Abstract
Classical scheduling theory assumed that a task may require for its processing only one processor at a time. This assumption is not obvious in the context of new parallel computer systems and parallel algorithms. In this work, we consider preemptive deterministic scheduling of multiprocessor tasks, each of which may require a set of processors at a time. In general, tasks may appear in the system in different moments of time. We will also consider the problem of scheduling such tasks in time windows on particular processors. The existence of low-order polynomial time algorithms for the above problems with C max and L max criteria will be analyzed. The general case of the problem can be solved using a linear programming approach.
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References
K.R. Baker, Introduction to Sequencing and Scheduling, Wiley, 1974.
L. Bianco, J. Błażewicz, P. Dell'Olmo and M. Drozdowski, Scheduling preemptive multiprocessor tasks on dedicated processors, Performance Evaluation 20(1994)361–371.
L. Bianco, J. Błażewicz, P. Dell'Olmo and M. Drozdowski, Preemptive scheduling of multiprocessor tasks on the dedicated processors system subject to minimal lateness, Information Processing Letters 46(1993)109–113.
J. Błażewicz, P. Dell'Olmo, M. Drozdowski and M.G. Speranza, Scheduling multiprocessor tasks on three dedicated processors, Information Processing Letters 41(1992)275–280; Corrigendum, IPL 49(1994)269–270.
J. Błażewicz, M. Drabowski and J. Węglarz, Scheduling multiprocessor tasks to minimize schedule length, IEEE Trans. Comput. C-35(1986)389–393.
J. Błażewicz, K. Ecker, G. Schmidt and J. Węglarz, Scheduling in Computer and Manufacturing Systems, 2nd ed., Springer, New York, 1994.
J. Błażewicz J.K. Lenstra and A.H.G. Rinnooy Kan, Scheduling subject to resource constraints: Classification and complexity, Discrete Applied Mathematics 5(1983)11–24.
E.G. Coffman, Jr. (ed.), Computer and Job-Shop Scheduling Theory, Wiley, 1976.
E.G. Coffman, Jr., M.R. Garey, D.S. Johnson and A.S. Lapaugh, Scheduling file transfers, SIAM J. Comp. 14(1985)744–780.
J. Du and J.Y-T. Leung, Complexity of scheduling parallel task systems, SIAM J. Discrete Math. 2(1989)473–487.
D.G. Feitelson and L. Rudolph, Gang scheduling performance benefits for fine-grain synchronization, Journal of Parallel and Distributed Computing 16(1992)306–318.
E.F. Gehringer, D.P. Siewiorek and Z. Segall, Parallel Processing. The CM* Experience, Digital Press, 1987.
R.I. Graham, E.L. Lawler, J.K. Lenstra and A.H.G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling: A survey, Ann. Discrete Math. 5(1979)287–326.
K.S. Hong and J.Y-T. Leung, On-line scheduling of real-time tasks, IEEE Trans. Comput. C-41 (1992)1326–1331.
J.A. Hoogeveen, S.L. van de Velde and B. Veltman, Complexity of scheduling multiprocessor tasks with prespecified processors allocations, Discrete Applied Mathematics 55(1994)259–272.
R. Jain, K. Somalwar, J. Werth and J.C. Browne, Scheduling parallel I/O operations in multiple bus systems, Journal of Parallel and Distributed Computing 16(1992)352–362.
H. Krawczyk and M. Kubale, An approximation algorithm for diagnostic test scheduling in multicomputer systems, IEEE Trans. Comput. C-34(1985)869–872
M. Kubale, The complexity of scheduling independent two-processor tasks on dedicated processors, Information Processing Letters 24(1987)141–147.
M. Kubale, Preemptive scheduling of two-processor tasks on dedicated processors (in Polish), Zeszyty Naukowe Politechniki Sl{ie55-3}skiej, seria: Automatyka 100, Nr kol. 1082(1990)146–153.
M. Kubale, File transfer scheduling within time windows (in Polish), Zeszyty Naukowe Politechniki Sl{ie55-4}skiej, seria: Automatyka 110(1992)69–76.
E.L. Lloyd, Concurrent task systems, Oper. Res. 29(1981)189–201.
G. Schmidt, Scheduling on semi-identical processors, Zeitschrift für Operations Research 28(1984) 153–162.
B. Veltmann, B.J. Lageweg and J.K. Lenstra, Multiprocessor scheduling with communication delays, Parallel Computing 16(1990)173–182.
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Bianco, L., Blazewicz, J., Dell'Olmo, P. et al. Preemptive multiprocessor task scheduling with release times and time windows. Annals of Operations Research 70, 43–55 (1997). https://doi.org/10.1023/A:1018994726051
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DOI: https://doi.org/10.1023/A:1018994726051