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Issue No.05 - May (2009 vol.58)

pp: 634-647

Kanghee Kim , Samsung Electronics Co. Ltd., Suwon

Chang-Gun Lee , Seoul National University, Seoul

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2008.208

ABSTRACT

This paper proposes a safe stochastic analysis for fixed-priority scheduling, which is applicable to a broader spectrum of periodic tasks than the ones analyzable by any of the existing techniques. The proposed analysis can find a safe upper-bound of deadline miss probability for periodic tasks with 1) arbitrary execution time distributions, 2) varying interrelease times with the period as the minimum, and 3) the maximum utilization factor U^{max} that can be greater than 1. One challenge for this is that the release times of tasks are not known a priori because we are not limiting the interrelease times of each task to a constant, i.e., the period. In such a situation, the relative phases of task instances at run time can be arbitrary. Thus, we need to consider all possible phase combinations among jobs to find the worst case deadline miss probability, which is not tractable. To handle this difficulty, we first derive the worst case phase combination for harmonic task sets. Then, we present a safe way to transform a nonharmonic task set to a harmonic task set such that the deadline miss probabilities obtained with the worst case phase combination for the transformed harmonic task set are guaranteed to be worse than those for the original nonharmonic task set with all possible phase combinations. Therefore, the worst case deadline miss probabilities of the transformed harmonic tasks can be used as safe upper-bounds of deadline miss probabilities of the original nonharmonic tasks. Through experiments, we show that the safe upper-bound computed by the proposed analysis is tight enough for practical uses.

INDEX TERMS

Real-time and embedded systems, scheduling, stochastic analysis, worst case analysis, periodic task model.

CITATION

Kanghee Kim, Chang-Gun Lee, "A Safe Stochastic Analysis with Relaxed Limitations on the Periodic Task Model",

*IEEE Transactions on Computers*, vol.58, no. 5, pp. 634-647, May 2009, doi:10.1109/TC.2008.208REFERENCES

- [1] L. Abeni and G. Buttazzo, “Stochastic Analysis of a Reservation Based System,”
Proc. Ninth Int'l Workshop Parallel and Distributed Real-Time Systems (WPDRTS '01), Apr. 2001.- [2] G. Bernat, A. Colin, and S. Petters, “WCET Analysis of Probabilistic Hard Real-Time Systems,”
Proc. 23rd IEEE Real-Time Systems Symp. (RTSS '02), Dec. 2002.- [4] A. Cervin, “Integrated Control and Real-Time Scheduling,” PhD thesis, Lund Inst. of Tech nology, 2003.
- [5] J.L. Díaz, J.M. López, M. García, A.M. Campos, K. Kim, and L. LoBello, “Pessimism in the Stochastic Analysis of Real-Time Systems: Concept and Applications,”
Proc. 25th IEEE Real-Time Systems Symp. (RTSS '04), Dec. 2004.- [6] M.K. Gardner, “Probabilistic Analysis and Scheduling of Critical Soft Real-Time Systems,” PhD thesis, School of Computer Science, Univ. of Illi nois, 1999.
- [7] C.-C. Han and H.-Y. Tyan, “A Better Polynomial-Time Schedulability Test for Real-Time Fixed-Priority Scheduling Algorithms,”
Proc. 18th IEEE Real-Time Systems Symp. (RTSS '97), Dec. 1997.- [9] J.F.C. Kingman, “Inequalities in the Theory of Queues,”
J. Royal Statistical Soc., Series B, vol. 32, pp. 102-110, 1970.- [14] J.P. Lehoczky, L. Sha, and Y. Ding, “The Rate-Monotonic Scheduling Algorithm: Exact Characterization and Average Case Behavior,”
Proc. 10th IEEE Real-Time Systems Symp. (RTSS '89), Dec. 1989.- [15] A. Leulseged and N. Nissanke, “Probabilistic Analysis of Multi-Processor Scheduling of Tasks with Uncertain Parameter,”
Proc. Ninth Int'l Conf. Real-Time and Embedded Computing Systems and Applications (RTCSA '03), Feb. 2003.- [19] M.-Y. Nam, C.-G. Lee, K. Kim, and M. Caccamo, “Time-Parameterized Sensing Task Model for Real-Time Tracking,”
Proc. 26th IEEE Real-Time Systems Symp. (RTSS '05), pp. 245-255, Dec. 2005.- [20] K.M. Obenland,
POSIX in Real-Time, http://www.xtrj.org/collectionposix_rtos.htm , 2001.- [21] A. Terrasa and G. Bernat, “Extracting Temporal Properties from Real-Time Systems by Automatic Tracing Analysis,”
Proc. Ninth Int'l Conf. Real-Time and Embedded Computing Systems and Applications (RTCSA '03), Feb. 2003.- [23] W. Yuan and K. Nahrstedt, “Energy-Efficient Soft Real-Time CPU Scheduling for Mobile Multimedia Systems,”
Proc. 19th ACM Symp. Operating Systems Principles (SOSP '03), pp. 149-163, Oct. 2003. |