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From local to global: an analysis of nearest neighbor balancing on hypercube

Published:01 May 1988Publication History
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Abstract

This paper will focus on the issue of load balancing on a hypercube network of N processors. We will investigate a typical nearest neighbor balancing strategy - in which workloads among neighboring processors are averaged at discrete time steps. The computation model allows tasks, described by independent random variables, to be generated and terminated at all times.

We assume that the random variables at all nodes have equal expected value and their variances are bounded by a constant d2, and we let the difference DIFF between the actual load on each node and the average load on the system describe the deviation of the load on a node from the global average value. The following analytical results are obtained:

  • The expected value of DIFF, denoted by E(DIFF), is 0.

  • The variance of DIFF, denoted by Var(DIFF), is independent of time t, and Var(DIFF)≤ 1.386d2 + 0.231 logN.

References

  1. 1 M.A.Igbal, J.H.Salts, S.H.Bokhari, A Comparative analysis of Static and Dynamic Load Balancing Strategies, Proceedings of the 1986 International Conference on Parallel Processing, Aug. 1986. pp.1040-1045.Google ScholarGoogle Scholar
  2. 2 Winifred I. Williams, Load Balancing and Hypercubes: A preliminary look, Proceedings of The Second Conference on Hypercube Multiprocessors, Sept. 1986. pp. 108- 113.Google ScholarGoogle Scholar
  3. 3 M.Livny, The study of load balancing algorithms for decentralized processing systems, ph.D. Dissertation. Veizman Institute of Science, Aug. 1983.Google ScholarGoogle Scholar
  4. 4 D. Eager, E.D.Lazowska and J.Zahorjan, A comparison of receiver initiated and sender initiated dynamic load sharing, Proc. of the ACM-SIGMETRICS Conf. on Measurement and Modeling of Computer Systems, Aug. 1985. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. 5 Kai Hwang and Raymond Chowkwanyun, Dynamic Load Balancing Methods for Distributed Supercomputing, CRI-TR87-02, Computer Research Institute, University of Southern California, Feb. 1987.Google ScholarGoogle Scholar
  6. 6 F.C.Lin and R.M.Keller, Gradient Model: A Demand- Driven Load Balancing Scheme, IEEE Conference on Distributed Systems, pp.329-336. 1986.Google ScholarGoogle Scholar
  7. 7 L.M.ni, C.Xu and T.B.Gendreau, A Distributed Drafting Algorithm for Load Balancing, IEEE Transections on Computers, vol. SE-11, No.10, pp. 1153-1161. Oct. 1985. Google ScholarGoogle ScholarDigital LibraryDigital Library

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          • Published in

            cover image ACM SIGMETRICS Performance Evaluation Review
            ACM SIGMETRICS Performance Evaluation Review  Volume 16, Issue 1
            May 1988
            266 pages
            ISSN:0163-5999
            DOI:10.1145/1007771
            Issue’s Table of Contents
            • cover image ACM Conferences
              SIGMETRICS '88: Proceedings of the 1988 ACM SIGMETRICS conference on Measurement and modeling of computer systems
              May 1988
              282 pages
              ISBN:0897912543
              DOI:10.1145/55595

            Copyright © 1988 ACM

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            Association for Computing Machinery

            New York, NY, United States

            Publication History

            • Published: 1 May 1988

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