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Probabilistic Model and Optimal Reorganization of B+-Tree with Physical Clustering
September-October 1997 (vol. 9 no. 5)
pp. 826-832

Abstract—We consider a variant of B+-tree called the B+-tree with physical clustering (BC), which is exemplified by VSAM key-sequenced datasets. In this file, logically contiguous data buckets are physically clustered in a storage unit called a region in order to enhance the efficiency of sequential processing. As a consequence, records in a bucket are redistributed over time according to two different split algorithms: bucket split and region split. A stochastic model of the disorganization of BC files is constructed using order statistics. Database administrators of on-line transaction systems often need to reorganize BC files before a region split occurs. An efficient algorithm for determining the optimal reorganization time of BC files is developed. Analytic results are validated by simulation. In passing, we discuss guidelines for load-time configuration of BC files.

[1] K. Allgeyer and K. Kratzer, "Expert System Based Configuration of VSAM Files," Proc. 13th Int'l Conf. Very Large Data Bases, pp. 150-156, 1987.
[2] R.A. Baeza-Yates, "Expected Behaviour of B+-Trees Under Random Insertions," Acta Information, vol. 26, pp. 439-471, 1989.
[3] R.A. Baeza-Yates and P. Larson, "Performance of B+-Trees with Partial Expansions," IEEE Trans. Knowledge Data Eng., vol. 1, no. 2, pp. 248-257, June 1989.
[4] D. Comer, “The Ubiquitous B-Tree,” ACM Computing Surveys, vol. 11, no. 2, pp. 121-137, June 1979.
[5] H.A. David, Order Statistics.New York: Wiley, 1981.
[6] D.G. Keehn and S.O. Lacy, "VSAM Dataset Design Parameters," IBM System J., vol. 13, no. 3, pp. 186-212, 1974.
[7] L. Kleinrock, Queueing Systems, Theory, vol. 1. New York: Wiley, 1975.
[8] K. Kuspert, "Storage Utilization in B+-Trees with a Generalized Overflow Technique," Acta Information, vol. 19, pp. 35-55, 1983.
[9] A. Law and W. Kelton, Simulation Modeling and Analysis,New York: McGraw-Hill, 1991.
[10] D.B. Lomet, “Partial Expansions for File Organizations with an Index,” ACM Trans. Database Systems, vol. 12, no. 1, pp. 65-84, Mar. 1987.
[11] D.B. Lomet, "A Simple Bounded Disorder File Organization with Good Performance," ACM Trans. Database System, vol. 13, no. 4, pp. 525-551, Dec. 1988.
[12] S. Martin, K. Allgeyer, and L. Lehmann, "Leistungsanalyse der Zugriffsmethode VSAM," Angewandte Informatik, vol. 27, no. 8, pp. 334-342, Aug. 1985.
[13] T. Nakamura and T. Mizoguchi, "An Analysis of Storage Utilization Factor in Block Split Data Structuring Scheme," Proc. Fourth Int'l Conf. Very Large Data Bases, pp. 489-495,Berlin, 1978.
[14] J.S. Park, R. Bartoszynski, P. De, and H. Pirkul, "Optimal Reorganization Policies for Stationary and Evolutionary Databases," Management Science, vol. 36, no. 5, pp. 613-631, May 1990.
[15] J.S. Park and V. Sridhar, "Probabilistic Model and Optimal Reorganization of B+-Tree with Physical Clustering," working paper, Dept. of Management Sciences, Univ. of Iowa, 1993.
[16] G. Pledger and F. Proschan, "Comparison of Order Statistics and of Spacings from Heterogeneous Distributions," Optimizing Methods in Statistics, J.S. Rustagi, ed. New York: Academic Press, pp. 89-13, 1971.
[17] J. Ranade, VSAM: Performance, Design, and Fine Tuning.New York: Macmillan, 1987.
[18] A.J. Smith, "Analysis of Long Term File Reference Patterns for Application to File Migration Algorithms," IEEE Trans. Software Eng., vol. 7, no. 4, pp. 403-417, July 1981.
[19] P.D. Welch, "The Statistical Analysis of Simulation Results," Computer Performance Modeling Handbook, S.S. Lavenberg, ed. New York: Academic Press, pp. 267-329, 1983.

Index Terms:
B+-tree, dynamic indexed files, physical database, VSAM, stochastic model of file dynamics, file reorganization, order statistics, simulation.
June S. Park, V. Sridhar, "Probabilistic Model and Optimal Reorganization of B+-Tree with Physical Clustering," IEEE Transactions on Knowledge and Data Engineering, vol. 9, no. 5, pp. 826-832, Sept.-Oct. 1997, doi:10.1109/69.634758
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