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Concurrent Task Systems

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  • Errol L. Lloyd

    (University of Pittsburgh, Pittsburgh, Pennsylvania)

Abstract

We study minimum execution time scheduling of computer task systems where each task may require control of several processors during each step of its execution. Such a task system consists of: m identical processors, tasks T 1 , …, T n , and a partial order on those tasks which represents precedence constraints. Associated with each task T 1 is a positive integral execution time τ 1 and a degree of concurrency q 1 ∈ (C-script) where (C-script) ⊆ {1, …, m }. Task T 1 must execute for τ 1 , steps and for each of those τ 1 steps it requires q 1 processors. Minimum length schedules for systems in which all task execution times are equal (concurrent UET task systems) are studied. Three sets of results are given. First, we show that scheduling concurrent UET task systems is NP-complete even if there are only three processors and each task has a degree of concurrency of either 1 or 2. Secondly, given any concurrent UET task system let r be the maximum degree of concurrency of any task. We show that the ratio of the length of an arbitrary list schedule for that system compared to the length of an optimal schedule is bounded above by (2 m − r )/( m − r + 1). We also show that the ratio ⌊(2 m − r )/( m − r + 1 )⌋ is achievable. Finally, we give an algorithm which produces optimal schedules for concurrent UET task systems on two processors.

Suggested Citation

  • Errol L. Lloyd, 1981. "Concurrent Task Systems," Operations Research, INFORMS, vol. 29(1), pages 189-201, February.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:1:p:189-201
    DOI: 10.1287/opre.29.1.189
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    Cited by:

    1. Blazewicz, Jacek & Liu, Zhen, 2002. "Linear and quadratic algorithms for scheduling chains and opposite chains," European Journal of Operational Research, Elsevier, vol. 137(2), pages 248-264, March.
    2. Oguz, C. & Fikret Ercan, M. & Edwin Cheng, T. C. & Fung, Y. F., 2003. "Heuristic algorithms for multiprocessor task scheduling in a two-stage hybrid flow-shop," European Journal of Operational Research, Elsevier, vol. 149(2), pages 390-403, September.
    3. Keqin Li, 1999. "Analysis of the List Scheduling Algorithm for Precedence Constrained Parallel Tasks," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 73-88, July.
    4. Roland Braune, 2022. "Packing-based branch-and-bound for discrete malleable task scheduling," Journal of Scheduling, Springer, vol. 25(6), pages 675-704, December.
    5. Oguz, Ceyda & Zinder, Yakov & Ha Do, Van & Janiak, Adam & Lichtenstein, Maciej, 2004. "Hybrid flow-shop scheduling problems with multiprocessor task systems," European Journal of Operational Research, Elsevier, vol. 152(1), pages 115-131, January.
    6. Blazwicz, Jacek & Liu, Zhen, 1996. "Scheduling multiprocessor tasks with chain constraints," European Journal of Operational Research, Elsevier, vol. 94(2), pages 231-241, October.
    7. Wu, Lingxiao & Wang, Shuaian, 2018. "Exact and heuristic methods to solve the parallel machine scheduling problem with multi-processor tasks," International Journal of Production Economics, Elsevier, vol. 201(C), pages 26-40.
    8. Dolgui, Alexandre & Kovalev, Sergey & Kovalyov, Mikhail Y. & Malyutin, Sergey & Soukhal, Ameur, 2018. "Optimal workforce assignment to operations of a paced assembly line," European Journal of Operational Research, Elsevier, vol. 264(1), pages 200-211.

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