Abstract
The problem considered is that of scheduling n preemptable tasks on m parallel processors, when each task requires for its processing a processor and one resource unit from the set of additional resources. The processing times of a task on different processors are unrelated. We present the method for solving this problem which is composed of two stages. In the first stage, a linear programming problem is solved giving the minimum schedule length and optimal task processing times on particular processors. On the basis of this solution, in the second stage the optimal schedule is constructed taking into account the resource constraints. Theorems are proved concerning the feasibility of the second stage algorithm, and the upper bound on the number of preemptions in the optimal schedule. The cases of independent and dependent tasks are considered.
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C. Berge: Théorie des graphes et ses applications, Chapt. X, Dunod, Paris 1958.
J. Błażewicz: Mean flow time scheduling under resource constraints, Preliminary Report PR-19/77, Technical University of Poznań/Poland/March 1977.
J. Błażewicz, W. Cellary, R. Słowiński, J. Węglarz: Deterministic problems of scheduling tasks on parallel processors. Part I. Sets of independent tasks, /in Polish/ Podstawy Sterowania 6, June 1976, 155–178.
M.R. Garey, R.L. Graham: Bounds for multiprocessor scheduling with resource constraints, SIAM J. on Computing 4, 1975, 187–200.
M.R. Garey, R.L. Graham, D.S. Johnson, A.C.-C. Yao: Resource constrained scheduling as generalized bin packing, J. Combinatorial Theory Ser. A, 21, 1976, 257–298.
M.R. Garey, D.S. Johnson: Complexity results for multiprocessor scheduling under resource constraints, SIAM J. on Computing 4, 1975, 397–411.
R.L. Graham, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnoy Kan: Optimization and approximation in deterministic sequencing and scheduling: a survey, Report BW 82/77, Mathematisch Centrum, Amsterdam, October 1977.
K.L. Krause, V.Y. Shen, H.D. Schwetman: Analysis of several task-scheduling algorithms for a model of multiprogramming computer system, J.ACM 22, 1975, 522–550, 24, 1977, 527.
E.L. Lawler, J. Labetoulle: Scheduling of parallel machines with preemptions, Proc. of the IXth Internat. Symp. on Mathematical Programming, Budapest, August 1976 /to appear/.
R. Słowiński: Algorithm FEASCHE — computer program in Fortran, Preliminary Report PR 10/77, Technical University of Poznań,/Poland/May 1977.
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Słowiński, R. (1978). Scheduling preemptable tasks on unrelated processors with additional resources to minimize schedule length. In: Bracchi, G., Lockemann, P.C. (eds) Information Systems Methodology. ECI 1978. Lecture Notes in Computer Science, vol 65. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08934-9_97
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DOI: https://doi.org/10.1007/3-540-08934-9_97
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