Processor Utilization Bounds for Real-Time Systems With Precedence Constraints


This paper presents a novel approach to computing tight upper bounds on the processor utilization for general real-time systems where tasks are composed of subtasks and precedence constraints may exist among subtasks of the same task. By careful analysis of preemption effects among tasks, the problem is formulated as a set of linear programming (LP) problems. Observations are made to reduce the number of LP problem instances required to be solved, which greatly improves the computation time of the utilization bounds. Furthermore, additional constraints are allowed to be included under certain circumstances to improve the quality of the bounds.

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  1. 1.

    Audsley, N., A. Burns, M. Richardson, K. Tindell, and A. J. Wellings. Applying New Scheduling Theory to Static Priority Preemptive Scheduling. Software Engineering Journal, vol. 8, no.5, pp. 284–292, 1993.

    Google Scholar 

  2. 2.

    Balarin, F. and A. Sangiovanni-Vincentelli. Schedule Validation for Embedded Reactive Real-Time Systems. Proceedings of Design Automation Conference, pp. 52–57, 1997.

  3. 3.

    Berkelaar, M.

  4. 4.

    Bini, E., G. Buttazzo, and G. Buttazzo. A Hyperbolic Bound for the Rate Monotonic Algorithm. IEEE Proceedings of the Euromicro Conference on Real-Time Systems, June 2001.

  5. 5.

    Burchard, A., J. Liebeherr, Y. Oh, and S. H. Son. New Strategies for Assigning Real-Time Tasks to Multiprocessor Systems. IEEE Transactions on Computers, vol. 44, no.12, pp. 1429–1442, December 1995.

    Google Scholar 

  6. 6.

    Dave, B., G. Lakshminarayana, and N. K. Jha. COSYN: Hardware-Software Co-Synthesis of Embedded Systems. IEEE Transactions on VLSI Systems, vol. 7, March 1999.

  7. 7.

    Dick, R. P. and N. K. Jha. MOGAC: A Multiobjective Genetic Algorithm for the Hardware-Software Co-Synthesis of Distributed Embedded Systems. IEEE Transactions on Computer-Aided Design, vol.17, October, 1998.

  8. 8.

    Dick, R. P., D. L. Rhodes, and W. Wolf. TGFF Task Graphs for Free. Proceedings of the Sixth International Workshop on Hardware/Software Codesign (CODES/CASHE'98), 1998, pp. 97–101.

  9. 9.

    Halang, W. A. and A. D. Stoyenko. Next Generation of Real-Time Operating Systems: Industrial Perspective. Proceedings of the NATO Advanced Study Institute on Real Time Computing, pp. 595–596, 1994.

  10. 10.

    Harbour, M. G., M. H. Klein, and J. P. Lehoczky. Timing Analysis for Fixed-Priority Scheduling of Hard Real-Time Systems. IEEE Transactions on Software Engineering, vol. 20, no.1, pp. 13–28, January 1994.

    Google Scholar 

  11. 11.

    Heath, M. T. Scientific Computing: An Introductory Survey, McGraw-Hill Companies, Inc., 1997.

  12. 12.

    Hu, X., J. G. D'Ambrosio, B. T. Murray, and D. Tang. Codesign of Architectures for Automotive Powertrain Modules. IEEE Micro, pp. 17–25, August 1994.

  13. 13.

    Hu, X. and G. Quan. Fast Performance Prediction for Periodic Task Systems. Proceedings of the Eighth International Workshop on Hardware/Software Codesign (CODES'00), 2000, pp. 72–76.

  14. 14.

    Lehoczky, J., L. Sha, and Y. Ding. The Rate Monotonic Scheduling Algorithm: Exact Characterization and Average Case Behavior. Proceedings of the 1989 IEEE Real-Time System Symposium, December 1989, pp. 166–171.

  15. 15.

    Liu, C. L. and J. W. Layland. Scheduling Algorithms for Multiprogramming in a Hard Real-Time Environment. Journal of the ACM, vol. 20, no.1, pp. 46–61, 1973.

    Google Scholar 

  16. 16.

    Liu, J. W. S. Real-Time Systems, Prentice Hall, NJ, 2000.

    Google Scholar 

  17. 17.

    Park, D., S. Natarajan, A. Kanevsky, and M. J. Kim. A Generalized Utilization Bound Test for Fixed-Priority Real-Time Scheduling. Proceedings of the Second International Workshop on Real-Time Computing Systems and Applications, October 1995, pp. 73–76.

  18. 18.

    Park, D., S. Natarajan, and A. Kanevsky. Fixed-Priority Scheduling of Real-Time Systems Using Utilization Bounds. Journal of Systems Software, vol. 33, pp. 57–63, 1996.

    Google Scholar 

  19. 19.

    Shenoy, G. V. Linear Programming Methods and Applications, John Wiley & Sons, Inc., NY, 1989.

    Google Scholar 

  20. 20.

    Silva-de-Oliveira, R. and J. da-Silva-Fraga. Fixed Priority Scheduling of Tasks with Arbitrary Precedence Constraints in Distributed Hard Real-Time Systems. Journal of Systems Architecture, vol. 46, no.11, pp. 991–1004, September 2000.

    Google Scholar 

  21. 21.

    T.-Y. Yen and W. Wolf. Performance Estimation for Real-Time Distributed Embedded Systems. IEEE Transactions on Parallel and Distributed Systems, vol. 9, no.11, pp. 1125–1136, November 1998.

    Google Scholar 

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Liu, H.(., Hu, X.S. Processor Utilization Bounds for Real-Time Systems With Precedence Constraints. Design Automation for Embedded Systems 7, 89–113 (2002).

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  • Precedence
  • real-time
  • utilization bound