A General Framework for Handling Commitment in Online Throughput Maximization

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11480)


We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive single-server schedule which maximizes the number of jobs that complete on time. To circumvent known impossibility results, we make a standard slackness assumption by which the feasible time window for scheduling a job is at least \(1+\varepsilon \) times its processing time, for some \(\varepsilon >0\). We quantify the impact that different provider commitment requirements have on the performance of online algorithms. Our main contribution is one universal algorithmic framework for online job admission both with and without commitments. Without commitment, our algorithm with a competitive ratio of \(\mathcal {O}(1/\varepsilon )\) is the best possible (deterministic) for this problem. For commitment models, we give the first non-trivial performance bounds. If the commitment decisions must be made before a job’s slack becomes less than a \(\delta \)-fraction of its size, we prove a competitive ratio of \(\mathcal {O}(\varepsilon /((\varepsilon -\delta )\delta ^2))\), for \(0<\delta <\varepsilon \). When a scheduler must commit upon starting a job, our bound is \(\mathcal {O}(1/\varepsilon ^2)\). Finally, we observe that for scheduling with commitment the restriction to the “unweighted” throughput model is essential; if jobs have individual weights, we rule out competitive deterministic algorithms.


  1. 1.
    Agrawal, K., Li, J., Lu, K., Moseley, B.: Scheduling parallelizable jobs online to maximize throughput. In: Bender, M.A., Farach-Colton, M., Mosteiro, M.A. (eds.) LATIN 2018. LNCS, vol. 10807, pp. 755–776. Springer, Cham (2018). Scholar
  2. 2.
    Azar, Y., Kalp-Shaltiel, I., Lucier, B., Menache, I., Naor, J., Yaniv, J.: Truthful online scheduling with commitments. In: Proceedings of the ACM Symposium on Economics and Computations (EC), pp. 715–732 (2015)Google Scholar
  3. 3.
    Bansal, N., Chan, H.-L., Pruhs, K.: Competitive algorithms for due date scheduling. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 28–39. Springer, Heidelberg (2007). Scholar
  4. 4.
    Baruah, S.K., Haritsa, J.R.: Scheduling for overload in real-time systems. IEEE Trans. Comput. 46(9), 1034–1039 (1997)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Baruah, S.K., Haritsa, J.R., Sharma, N.: On-line scheduling to maximize task completions. In: Proceedings of the IEEE Real-Time Systems Symposium (RTSS), pp. 228–236 (1994)Google Scholar
  6. 6.
    Baruah, S.K., et al.: On the competitiveness of on-line real-time task scheduling. Real-Time Syst. 4(2), 125–144 (1992)CrossRefGoogle Scholar
  7. 7.
    Canetti, R., Irani, S.: Bounding the power of preemption in randomized scheduling. SIAM J. Comput. 27(4), 993–1015 (1998)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Chen, L., Megow, N., Schewior, K.: An \(\cal{O}(\log m)\)-competitive algorithm for online machine minimization. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 155–163 (2016)Google Scholar
  9. 9.
    Chen, L., Megow, N., Schewior, K.: The power of migration in online machine minimization. In: Proceedings of the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 175–184 (2016)Google Scholar
  10. 10.
    DasGupta, B., Palis, M.A.: Online real-time preemptive scheduling of jobs with deadlines. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 96–107. Springer, Heidelberg (2000). Scholar
  11. 11.
    Ferguson, A.D., Bodík, P., Kandula, S., Boutin, E., Fonseca, R.: Jockey: guaranteed job latency in data parallel clusters. In: Proceedings of the European Conference on Computer Systems (EuroSys), pp. 99–112 (2012)Google Scholar
  12. 12.
    Garay, J.A., Naor, J., Yener, B., Zhao, P.: On-line admission control and packet scheduling with interleaving. In: Proceedings of the IEEE International Conference on Computer Communications (INFOCOM), pp. 94–103 (2002)Google Scholar
  13. 13.
    Georgiadis, L., Guérin, R., Parekh, A.K.: Optimal multiplexing on a single link: delay and buffer requirements. IEEE Trans. Inf. Theory 43(5), 1518–1535 (1997)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Goldwasser, M.H.: Patience is a virtue: the effect of slack on competitiveness for admission control. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 396–405 (1999)Google Scholar
  15. 15.
    Im, S., Moseley, B.: General profit scheduling and the power of migration on heterogeneous machines. In: Proceedings of the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 165–173 (2016)Google Scholar
  16. 16.
    Kalyanasundaram, B., Pruhs, K.: Maximizing job completions online. J. Algorithms 49(1), 63–85 (2003)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Koren, G., Shasha, D.E.: MOCA: a multiprocessor on-line competitive algorithm for real-time system scheduling. Theor. Comput. Sci. 128(1–2), 75–97 (1994)CrossRefGoogle Scholar
  18. 18.
    Koren, G., Shasha, D.E.: Dover: an optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM J. Comput. 24(2), 318–339 (1995)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Liebeherr, J., Wrege, D.E., Ferrari, D.: Exact admission control for networks with a bounded delay service. IEEE/ACM Trans. Netw. 4(6), 885–901 (1996)CrossRefGoogle Scholar
  20. 20.
    Lipton, R.: Online interval scheduling. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 302–311 (1994)Google Scholar
  21. 21.
    Lucier, B., Menache, I., Naor, J., Yaniv, J.: Efficient online scheduling for deadline-sensitive jobs: extended abstract. In: Proceedings of the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 305–314 (2013)Google Scholar
  22. 22.
    Pruhs, K., Stein, C.: How to schedule when you have to buy your energy. In: Proceedings of the International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APROX), pp. 352–365 (2010)CrossRefGoogle Scholar
  23. 23.
    Schwiegelshohn, C., Schwiegelshohn, U.: The power of migration for online slack scheduling. In: Proceedings of the European Symposium of Algorithms (ESA), vol. 57, pp. 75:1–75:17 (2016)Google Scholar
  24. 24.
    Woeginger, G.J.: On-line scheduling of jobs with fixed start and end times. Theor. Comput. Sci. 130(1), 5–16 (1994)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Yaniv, J.: Job scheduling mechanisms for cloud computing. Ph.D. thesis, Technion, Israel (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of HoustonHoustonUSA
  2. 2.Department for Mathematics/Computer ScienceUniversity of BremenBremenGermany
  3. 3.Fakultät für InformatikTechnische Universität MünchenMünchenGermany
  4. 4.Département d’InformatiqueÉcole Normale SupérieureParisFrance
  5. 5.Department of IEORColumbia UniversityNew YorkUSA

Personalised recommendations