Skip to main content

A Survey of Mathematical Results in Flow-Time Scheduling for Computer Systems

  • Chapter
GI Gesellschaft für Informatik e. V.

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1))

Abstract

In a broad sense the problems most central to the design of operating systems are sequencing problems. This is reflected in the term, operating systems, itself. These problems include sequencing to ensure mutually exclusive use of a resource, determinacy, avoidance of deadlocks, or synchronized execution of tasks; sequencing to make efficient use of memory and input/output resources; and sequencing task executions to optimize performance measures such as schedule-length and mean finishing time. (A mathematical treatment of these classes of problems can be found in [1]). Clearly, the first objective in the study of these problems has been and is the discovery of algorithms that are optimal in some desirable sense, or if optimality implies an excessive implementation cost, heuristic algorithms that are easily implemented and whose performance is reasonably close to the optimal. The frequently difficult mathematics associated with these studies is concerned with proofs of optimality, general complexity analyses, and the analysis of the performance of algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Coffman, E. G. and P. J. Denning, Operating Systems Theory, Prentice-Hall, July 1973.

    Google Scholar 

  2. Conway, R. W., W. L. Maxwell, and L. W. Miller, Theory of Scheduling, Addison-Wesley, 1967.

    Google Scholar 

  3. Graham, R. L., “Bounds on Multiprocessing Anomalies and Related Packing Algorithms”, AFIPS Conference Proceedings, Vol. 40, 1972, pp. 205–217.

    Google Scholar 

  4. Clark, W., The Gantt Chart, (3rd Edition), Pitman and Sons, Ltd., London, 1952.

    Google Scholar 

  5. Graham, R. L., “Bounds on Multiprocessing Timing Anomalies”, SIAM J. on Applied Math., Vol. 17, No. 2, March 1969, pp. 416–429.

    MATH  Google Scholar 

  6. Bruno, J. L., E. G. Coffman, and R. Sethi, “Scheduling Independent Tasks to Reduce Mean Finishsng Time”, Tech. Rep., Computer Science Dept, Pennsylvania State Univ. 1973.

    Google Scholar 

  7. Horowitz, Ellis, Computer Science Dept., Cornell University (private communication).

    Google Scholar 

  8. Hoperoft, J. E. and J. D. Ullman, Formal Languages and Their Relation to Automata, Addison-Wesley, 1969.

    Google Scholar 

  9. Karp, R. M., “Reducibility among Combinatorial Problems”, Tech. Rep. No. 3 Computer Science Dept., Univ. of California, Berkeley, 1972.

    Google Scholar 

  10. Cook, S. A., “The Complexity of Theorem-Proving Procedures”, Third Ann. ACM Symp. on Theory of Computing, May 1971, pp. 151–158.

    Google Scholar 

  11. McNaughton, R., “Scheduling with Deadlines and Loss Functions”, Management Science, Vol. 12, No. 1, Oct. 1959.

    Google Scholar 

  12. Ford, F. L. and D. R. Fulkerson, Flows in Networks, Princeton Univ. Press, 1962.

    Google Scholar 

  13. Fujii, M., T. Kasami, and K. Ninomiya, “Optimal Sequencing of Two Equivalent Processors”, SIAM J. of Applied Math., Vol. 17, No. 3, 1969, pp. 784–789 (Erratum. Vol. 20, No. 1, 1971, p. 141.)

    Google Scholar 

  14. Edmonds, J., “Path, Trees, and Flowers”, Can. J. of Math. Vol. 17, 1965, pp. 449–467.

    Google Scholar 

  15. Coffman, E. G. and R. L. Graham, ‘Optimal Scheduling for Two-Processor Systems“, Acta Informatica, Vol. 1, No. 3, 1972, pp. 200–213.

    MathSciNet  Google Scholar 

  16. Hu, T. C., “Parallel Sequencing and Assembly Line Problems”, Operations Research, Vol. 9, No. 6, Nov. 1961, pp. 841–848.

    Google Scholar 

  17. Mentz, R. R. and E. G. Coffman, “Preemptive Scheduling of Real-Time Tasks on Multiprocessor Systems”, J. of the ACM, Vol. 17, No. 2, April 1970, pp. 324–338.

    Google Scholar 

  18. Muntz, R. R. and E. G. Coffman, “Optimal Preemptive Scheduling on Two-Processor Systems”, IEEE Trans. on Computers, Vol. C-18, No. 11, Nov. 1969, pp. 1014–1020.

    Google Scholar 

  19. Eastman, W. L., S. Evert, and I. M. Isaacs, “Bounds for the Optimal Scheduling of n jobs on m Processors”, Management Science, Vol. 11, No. 2, 1964, pp. 268–279.

    Google Scholar 

  20. Liu, C. L., “Optimal Scheduling on Multiprocessor Computing Systems”, Proc., Sw. and Auto. Theory Symp., Oct. 1972.

    Google Scholar 

  21. Ullman, J. D., “Polynomial Complete Scheduling Problems”, Tech. Rep. No. 9, Computer Science Dept., Univ. of California, Berkeley, March 1973.

    Google Scholar 

  22. Johnson, S. M., “Optimal Two and Three Stage Production Schedules with Set-up Times Included”, Nair. Res. and Log. Quart., Vol. 1, No. 1, March 1954.

    Google Scholar 

  23. Jackson, J. R., “An Extension of Johnson’s Results on Job-Lot Scheduling”, Nay. Res. and Log. Quart., Vol. 3, No. 3, Sept. 1956.

    Google Scholar 

  24. Horn, W. A., “Single-Machine Job Sequencing with Tree-Like Precedence Ordering and Linear Delay Penalties”, SIAM J. of Applied Math., Vol. 23, No. 2, Sept. 1972, pp. 189–202.

    MathSciNet  MATH  Google Scholar 

  25. Sydney, J. B., “One Machine Sequencing with Precedence Relations and Deferral Costs”, Working Paper No. 125, Fac. of Commerce and Bus. Ad., Univ. of British Columbia, 1972.

    Google Scholar 

  26. Fernandez, E. and B. Bussell, “Bounds on the Number of Processors and Time for Multiprocessor Optimal Schedule”, Tech. Rep. Computer Science Dept., Univ. of California, Los Angeles, 1973.

    Google Scholar 

  27. Muntz, R. R., Scheduling of Computations on Multiprocessor Systems: The Preemptive Assignment Discipline, Ph.D. Thesis, Elect. Eng. Dept., Princeton Univ., 1969.

    Google Scholar 

  28. Chen, Y. E. and D. L. Epley, ‘Memory Requirements in a Multiprocessing Environment“, Journal of the ACM, Vol. 19, No. 1, Jan. 1972.

    Google Scholar 

  29. Barskiy, A. B., “Minimizing the Number of Computing Devices Needed to Realize a Computational Process within a Specified Time”, Eng. Cybernetics (USSR), No. 6, pp. 59–63 (translation from Russian) 1968.

    Google Scholar 

  30. Baer, J. L., “A Survey of Some Theoretical Aspects of Multiprocessing”, ACM Comp. Surveys, Vol. 5, No. 1, March 1973, pp. 31–80.

    Google Scholar 

  31. Shen, V. Y. and Y. E. Chen, “A Scheduling Strategy f€E the Flow-Shop Problem in a System with Two Classes of Processors”, Proc. 6 Ann. Conf. Info. Sys. and Sci. March 1972, Elect. Eng. Dept., Princeton Univ.

    Google Scholar 

  32. Schindler, S. and W. Simonsmeie: “The Class of All Optimal Schedules for Two-Processor Systems”, Proc. 7 Ann. Conf. on Info. Sys. and Sci., Elect. Eng. Dept., Princeton Univ., March 1973.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Coffman, E.G. (1973). A Survey of Mathematical Results in Flow-Time Scheduling for Computer Systems. In: Brauer, W. (eds) GI Gesellschaft für Informatik e. V.. Lecture Notes in Computer Science, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-41148-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-41148-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-40668-7

  • Online ISBN: 978-3-662-41148-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics