, Volume 15, Issue 6, pp 600–625 | Cite as

Proportionate progress: A notion of fairness in resource allocation

  • S. K. Baruah
  • N. K. Cohen
  • C. G. Plaxton
  • D. A. Varvel


Given a set ofn tasks andm resources, where each taskx has a rational weightx.w=x.e/x.p,0<x.w<1, aperiodic schedule is one that allocates a resource to a taskx for exactlyx.e time units in each interval [x.p·k, x.p·(k+1)) for allk∈N. We define a notion of proportionate progress, called P-fairness, and use it to design an efficient algorithm which solves the periodic scheduling problem.

Key words

Euclid's algorithm Fairness Network flow Periodic scheduling Resource allocation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. K. Baruah, R. R. Howell, and L. E. Rosier. Algorithms and complexity concerning the preemptive scheduling of periodic, real-time tasks on one processor.Real-Time Systems, 2:301–324, 1990.Google Scholar
  2. [2]
    M. Blum, R. W. Floyd, V. R. Pratt, R. L. Rivest, and R. E. Tarjan. Time bounds for selection.Journal of Computer and System Sciences, 7:448–461, 1973.Google Scholar
  3. [3]
    X. Deng. Mathematical Programming: Complexity and Applications. Ph.D. thesis, Department of Operations Research, Stanford University, Stanford, CA, September 1989.Google Scholar
  4. [4]
    L. R. Ford, Jr., and D. R. Fulkerson.Flows in Networks. Princeton University Press, Princeton, NJ, 1962.Google Scholar
  5. [5]
    M. R. Garey and D. S. Johnson.Computers and Intractability.A Guide to the Theory of NP-Completeness. Freeman, New York, 1979.Google Scholar
  6. [6]
    D. S. Hirschberg and C. K. Wong. A polynomial-time algorithm for the knapsack problem with two variables.Journal of the Association for Computing Machinery, 23:147–154, 1976.Google Scholar
  7. [7]
    W. A. Horn. Some simple scheduling algorithms.Naval Research Logistics Quarterly, 21:177–185, 1974.Google Scholar
  8. [8]
    R. Kannan. A polynomial algorithm for the two-variable integer programming problem.Journal of the Association for Computing Machinery, 27:118–122, 1980.Google Scholar
  9. [9]
    H. W. Lenstra, Jr. Integer programming with a fixed number of variables.Mathematics of Operations Research, 8:538–548, 1983.Google Scholar
  10. [10]
    J. Y.-T. Leung. A new algorithm for scheduling periodic, real-time tasks.Algorithmica, 4:209–219, 1989.CrossRefGoogle Scholar
  11. [11]
    C. L. Liu. Scheduling Algorithms for Multiprocessors in a Hard-Real-Time Environment. JPL Space Programs Summary 37–60, vol. II, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, pages 28–37, November, 1969.Google Scholar
  12. [12]
    C. L. Liu and J. W. Layland. Scheduling algorithms for multiprogramming in a hard-real-time environment.Journal of the Association for Computing Machinery, 20:46–61, 1973.Google Scholar
  13. [13]
    H. E. Scarf. Production sets with indivisibilities, Part I: Generalities.Econometrica, 49:1–32, 1981.Google Scholar
  14. [14]
    H. E. Scarf. Production sets with indivisibilities, Part II: The case of two activities.Econometrica, 49:395–423, 1981.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1996

Authors and Affiliations

  • S. K. Baruah
    • 1
  • N. K. Cohen
    • 1
  • C. G. Plaxton
    • 1
  • D. A. Varvel
    • 1
  1. 1.Department of Computer ScienceUniversity of TexasAustinUSA

Personalised recommendations