant and P.S. Yu, "Design and Modeling of Clustered RAID," Proc. 22th Int'l Symp. Fault Tolerant Computing Systems, pp. 140-149,Boston, July 1992.
[15] A. Merchant and P.S. Yu,“An analytic model of reconstruction time in mirrored disks,” Performance Evaluation, vol. 14, Jan. 1994.
[16] L. Golubchik, J.C.-S. Lui, and R.R. Muntz, “Chained Declustering: Load Balancing and Robustness to Skew and Failure,” Proc. RIDE-TQP Workshop, Feb. 1992.
[17] D. Towsley,S. Chen,, and S-P. Yu,“Performance analysis of a fault tolerant mirrored disk system,” Tech. Rep COINS Tech. Report 91-14, Univ. of Mass, Amherst, Mass., 1991.
[18] G. Copeland and T. Keller, “A Comparison of High-Availability Media RecoveryTechniques,” Proc. ACM SIGMOD Conf., pp. 98–109, 1989.
[19] P.M. Chen and D.A. Patterson, "Maximizing Performance in a Striped Disk Array," Proc. 17th Int'l Symp. Computer Architecture,Seattle, pp. 322-331, May 1990.
[20] G. Weikum, P. Zabback, and P. Scheuermann, "Dynamic File Allocation in Disk Arrays," Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 406-415, 1991.
[21] G. Weikum and P. Zabback,“Tuning of striping units in disk-array-based file systems,” Proc. 2nd Int’l. Workshop on Research Issues in Data Engineering, Tempe, Ariz., pp. 80-87, Feb. 1992.
[22] P. Scheuermann,G. Weikum,, and P. Zabback,“Automatic tuning of data placement and load balancing in disk arrays,” Tech Rpt., ETH,Zurich, Switzerland, Apr. 1992.
[23] J. Wolf, “The Placement Optimization Program: A Practical Solution to the Disk File Assignment Problem,” Proc. Int'l Conf. Measurement and Modeling of Computer Systems, pp. 1-10, 1989.
[24] O.J. Boxma and J.W. Cohen,“The M/G/1 queue with permanent customers,” IEEE Journ. Selected Areas in Communications, vol. 9, pp. 179-184, Feb. 1991.
[25] L. Durivault and R. Melson,“An expression for the maximum of Erlang random variables,” Tech. Rep. RC 16751, IBM, Nov. 1991.
[26] J. Abate and W. Whitt,“The Fourier-series method for inverting transforms of probability distributions,” Queuing Systems, vol. 10, no. 1-2, pp. 5-88, 1992.
[27] A. Law and W. Kelton, Simulation Modeling and Analysis,New York: McGraw-Hill, 1991.
[28] D.L. Jagerman and B. Sengupta,“A functional equation arising in a queue with a gating mechanism,” Probability in the engineering and informational sciences, vol. 3, pp. 417-422, 1989.
[29] D.R. Cox and V. Isham Point Processes. , Chapman and Hall, 1980

Index Terms:
Disk arrays, mirrored disks, chained declustering, stochastic modeling, M/G/1 queues, transform methods, point processes, iterative functional equations.
Philip S. Yu, Arif Merchant, "Analytic Modeling and Comparisons of Striping Strategies for Replicated Disk Arrays," IEEE Transactions on Computers, vol. 44, no. 3, pp. 419-433, March 1995, doi:10.1109/12.372034
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