Summary
The mean flow time of a schedule provides a measure of the average time that a task spends within a computer system, and also the average number of unfinished tasks in the system. The mean flow time of a schedule is defined to be the sum of the finishing times of all tasks in the system. On a system of identical processors O(nlog n) algorithms exist for determining minimal mean flow time schedules for n independent tasks. In general, there will be a large class C of schedules, of widely differing lengths, that all minimize mean flow time. The problem of finding the shortest schedule in C is NP-complete. We give heuristics that find schedules in C that are no more than 25% longer than the shortest schedule in C. The advantage of a short schedule is that processor utilization is high.
Similar content being viewed by others
References
Bruno, J. L., Coffman, E. G. Jr., Sethi, R.: Scheduling independent tasks to reduce mean finishing time. Comm. ACM 17, 382–387 (1974)
Bruno, J. L., Coffman, E. G. Jr., Sethi, R.: Algorithms for minimizing mean flow time. Information Processing 74. Amsterdam: 1974 p. 504–510 North-Holland
Conway, R. W., Maxwell, W. L., Miller, L. W.: Theory of scheduling. Reading (Mass.): Addison Wesley, 1967
Garey, M. R., Johnson, D. S.: Complexity results for multiprocessor scheduling under resource constraints. SIAM J. Computing 4, 399–411 (1975)
Graham, R. L.: Bounds on multiprocessing anomalies and related packing algorithms. Proc. AFIPS SJCC 40 Montvale (N.J.): AFIPS-Press 1972 p. 205–217
Horowitz, E., Sahni, S.: Exact and approximate algorithms for scheduling nonidentical processors. Tech. Rep. 74-22, University of Minnesota, Minneapolis, Minn. Sep 74 (to appear, JACM)
Karp, R. M.: Reducibility among combinatorial problems. In: R. E. Miller and J. W. Thatcher (ed.): Complexity of computer computations. New York, N.Y.: Plenum Press 1972 p. 85–101
Ullman, J. D.: NP-complete scheduling problems. J. Computer and System Sciences 10, 3 384–393 (1975)
Author information
Authors and Affiliations
Additional information
Partial support provided by NSF Grant GJ-28290
Rights and permissions
About this article
Cite this article
Coffman, E.G., Sethi, R. Algorithms minimizing mean flow time: schedule-length properties. Acta Informatica 6, 1–14 (1976). https://doi.org/10.1007/BF00263740
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00263740