Abstract
In this paper, we present a simple recursive equation and an iterative procedure to determine the best-case response times of periodic tasks under fixed-priority preemptive scheduling and arbitrary phasings. The approach is of a similar nature as the one used to determine worst-case response times (Joseph and Pandya, 1986) in the sense that where a critical instant is considered to determine the latter, we base our analysis on an optimal instant. Such an optimal instant occurs when all higher priority tasks have a simultaneous release that coincides with the completion of an execution of the task under consideration. The resulting recursive equation closely resembles the one for worst-case response times. The iterative procedure is illustrated by means of a small example. Next, we apply the best-case response times to analyze jitter in distributed multiprocessor systems. To this end, we discuss the effect of the best-case response times on completion jitter, as well as the effect of release jitter on the best-case response times. The newly derived best-case response times generally result in tighter bounds on jitter, in turn leading to tighter worst-case response time bounds.
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REFERENCES
Audsley, N. C., A. Burns, M. F. Richardson, K. Tindell, and A. J. Wellings, “Applying new scheduling theory to static priority pre-emptive scheduling,” Software Eng. J., 8, 284–292, (1993).
Audsley, N. C., A. Burns, M. F. Richardson, and A. J. Wellings, “Hard real-time scheduling: The deadline monotonic approach,” in Proceedings 8th IEEE Workshop on Real-Time Operating Systems and Software, 1991, pp. 133–137.
Bril, R. J., E. F. M. Steffens, and W. F. J. Verhaegh, “Best-case response times of real-time tasks,” in Proceedings Philips Workshop on Scheduling and Resource Management (SCHARM), pp. 19–27, June 2001. http://www. extra.research. philips.com/publ/nl-ms/r-20.914.pdf.
Joseph, M., (ed), Real-Time Systems: Specification, Verification and Analysis, Prentice Hall, 1996.
Joseph, M. and P. Pandya, “Finding response times in a real-time system,” Comput. J., 29, 390–395, (1986).
Kim, T., J. Lee, H. Shin, and N. Chang, “Best case response time analysis for improved schedulability analysis of distributed real-time tasks,” in Proceedings ICDCS Workshop on Distributed Real-Time Systems, 2000, pp. B14–B20.
Kim, T., H. Shin, and N. Chang, “A jitter analysis for improved schedulability of distributed real-time tasks”, J. KISS Comput. Syst. and Theory, 27, 506–517, (2000) (in Korean).
Klein, M. H., T. Ralya, B. Pollak, R. Obenza, and M. González Harbour, A Practitioner's Handbook for Real-Time Analysis: Guide to Rate Monotonic Analysis for Real-Time Systems, Kluwer Academic Publishers, 1993.
Liu, C. L. and J. W. Layland, “Scheduling algorithms for multiprogramming in a real-time environment,” J. ACM, 20, 46–61, (1973).
Palencia Gutiérrez, J. C., J. J. Gutiérrez García, and M. González Harbour, “Best-case analysis for improving the worst-case schedulability test for distributed hard real-time systems,” in Proceedings of the 10th EuroMicro Workshop on Real-Time Systems, 1998, pp. 35–44.
Tindell, K. W., A. Burns, and A. J. Wellings, “An extendible approach for analyzing fixed priority hard real-time tasks,” Real-Time Sys., 6, 133–151, (1994).
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Bril, R.J., Steffens, E.F. & Verhaegh, W.F. Best-Case Response Times and Jitter Analysis of Real-Time Tasks. Journal of Scheduling 7, 133–147 (2004). https://doi.org/10.1023/B:JOSH.0000014069.63823.e7
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DOI: https://doi.org/10.1023/B:JOSH.0000014069.63823.e7