Skip to main content
Log in

Analysis of computer job control under uncertainty

  • Computer Methods
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

Various policies for controlling jobs in a problem-oriented computer system are considered. The proposed algorithms belong to the class of search algorithms; they require a large (and, typically, unknown) amount of computations. The problem is to select a dynamic policy for redistributing resources between jobs under uncertainty. The analysis of resource reallocation rules uses probability theory and computer simulation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. Garonne, I. Stokes-Rees, and A. Tsaregorodsev, “DIRAC: A Scalable Lightweight Architecture for High Throughput Computing,” in Proc. 5th IEEE/ACM Int. Workshop on Grid Computing (IEEE Computer Society, Washington, DC, 2004), pp. 19–25.

    Google Scholar 

  2. V. Garonne, A. Tsaregorodtsev, and E. Caron, “A Study of Meta-Scheduling Architectures for High Throughput Computing: Pull Versus Push,” in Proc. 4th Int. Symp. on Parallel and Distributed Computing (IEEE Computer Society, Washington, DC, 2005), pp. 226–233.

    Google Scholar 

  3. A. V. Zabrodin, V. K. Levin, and V. V. Korneev, “Massively Parallel Systems MVS-100 and MVS-1000,” in Trudy nauchnoi sessii MIFI, Moscow, 2000 (Proc. of Research Session, Moscow Institute of Engineering Physics) (MIFI, Moscow, 2000), vol. 2, pp. 194–195 [in Russian].

    Google Scholar 

  4. A. V. Baranov, A. V. Kiselev, V. V. Korneev, et al., “Managing a Network Distributed Computing System,” in Trudy Pervoi Vserossiiskoi nauchnji konferentsii “Metody i sredstva obrabotki informatsii” (Proc. of the First All-Russia Conf. on Methods and Tools for Data Processing) (Mosk. Gos. Univ., Moscow, 2003), pp. 98–103 [in Russian].

    Google Scholar 

  5. A. V. Baranov, A. V. Kiselev, V. V. Korneev, et al., “Software Batch “Piramida” for Organizing Parallel Computations with Data Parallelization,” in Trudy mezhdunarodnoi superkomp’yuternoi konferentsii i konferentsii molodykh uchenykh “Nauchnyi servis v seti Internet: Superkomp’yuternye tsentry i zadachi” (Proc. of the Int. and Young Researchers Conf. on Scientific Services on the Internet: Supercomputer Centers and Problems) (Mosk. Gos. Univ., Moscow, 2010), pp. 299–302 [in Russian].

    Google Scholar 

  6. A. V. Ronzhin and V. N. Surikov, “On the Mathematical Problems of Using High-Performance Computing in Random Search,” in Materialy mezhdunarodnoi nauchno-tekhnicheskoi konferentsii “Superkomp’yuternye tekhnologii: razrabotka, programmirovanie, primenenie” (Proc. of the Int. Conf. on Supercomputer Technologies: Development, Programming, and Application) (Yuzhnyi federal’nyi un-t, Rostov-on-Don, 2010), Vol. 2, pp. 239–243 [in Russian].

    Google Scholar 

  7. M. G. Konovalov, Yu. E. Malashenko, and I. A. Nazarova, “Job Control in Heterogeneous Computing Systems,” J. Comput. Syst. Sci. Int. 50, 220–237 (2011).

    Article  MathSciNet  Google Scholar 

  8. M. Pinedo, Scheduling: Theory, Algorithms, and Systems, 3rd ed. (Springer, Heidelberg, 2002).

    MATH  Google Scholar 

  9. V. S. Tanaev, V. S. Gordon, and Ya. M. Shafranskii, Scheduling Theory. Single-Stage Systems (Nauka, Moscow, 1984; Kluwer, Dordrecht, 1994).

    Google Scholar 

  10. J. Nino-Mora, “Stochastic Scheduling,” in Encyclopedia of Optimization, Ed. by C. A. Floudas and P. M. Pardalos (Kluwer, Dordrecht, 2001), Vol. 5, pp. 367–372.

    Google Scholar 

  11. Handbook of Scheduling: Algorithms, Models, and Performance Analysis, Ed. by J. Y.-T Leung (Chapman & Hall/CRC, New York, 2004).

    MATH  Google Scholar 

  12. M. H. Rothkopf, “Scheduling with Random Service Times,” Man. Sci., No. 12, 707–713 (1966).

  13. R. Conway, W. Maxwell, and L. Miller, Theory of Scheduling, Addison-Wesley, Reading, Mass., 1967; Nauka, Mocow, 1975).

    MATH  Google Scholar 

  14. H. M. Soroush and L. D. Fredendall, “The Stochastic Single Machine Scheduling Problem with Earliness and Tardiness Costs,” European J. Oper. Res. 77, 287–302 (1994).

    Article  MATH  Google Scholar 

  15. V. Portougal and D. Trietsch, “Setting due Dates in a Stochastic Single Machine Environment,” Comput. Oper. Res. 33, 1681–1694 (2006).

    Article  MATH  Google Scholar 

  16. K. R. Baker and D. Trietsch, “Safe Scheduling: Setting due Dates in Single-Machine Problems,” European J. Oper. Res. 196, 69–77 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  17. X. Cai and X. Zhou, “Stochastic Scheduling with Asymmetric Earliness and Tardiness Penalties Under Random Machine Breakdowns,” J. Probability in the Engineering and Informational Sciences archive 20(Iss. 4), 635–654 (2006).

    MathSciNet  MATH  Google Scholar 

  18. W. Jang and C. M. Klein, “Minimizing the Expected Number of Tardy Jobs when Processing Times are Normally Distributed,” Oper. Res. Lett. 30, 100–106 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  19. W. Jang, C. V. Klein, and D. Seo, “Single Machine Stochastic Scheduling to Minimize the Expected Number of Tardy Jobs Using Mathematical Programming Models,” J. Comput. Industr. Eng. 48(2), 153–161 (2005).

    Article  Google Scholar 

  20. X. Cai, L. Wang, and X. Zhou, “Single-Machine Scheduling to Stochastically Minimize Maximum Lateness,” J. Scheduling 10(3), 293–301 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  21. D. Ronconi and W. Powell, “Minimizing Total Tardiness in a Stochastic Single Machine Scheduling Problem Using Approximate Dynamic Programming,” J. Scheduling 13(6), 597–607 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  22. X. Cai and X. Zhou, “Stochastic Scheduling with Earliness and Tardiness Penalties,” in Handbook of Scheduling: Algorithm, Models, and Performance Analysis, Ed. by J. Y.-T Leung (Chapman & Hall/CRC, New York, 2004).

    Google Scholar 

  23. K. D. Glazebrook, “Scheduling Tasks with Exponential Service Times on Parallel Processors,” J. Appl. Probability 16, 685–689 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  24. R. R. Weber, “Scheduling Jobs with Stochastic Processing Requirements on Parallel Machines to Minimize Makespan or Flowtime,” J. Appl. Probability 19, 167–182 (1982).

    Article  MATH  Google Scholar 

  25. R. R. Weber, P. Varaiya, and J. Walrand, “Scheduling Jobs with Stochastically Ordered Processing Times on Parallel Machines to Minimize Expected Flowtime,” J. Appl. Probability 23, 841–847 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  26. C. Jagtenberg, U. Schwiegelshohn, and M. Uetz, “Lower Bounds for Smith’s Rule in Stochastic Machine Scheduling,” Lect. Notes Comput. Sci. 6534, 142–153 (2011).

    Article  Google Scholar 

  27. G. Weiss, “Approximation Results in Parallel Machines Stochastic Scheduling,” Ann. Oper. Res. 26(1), 195–242 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  28. J. Bruno, P. Downey, and G. N. Frederickson, “Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan,” J. ACM 28, 100–113 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  29. A. K. Agrawala, E. G. Coffman, M. R. Garey, et al., “A Stochastic Optimization Algorithm Minimizing Expected Flow Times on Uniform Processors,” IEEE Trans. Comput. 33, 351–356 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Righter, “Job Scheduling to Minimize Expected Weighted Flowtime on Uniform Processors,” Syst. Control Lett. 10, 211–216 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  31. E. G. Coffman, L. Flatto, M. R. Garey, et al., “Minimizing Expected Makespans on Uniform Processor Systems,” Advances Appl. Probability 19, 177–201 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  32. N. Megow, M. Uetz, and T. Vredeveld, “Models and Algorithms for Stochastic Online Scheduling,” Math. Oper. Res. 31(3), 513–525 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  33. T. Vredeveld, “Stochastic Online Scheduling,” Technical report no. RM/09/052 (Maastricht Univ., Maastricht, 2009).

    Google Scholar 

  34. M. Pinedo, “Offline Deterministic Scheduling, Stochastic Scheduling, and Online Deterministic Scheduling: A Comparative Overview,” Handbook of Scheduling: Algorithm, Models, and Performance Analysis, Ed. by J. Y.-T Leung (Chapman & Hall/CRC, New York, 2004).

    Google Scholar 

  35. P. E. Golosov, “Techniques for the Distribution of Typical Jobs with Random Processing Time and a Decreasing Function of the Solution Utility Loss in a Distributed Heterogeneous Computer System,” in Nauchnyi servis v seti Internet: masshtabiruemost’, parallel’nost’, effektivnost’: Tr. Vserossiiskoi superkomp’yuternoi konferentsii (Proc. of the All-Russia Supercomputer Conf. on the Scientific Services on the Internet: Scalability, Parallelism, and Efficiency) (Mosk. Gos. Univ., Moscow, 2009), pp. 114–116 [in Russian].

    Google Scholar 

  36. P. E. Golosov, Extended Abstract of Candidate’s Dissertation in Technical Sciences (Mosk. gos. in-t elektroniki i matematiki, Moscow, 2010).

  37. H. A. David, Order statistics (Wiley, New York, 1970; Nauka, Moscow, 1979).

    MATH  Google Scholar 

  38. P. S. Golosov, M. V. Kozlov, Yu. E. Malashenko, et al., A Model of the Control System for a Specialized Computer System (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2010) [in Russian].

    Google Scholar 

  39. M. V. Kozlov, Yu. E. Malashenko, I. A. Nazarova, et al., Analysis of a Computer System Control Modes under Uncertainty (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2011) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © P.E. Golosov, M.V. Kozlov, Yu.E. Malashenko, I.A. Nazarova, A.F. Ronzhin, 2012, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2012, No. 1, pp. 50–66.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Golosov, P.E., Kozlov, M.V., Malashenko, Y.E. et al. Analysis of computer job control under uncertainty. J. Comput. Syst. Sci. Int. 51, 49–64 (2012). https://doi.org/10.1134/S1064230711060062

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064230711060062

Keywords

Navigation