Abstract
In this paper, we study the problem of scheduling a set of n periodic preemptive independent hard real-time tasks on the minimum number of processors. We assume that the partitioning strategy is used to allocate the tasks to the processors and the EDF method is used to schedule the tasks on each processor. It is known that this scenario is NP-hard; thus, it is unlikely to find a polynomial time algorithm to schedule the tasks on the minimum number of processors. In this work, we derive a lower and an upper bound for the number of processors required to satisfy the constraints of our problem. We also compare a number of heuristic algorithms with each other and with the bounds derived in this paper. Numerical results demonstrate that our lower bound is very tight and it is very close to the optimal solution.
This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.
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References
Alvim, A.C.F., Glover, F., Ribeiro, C.C., Aloise, D.J.: Local search for the bin packing problem. In: Hansen, P., Ribeiro, C.C. (eds.) MIC 1999. Extended Abstracts of the III Metaheuristics International Conference, Angra dos Reis, Brazil, pp. 7–12 (1999)
Carpenter, J., Funk, S., Holman, P., Srinivasan, A., Anderson, J., Baruah, S.: A Categorization of Real-time Multiprocessor Scheduling Problems and Algorithms. In: Leung, J.Y. (ed.) Handbook of Scheduling: Algorithms, Models, and Performance Analysis, CRC Press, Boca Raton, FL, USA (2004)
Chekuri, C., Motwani, R., Natarajan, B., Stein, C.: Approximation techniques for average completion time scheduling. SIAM Journal on Computing 31(1), 146–166 (2001)
Coffman Jr., Galambos, G., Martello, S., Vigo, D.: Bin Packing Approximation Algorithms: Combinatorial Analysis. In: Du, D., Pardalos, P. (eds.) Handbook of Combinatorial Optimization, Kluwer, Amsterdam (1998)
Coffman, E.G., Garey Jr., M.R., Johnson, D.S.: Approximation algorithms for NP-hard problems. In: Chapter Approximation algorithm for bin packing: A survey, pp. 46–93. PWS, Boston, MA, USA (1996)
Garey, M.R., Johnson, D.S.: A 71/60 theorem for bin packing. Journal of Complexity 1, 65–106 (1985)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)
Joseph, M.: Real-time Systems: Specification, Verification and Analysis. In: Series F: Computer and Systems Sciences. NATO ASI Series, Prentice Hall, Englewood Cliffs (1996)
Kao, C.-Y., Lin, F.-T.: A Stochastic Approach for the One-Dimensional Bin-Packing Problems. In: Proceedings of 1992 IEEE International Conference on System, Man, and Cyberbetics, Chicago, Illinois, October 18-21, 1992, IEEE Computer Society Press, Los Alamitos (1992)
Krishna, C.M., Shin, K.G.: Real-Time Systems. MIT Press and McGraw-Hill, Cambridge (1997)
Laplante, P.A.: Real-time Systems Design and Analysis, An Engineer Handbook. IEEE Computer Society, IEEE Press, Los Alamitos (1993)
Lopez, J.M., Garcýa, M., Dýaz, J.L., Garcýa, D.F.: Utilization Bounds for Multiprocessor Rate-Monotonic Scheduling. Real Time Systems 24(1) (January 2003)
Lopez, J.M., Dýaz, J.L., Garcýa, D.F.: Minimum and Maximum Utilization Bounds for Multiprocessor Rate Monotonic Scheduling. IEEE Transaction on Parallel and Distributed Systems 15(7), 642–653 (2004)
Martello, S., Toth, P.: Knapsack problems. John Wiley and Sons, Chichester (1990)
Minyi, Y., Lei, Z.: A simple proof of the inequality MFFD(L) = 71/60 OPT(L) + 1, L for the MFFD bin-packing algorithm. Acta Mathematicae Applicatae Sinica 11, 318–330 (1995)
Mohammadi, A., Akl, S.: Scheduling algorithms for real-time systems. Technical Report No.2005-499 School of Computing Queen’s University (2005)
Stankovic, J.A., Ramamritham, K.: Tutorial Hard Real-Time Systems. IEEE Computer Society Press, Los Alamitos (1988)
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Mohammadi, A., Akl, S.G. (2007). Number of Processors with Partitioning Strategy and EDF-Schedulability Test: Upper and Lower Bounds with Comparison. In: Stojmenovic, I., Thulasiram, R.K., Yang, L.T., Jia, W., Guo, M., de Mello, R.F. (eds) Parallel and Distributed Processing and Applications. ISPA 2007. Lecture Notes in Computer Science, vol 4742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74742-0_5
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DOI: https://doi.org/10.1007/978-3-540-74742-0_5
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