Utilization bound revisited

Utilization bound is a well-known concept introduced in the seminal paper of Liu and Layland (1973), which provides a simple and practical way to test the schedulability of a real-time task set. The original utilization bound for the fixed-priority scheduler was given as a function of the number of tasks in the periodic task set. In this paper, we define the utilization bound as a function of the information about the task set. By making use of more than just the number of tasks, better utilization bound over the Liu and Layland bound can be achieved. We investigate in particular the bound given a set of periods for which it is still unknown if there is a polynomial algorithm for the exact bound. By investigating the relationships among the periods, we derive algorithms that yield better bounds than the Liu and Layland bound and the harmonic chain bound. Randomly generated task sets are tested against different bound algorithms. We also give a more intuitive proof of the harmonic chain bound and derive a computationally simpler algorithm.

[1]  Mark Klein,et al.  A practitioner's handbook for real-time analysis - guide to rate monotonic analysis for real-time systems , 1993, The Kluwer international series in engineering and computer science.

[2]  Dong-Won Park,et al.  A generalized utilization bound test for fixed-priority real-time scheduling , 1995, Proceedings Second International Workshop on Real-Time Computing Systems and Applications.

[3]  C.-C. J. Han,et al.  A better polynomial-time schedulability test for real-time multiframe tasks , 1998, Proceedings 19th IEEE Real-Time Systems Symposium (Cat. No.98CB36279).

[4]  Kang G. Shin,et al.  A New Performance Measure for Scheduling Independent Real-Time Tasks , 1993, J. Parallel Distributed Comput..

[5]  Sang Hyuk Son,et al.  Assigning Real-Time Tasks to Homogeneous Multiprocessor Systems , 1994 .

[6]  Naijun Zhan,et al.  A Formal Proof of the Rate Monotonic Scheduler , 1999, RTCSA.

[7]  Rami G. Melhem,et al.  An efficient RMS admission control and its application to multiprocessor scheduling , 1998, Proceedings of the First Merged International Parallel Processing Symposium and Symposium on Parallel and Distributed Processing.

[8]  Aloysius K. Mok,et al.  A multiframe model for real-time tasks , 1996, 17th IEEE Real-Time Systems Symposium.

[9]  Alan Burns,et al.  Effective Analysis for Engineering Real-Time Fixed Priority Schedulers , 1995, IEEE Trans. Software Eng..

[10]  James W. Layland,et al.  Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environment , 1989, JACM.

[11]  Ching-Chih Han,et al.  A better polynomial-time schedulability test for real-time fixed-priority scheduling algorithms , 1997, Proceedings Real-Time Systems Symposium.

[12]  Tei-Wei Kuo,et al.  Load adjustment in adaptive real-time systems , 1991, [1991] Proceedings Twelfth Real-Time Systems Symposium.

[13]  Raymond R. Devillers,et al.  Liu and Layland's schedulability test revisited , 2000, Inf. Process. Lett..

[14]  Mikael Sjödin,et al.  Improved response-time analysis calculations , 1998, Proceedings 19th IEEE Real-Time Systems Symposium (Cat. No.98CB36279).

[15]  John P. Lehoczky,et al.  Fixed priority scheduling of periodic task sets with arbitrary deadlines , 1990, [1990] Proceedings 11th Real-Time Systems Symposium.

[16]  Omri Serlin,et al.  Scheduling of time critical processes , 1899, AFIPS '72 (Spring).

[17]  Alan Burns,et al.  Applying new scheduling theory to static priority pre-emptive scheduling , 1993, Softw. Eng. J..

[18]  Sang Hyuk Son,et al.  New Strategies for Assigning Real-Time Tasks to Multiprocessor Systems , 1995, IEEE Trans. Computers.

[19]  Joseph Y.-T. Leung,et al.  On the complexity of fixed-priority scheduling of periodic, real-time tasks , 1982, Perform. Evaluation.

[20]  Tei-Wei Kuo,et al.  Utilization bound re-visited , 1999, Proceedings Sixth International Conference on Real-Time Computing Systems and Applications. RTCSA'99 (Cat. No.PR00306).

[21]  Giorgio C. Buttazzo,et al.  Biasing effects in schedulability measures , 2004, Proceedings. 16th Euromicro Conference on Real-Time Systems, 2004. ECRTS 2004..

[22]  Alan Burns,et al.  Fixed priority pre-emptive scheduling: An historical perspective , 1995, Real-Time Systems.

[23]  Mathai Joseph,et al.  Finding Response Times in a Real-Time System , 1986, Comput. J..