Advertisement

The Journal of Supercomputing

, Volume 37, Issue 2, pp 197–222 | Cite as

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

  • Mehdi Kargahi
  • Ali Movaghar
Article

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.

Keywords

analytical methods approximation methods earliest-deadline-first (EDF) multiprocessor systems performance modeling soft real-time (SRT) systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. Baccelli, P. Boyer and G. Hebuterne. Single-server Queues with Impatient Customers. Adv. Appl. Probab., 16:887–905, 1984.zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    D. Y. Barrer. Queueing with Impatient Customers and Ordered Service. Oper. Res., 5:650–656, 1957.MathSciNetCrossRefGoogle Scholar
  3. 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.Google Scholar
  4. 4.
    A. Brandt and M. Brandt. On the M(n)/M(n)/s Queue with Impatient Calls. Performance Evaluation, 35:1–18, 1999.CrossRefGoogle Scholar
  5. 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. 6.
    D. J. Daley. General Customer Impatience in Queue GI/G/1. J. Appl. Probab., 2:186–205, 1965.zbMATHMathSciNetCrossRefGoogle Scholar
  7. 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.zbMATHMathSciNetCrossRefGoogle Scholar
  8. 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.Google Scholar
  9. 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.Google Scholar
  10. 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.MathSciNetCrossRefGoogle Scholar
  11. 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.Google Scholar
  12. 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.Google Scholar
  13. 13.
    K. Kant. Introduction to Computer System Performance Evaluation, McGraw-Hill, 1992.Google Scholar
  14. 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.zbMATHMathSciNetCrossRefGoogle Scholar
  15. 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.Google Scholar
  16. 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. 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.Google Scholar
  18. 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.zbMATHMathSciNetGoogle Scholar
  19. 19.
    A. Movaghar. On Queueing with Customer Impatience until the Beginning of Service. Queueing Systems, 29:337–350, 1998.zbMATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    A. Movaghar. On queueing with customer impatience until the end of service. Stochastic Models, 22:149–173, 2006.MathSciNetzbMATHGoogle Scholar
  21. 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. 22.
    C. Palm. Methods for judging the annoyance caused by congestion. Tele, 2:1–20, 1953.Google Scholar
  23. 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.zbMATHMathSciNetGoogle Scholar
  24. 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.Google Scholar
  25. 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. 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.Google Scholar
  27. 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.Google Scholar
  28. 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.Google Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Computer EngineeringSharif University of TechnologyTehranIran

Personalised recommendations