skip to main content
research-article

Nonutilization bounds and feasible regions for arbitrary fixed-priority policies

Published:05 May 2011Publication History
Skip Abstract Section

Abstract

Prior research on schedulability bounds focused primarily on bounding utilization/ as a means to meet deadline constraints. Nontrivial bounds were found for a handful of scheduling policies in which utilization is directly related to the ability of the policy to meet deadlines. Examples include rate-monotonic, deadline-monotonic, and EDF scheduling. For most other scheduling policies, however, utilization is not correlated with schedulability. For example, shortest-job-first can miss deadlines at an arbitrarily low utilization. This raises the question of whether or not some other nonutilization-based metric might be more indicative of schedulability in those cases. This article answers the above question positively by extending the notion of schedulability bounds, in a uniform manner, to arbitrary (fixed) priorities and nonutilization metrics. We present a simple function that generates the schedulability metric to be bounded from the definition of a fixed-priority scheduling policy, and derive a nontrivial schedulability bound on that metric for aperiodic tasks. It is shown that the generated metrics and bounds are valid in that no deadline misses occur when these bounds are not violated. This result allows efficient real-time admission control to be performed in systems with arbitrary fixed-priority scheduling policies. As an example, we illustrate applying schedulability bounds for admission control to shortest-job-first and velocity-monotonic scheduling. While the proposed nonutilization bounds and feasible regions are derived for fixed-priority scheduling policies, the authors are investigating extensions of the results to dynamic-priority scheduling.

References

  1. Abdelzaher, T. and Sharma, V. 2003. A synthetic utilization bound for aperiodic tasks with resource requirements. In Proceedings of the 15th Euromicro Conference on Real-Time Systems.Google ScholarGoogle Scholar
  2. Abdelzaher, T., Sharma, V., and Lu, C. 2004a. A utilization bound for aperiodic tasks and priority driven scheduling. IEEE Trans. Comput. 53, 3, 334--35. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Abdelzaher, T., Thaker, G., and Lardieri, P. 2004b. A feasible region for meeting aperiodic end-to-end deadlines in resource pipelines. In Proceedings of the International Conference on Distributed Computing Systems. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Abdelzaher, T. F. and Lu, C. 2001. Schedulability analysis and utilization bounds for highly scalable real-time services. In Proceedings of the IEEE Real-Time Technology and Applications Symposium. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Andersson, B. and Ekelin, C. 2005. Exact admission-control for integrated aperiodic and periodic tasks. In Proceedings of the Real-Time and Embedded Technology and Applications Symposium. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Audsley, A. N., Burns, A., Richardson, M., and Tindell, K. 1993. Applying new scheduling theory to static priority pre-emptive scheduling. Softw. Eng. J. 8, 284--292.Google ScholarGoogle ScholarCross RefCross Ref
  7. Baruah, S., Mok, A., and Rosier, L. 1990. Algorithms and complexity concerning the preemptively scheduling of periodic, real-time tasks on one processor. Real-Time Syst. J. 2, 301--324. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Bini, E., Buttazzo, G., and Buttazzo, G. 2001. A hyperbolic bound for the rate monotonic algorithm. In Proceedings of the 13th Euromicro Conference on Real-Time Systems. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Caccamo, M. and Sha, L. 2001. Aperiodic servers with resource constraints. In Proceedings of the IEEE Real-Time Systems Symposium. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Chen, X. and Mohapatra, P. 1999. Lifetime behavior and its impact on Web caching. In Proceedings of the IEEE Workshop on Internet Applications. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Cormen, Thomas H. Leiserson, C. E., Rivest, R. L., and Stein, C. 2001. Introduction to Algorithms, 2nd Ed. MIT Press, Cambridge, MA. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Han, C.-C. 1998. A better polynomial-time schedulability test for real-time multiframe tasks. In Proceedings of the 19th IEEE Real-Time Systems Symposium. 104--113. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Jeffay, K. and Stone, D. L. 1993. Accounting for interrupt handling costs in dynamic priority task systems. In Proceedings of the 14th IEEE Real-Time Systems Symposium. 212--221.Google ScholarGoogle Scholar
  14. Kuo, T. W. and Mok, A. K. 1991. Load adjustment in adaptive real-time systems. In Proceedings of the IEEE Real-Time Systems Symposium.Google ScholarGoogle Scholar
  15. Lehoczky, J. P., Sha, L., and Ding, Y. 1989. The rate monotonic scheduling algorithm: Exact characterization and average case behaviour. In Proceedings of the 10th IEEE Real-Time Systems Symposium. 166--171.Google ScholarGoogle Scholar
  16. Liu, C. L. and Layland, J. W. 1973. Scheduling algorithms for multiprogramming in a hard-real-time environment. J. ACM 20, 1, 46--61. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Liu, J. 2000. Real-Time Systems. Prentice Hall PTR, Englewood Cliffs, NJ.Google ScholarGoogle Scholar
  18. Liu, X. and Abdelzaher, T. 2006. On non-utilization bounds for arbitrary fixed priority policies. In Proceedings of the 12th IEEE Real-Time and Embedded Technology and Applications Symposium (RTAS). Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Liu, X., Heo, J., and Sha, L. 2005. Modeling 3-tiered Web applications. In Proceedings of the 13th Annual Meeting of the IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS). Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Lu, C., Blum, B. M., Abdelzaher, T. F., Stankovic, J. A., and He, T. 2002. Rap: A real-time communication architecture for large-scale wireless sensor networks. In Proceedings of the 8th IEEE Real-Time and Embedded Technology and Applications Symposium (RTAS). Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Mok, A. K. and Chen, D. 1997. A multiframe model for real-time tasks. IEEE Trans. Softw. Eng. 23, 10, 635--645. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Pandya, M. and Malek, M. 1998. Minimum achievable utilization for fault-tolerant processing of periodic tasks. IEEE Trans. Comp. 47, 10, 1102--1112. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Park, D.-W., Natarajan, S., and Kanevsky, A. 1996. Fixed-priority scheduling of real-time systems using utilization bounds. J. Syst. Softw. 33, 1, 57--63. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Shih, W. K., Liu, J., and Liu, C. L. 1993. Modified rate-monotonic algorithm for scheduling periodic jobs with deferred deadlines. IEEE Trans. Softw. Eng. 19, 12, 1171--1179. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Strosnider, J. K., Lehoczky, J. P., and Sha, L. 1995. The deferrable server algorithm for enhanced aperiodic responsiveness in hard real-time environments. IEEE Trans. Comp. 44, 1, 73--91. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Thuel, S. R. and Lehoczky, J. P. 1994. Algorithms for scheduling hard aperiodic tasks in fixed-priority systems using slack stealing. In Proceedings of the Real-Time Systems Symposium. 22--33.Google ScholarGoogle Scholar
  27. Wu, J., Liu, J.-C., and Zhao, W. 2005. On schedulability bounds of static priority schedulers. In Proceedings of the Real-Time and Embedded Technology and Applications Symposium. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Nonutilization bounds and feasible regions for arbitrary fixed-priority policies

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in

        Full Access

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader
        About Cookies On This Site

        We use cookies to ensure that we give you the best experience on our website.

        Learn more

        Got it!