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.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Coffman, E. G. and P. J. Denning, Operating Systems Theory, Prentice-Hall, July 1973.
Conway, R. W., W. L. Maxwell, and L. W. Miller, Theory of Scheduling, Addison-Wesley, 1967.
Graham, R. L., “Bounds on Multiprocessing Anomalies and Related Packing Algorithms”, AFIPS Conference Proceedings, Vol. 40, 1972, pp. 205–217.
Clark, W., The Gantt Chart, (3rd Edition), Pitman and Sons, Ltd., London, 1952.
Graham, R. L., “Bounds on Multiprocessing Timing Anomalies”, SIAM J. on Applied Math., Vol. 17, No. 2, March 1969, pp. 416–429.
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.
Horowitz, Ellis, Computer Science Dept., Cornell University (private communication).
Hoperoft, J. E. and J. D. Ullman, Formal Languages and Their Relation to Automata, Addison-Wesley, 1969.
Karp, R. M., “Reducibility among Combinatorial Problems”, Tech. Rep. No. 3 Computer Science Dept., Univ. of California, Berkeley, 1972.
Cook, S. A., “The Complexity of Theorem-Proving Procedures”, Third Ann. ACM Symp. on Theory of Computing, May 1971, pp. 151–158.
McNaughton, R., “Scheduling with Deadlines and Loss Functions”, Management Science, Vol. 12, No. 1, Oct. 1959.
Ford, F. L. and D. R. Fulkerson, Flows in Networks, Princeton Univ. Press, 1962.
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.)
Edmonds, J., “Path, Trees, and Flowers”, Can. J. of Math. Vol. 17, 1965, pp. 449–467.
Coffman, E. G. and R. L. Graham, ‘Optimal Scheduling for Two-Processor Systems“, Acta Informatica, Vol. 1, No. 3, 1972, pp. 200–213.
Hu, T. C., “Parallel Sequencing and Assembly Line Problems”, Operations Research, Vol. 9, No. 6, Nov. 1961, pp. 841–848.
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.
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.
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.
Liu, C. L., “Optimal Scheduling on Multiprocessor Computing Systems”, Proc., Sw. and Auto. Theory Symp., Oct. 1972.
Ullman, J. D., “Polynomial Complete Scheduling Problems”, Tech. Rep. No. 9, Computer Science Dept., Univ. of California, Berkeley, March 1973.
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.
Jackson, J. R., “An Extension of Johnson’s Results on Job-Lot Scheduling”, Nay. Res. and Log. Quart., Vol. 3, No. 3, Sept. 1956.
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.
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.
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.
Muntz, R. R., Scheduling of Computations on Multiprocessor Systems: The Preemptive Assignment Discipline, Ph.D. Thesis, Elect. Eng. Dept., Princeton Univ., 1969.
Chen, Y. E. and D. L. Epley, ‘Memory Requirements in a Multiprocessing Environment“, Journal of the ACM, Vol. 19, No. 1, Jan. 1972.
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.
Baer, J. L., “A Survey of Some Theoretical Aspects of Multiprocessing”, ACM Comp. Surveys, Vol. 5, No. 1, March 1973, pp. 31–80.
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.
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.
Editor information
Editors and Affiliations
Rights 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