Skip to main content
SpringerLink
Log in

A Method for Performance Analysis of Earliest-Deadline-First Scheduling Policy

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

This paper introduces an analytical method to approximate the fraction of jobs missing their deadlines in a soft real-time system when the earliest-deadline-first (EDF) scheduling policy is used. In the system, jobs either all have deadlines until the beginning of service (DBS) and are non-preemptive, or have deadlines until the end of service (DES) and are preemptive. In the former case, the system is represented by an M/M/m/EDF+G model, i.e., a multi-sever queue with Poisson arrival, exponential service, and generally distributed relative deadlines. In the latter case, it is represented by an M/M/1/EDF+G model, i.e., a single-server queue with the same specifications as before. EDF is known to be optimal in both of the above cases. The optimality property of EDF scheduling policy is used for the estimation of a key parameter, namely the loss rate when there are n jobs in the system. The estimation is possible by assuming an upper bound and a lower bound for this parameter and then linearly combining these two bounds together. The resulting Markov chains can then be easily solved numerically. Comparing numerical and simulation results, we find that the existing errors are relatively small.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. Baccelli, P. Boyer and G. Hebuterne. Single-server Queues with Impatient Customers. Adv. Appl. Probab., 16:887–905, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. Y. Barrer. Queueing with Impatient Customers and Ordered Service. Oper. Res., 5:650–656, 1957.

    Article  MathSciNet  Google Scholar 

  3. O. J. Boxma and P. R. de Wall. Multiserver Queues with Impatient Customers. In Proceedings of the 14 th International Teletraffic Congress (ITC 14), Antibes, France, 743–756, 1994.

  4. A. Brandt and M. Brandt. On the M(n)/M(n)/s Queue with Impatient Calls. Performance Evaluation, 35:1–18, 1999.

    Article  Google Scholar 

  5. A. Brandt and M. Brandt. Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s + GI system. Queueing Systems, 41:73–94, 2002.

    Google Scholar 

  6. D. J. Daley. General Customer Impatience in Queue GI/G/1. J. Appl. Probab., 2:186–205, 1965.

    Article  MATH  MathSciNet  Google Scholar 

  7. B. Doytchinov, J. Lehoczky, and S. Shreve. Real-Time Queues in Heavy Traffic with Earliest-Deadline-First Queue Discipline. Annals of Appl. Probab., 11:332–379, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  8. L. George, P. Muhlethaler, and N. Rivierre. Optimality and Non-Preemptive Real-Time Scheduling Revisited. Rapport de Recherche RR-2516, INRIA, Le Chesnay Cedex, France, 1995.

  9. L. George, N. Rivierre, and M. Spuri. Preemptive and Non-Preemptive Real-Time Uni-Processor Scheduling. Rapport de Recherche RR-2966, INRIA, Le Chesnay Cedex, France, 1996.

  10. J. Hong, X. Tan, and D. Towsley. A Performance Analysis of Minimum Laxity and Earliest Deadline Scheduling in a Real-Time System. IEEE Transactions on Computers, 38(12):1736–1744, 1989.

    Article  MathSciNet  Google Scholar 

  11. M. Kargahi and A. Movaghar. A Method for Performance Analysis of Earliest-Deadline-First Scheduling Policy. In Proceedings of the 2004 IEEE International Conference on Dependable Systems and Networks (DSN’04), Florence, Italy, 826–834, 2004.

  12. M. Kargahi and A. Movaghar. Non-Preemptive Earliest-Deadline-First Scheduling Policy: A Performance Study. In Proceedings of the 2005 IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS’05), Georgia, Atlanta, USA, 201–210, 2005.

  13. K. Kant. Introduction to Computer System Performance Evaluation, McGraw-Hill, 1992.

  14. L. Kruk, J. P. Lehoczky, S. Shreve, and S. N. Yeung. Earliest-Deadline-First Service in Heavy-Traffic Acyclic Networks. Annals of Appl. Probab., 14(3):1306–1352, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. P. Lehoczky. Real-Time Queueing Theory. In Proceedings of the 17 th IEEE Real-Time Systems Symposium, Washington, D.C., USA, 186–195, 1996.

  16. J. P. Lehoczky. Using Real-Time Queueing Theory to Control Lateness in Real-Time Systems. Performance Evaluation Review, 25(1):158–168, 1997.

    Google Scholar 

  17. A. Leulseged and N. Nissanke. Probabilistic Analysis of Multi-processor Scheduling of Tasks with Uncertain Parameters. In Proceedings of the 9 th International Conference on Real-Time and Embedded Computing Systems and Applications (RTCSA 2003), LNCS 2968:103–122, Springer-Verlag, 2004.

  18. C. L. Liu and J. W. Layland. Scheduling Algorithms for Multiprogramming in a Hard Real-Time Environment. J. Assoc. Compu. Machinary, 20(1):46–61, 1973.

    MATH  MathSciNet  Google Scholar 

  19. A. Movaghar. On Queueing with Customer Impatience until the Beginning of Service. Queueing Systems, 29:337–350, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  20. A. Movaghar. On queueing with customer impatience until the end of service. Stochastic Models, 22:149–173, 2006.

    MathSciNet  MATH  Google Scholar 

  21. N. Nissanke, A. Leulseged, and S. Chillara. Probabilistic Performance Analysis in Multiprocessor Scheduling. J. Computing and Control Engineering, 13(4):171–179, 2002.

    Google Scholar 

  22. C. Palm. Methods for judging the annoyance caused by congestion. Tele, 2:1–20, 1953.

    Google Scholar 

  23. S. S. Panwar, D. Towsley, J. K. Wolf. Optimal Scheduling Policies for a Class of Queues with Customer Deadlines to the Beginning of Service. J. Assoc. Comput., 35(4):832–844, 1988.

    MATH  MathSciNet  Google Scholar 

  24. Q. Qiu, Q. Wu, and M. Pedram. Dynamic Power Management in a Mobile Multimedia System with Guaranteed Quality-of-Service. In Proceedings of the 38th conference on Design automation (DAC’01), 834–839, 2001.

  25. V. Raghunathan, C. Schurgers, S. Park, and M. B. Srivastava. Energy aware wireless microsensor networks. IEEE Signal Processing Magazine, 19(2):40–50, 2002.

    Google Scholar 

  26. D. Towsley and S. S. Panwar. On the Optimality of Minimum Laxity and Earliest Deadline Scheduling for Real-Time Multiprocessors. In Proceedings of IEEE EUROMICRO-90 Workshop on Real-Time, 17–24, 1990.

  27. D. Towsley and S. S. Panwar. Optimality of the Stochastic Earliest Deadline Policy for the G/M/c Queue Serving Customers with Deadlines. In Proceedings of the Second ORSA Telecommunications Conference, 1992.

  28. W. Zhao and J. A. Stankovic. Performance Analysis of FCFS and Improved FCFS Scheduling Algorithms for Dynamic Real-Time Computer Systems. In Proceedings of IEEE Real-Time Systems Symposium, California, USA, 156–165, 1989.

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Sharif University of Technology, Tehran, Iran

    Mehdi Kargahi & Ali Movaghar

Authors
  1. Mehdi Kargahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Movaghar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mehdi Kargahi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kargahi, M., Movaghar, A. A Method for Performance Analysis of Earliest-Deadline-First Scheduling Policy. J Supercomput 37, 197–222 (2006). https://doi.org/10.1007/s11227-006-5944-2

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-006-5944-2

Keywords

Search

Navigation