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Journal of Scheduling

, Volume 17, Issue 2, pp 173–183 | Cite as

Online scheduling with preemption or non-completion penalties

  • Stanley P. Y. Fung
Article

Abstract

We consider online preemptive scheduling problems where jobs have deadlines and the objective is to maximize the total weight of jobs completed before their deadlines. In the first problem, preemptions are not free but incur a penalty. In the second problem, a job has to be accepted or rejected immediately upon arrival, and may need to be immediately allocated a fixed scheduling interval as well; if these accepted jobs are not eventually completed, the job is lost, and a penalty is incurred. We give an algorithm with the optimal competitive ratio for the first problem, and new and improved algorithms for the second problem, under different models of preemptions and job weights.

Keywords

Online algorithms Competitive analysis Immediate notification Immediate decision Preemption penalty 

Notes

Acknowledgments

Part of this work was done while the author was on study leave granted by the University of Leicester.

References

  1. Baruah, S. K., Koren, G., Mao, D., Mishra, B., Raghunathan, A., Rosier, L. E., et al. (1992). On the competitiveness of on-line real-time task scheduling. Real-Time Systems, 4, 125–144.CrossRefGoogle Scholar
  2. Ding, J., Ebenlendr, T., Sgall, J., & Zhang, G. (2007). Online scheduling of equal-length jobs on parallel machines. In Proceedings of 15th European Symposium on Algorithms, Vol. 4698 of Lecture Notes in Computer Science (pp. 427–438). New York: Springer.Google Scholar
  3. Ding, J., & Zhang, G. (2006). Online scheduling with hard deadlines on parallel machines. In Proceedings of 2nd International Conference on Algorithmic Aspects in Information and Management, Vol. 4041 of Lecture Notes in Computer Science (pp. 32–42). New York: Springer.Google Scholar
  4. Dürr, C., Jez, L., & Nguyen, K. T. (2009). Online scheduling of bounded length jobs to maximize throughput. In Proceedings of 7th International Workshop in Approximation and Online Algorithms, Vol. 5893 of Lecture Notes in Computer Science (pp. 116–127). New York: Springer.Google Scholar
  5. Ebenlendr, T., & Sgall, J. (2008). A lower bound for scheduling of unit jobs with immediate decision on parallel machines. In Proceedings of 6th Workshop on Approximation and Online Algorithms, Vol. 5426 of Lecture Notes in Computer Science (pp. 43–52). New York: Springer.Google Scholar
  6. Fung, S. P. Y. (2008). Lower bounds on online deadline scheduling with preemption penalties. Information Processing Letters, 108(4), 214–218.CrossRefGoogle Scholar
  7. Fung, S. P. Y., Zheng, F., Chan, W.-T., Chin, F. Y. L., Poon, C. K., & Wong, P. W. H. (2008). Improved on-line broadcast scheduling with deadlines. Journal of Scheduling, 11(4), 299–308.CrossRefGoogle Scholar
  8. Goldwasser, M. H., & Kerbikov, B. (2003). Admission control with immediate notification. Journal of Scheduling, 6, 269–285.CrossRefGoogle Scholar
  9. Hoogeveen, H., Potts, C. N., & Woeginger, G. J. (2000). On-line scheduling on a single machine: Maximizing the number of early jobs. Operations Research Letters, 27(5), 193–197.CrossRefGoogle Scholar
  10. Koren, G., & Shasha, D. (1995). \(D^{over}\): An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24, 318–339.CrossRefGoogle Scholar
  11. Nguyen, K. T. (2011). Improved online scheduling in maximizing throughput of equal length jobs. In Proceedings of 6th International Computer Science Symposium in Russia, Vol. 6651 of Lecture Notes in Computer Science (pp. 429–442). New York: Springer.Google Scholar
  12. Thibault, N., & Laforest, C. (2009). Online time constrained scheduling with penalties. In Proceedings of 23rd IEEE International Symposium on Parallel and Distributed Processing.Google Scholar
  13. Ting, H.-F. (2006). A near optimal scheduler for on-demand data broadcasts. In Proceedings of 6th Italian Conference on Algorithms and Complexity, Vol. 3998 of Lecture Notes in Computer Science (pp. 163–174). New York: Springer.Google Scholar
  14. Woeginger, G. J. (1994). On-line scheduling of jobs with fixed start and end times. Theoretical Computer Science, 130(1), 5–16.CrossRefGoogle Scholar
  15. Zheng, F., Dai, W., Xiao, P., & Zhao, Y. (2005). Competitive strategies for on-line production order disposal problem. In Proceedings of 1st International Conference on Algorithmic Applications in Management (pp. 46–54).Google Scholar
  16. Zheng, F., Xu, Y., & Poon, C. K. (2009). On job scheduling with preemption penalties. In Proceedings of 5th International Conference on Algorithmic Aspects in Information and Management, Vol. 5564 of Lecture Notes in Computer Science (pp. 315–325). New York: Springer.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of LeicesterLeicesterUK

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