When there is a mismatch between the cardinality of a periodic task set and the priority levels supported by the underlying hardware systems, multiple tasks are grouped into one class so as to maintain a specific level of confidence in their accuracy. However, such a transformation is achieved at the expense of the loss of schedulability of the original task set. We further investigate the aforementioned problem and report the following contributions: (i) a novel technique for mapping unlimited priority tasks into a reduced number of classes that do not violate the schedulability of the original task set and (ii) an efficient feasibility test that eliminates insufficient points during the feasibility analysis. The theoretical correctness of both contributions is checked through formal verifications. Moreover, the experimental results reveal the superiority of our work over the existing feasibility tests by reducing the number of scheduling points that are needed otherwise.
If the inline PDF is not rendering correctly, you can download the PDF file here.
Audsley N.C. Burns A. Tindell K. and A. Wellings (1993). Applying new scheduling theory to static priority preemptive scheduling Software Engineering Journal8(5): 284–292.
Audsley N.C. (2001). On priority assignment in fixed priority scheduling Information Processing Letters79(1): 39–44.
Bini E. Buttazzo G.C. and Buttazzo G. (2001). A hyperbolic bound for the rate monotonic algorithm Proceedings of the 13th Euromicro Conference on Real-Time Systems Washington DC USA pp.59–66.
Bini E. and Buttazzo G.C. (2004). Schedulability analysis of periodic fixed priority systems IEEE Transactions on Computers53(11): 1462–1473.
Bini E. Natale M.D. and Buttazzo G. (2008). Sensitivity analysis for fixed-priority real-time systems Real-Time Systems39(1–3): 5–30.
Burns A. and Wellings A.J. (2009). Real-Time Systems and Programming Languages 4th Edn. Addison Wesley Longmain.
Davis R.I. Zabos A. and Burns A. (2008). Efficient exact schedulability tests for fixed priority real-time systems IEEE Transactions on Computers57(9): 1261–1276.
Han C.C. and Tyan H.Y. (1997). A better polynomial-time schedulability test for real-time fixed-priority scheduling algorithms Proceedings of the 18th IEEE Real-Time Systems Symposium (RTSS ’97) Washington DC USA p. 36.
Hong K.S. and Leung J.Y.-T. (1992). On-line scheduling of real-time tasks IEEE Transactions on Computers41(10):1326–1331.
Joseph M. and Pandya P.K. (1986). Finding response times in a real-time system The Computer Journal29(5): 390–395.
Katcher D.I. Arakawa H. and Strosnider J.K. (1993). Engineering and analysis of fixed priority schedulers IEEE Transactions on Software Engineering19(9): 920–934.
Katcher D.I. Sathaye S.S. and Strosnider J.K. (1995). Fixed priority scheduling with limited priority levels IEEE Transactions on Computers44(9): 1140–1144.
Kopetz H. (1997). Real-Time Systems Design Principles for Distributed Embedded Applications Kluwer Academic Publishers Norwell MA.
Laplante P.A. Kartalopoulos S.V. Akay M. El-Hawary M.E. Periera F. M.B. Anderson J. B. Leonardi R. Singh C. Baker R.J. Montrose M. Tewksbury S. Brewer J.E. Newman M.S. and Zobrist G. (2004). Real-Time Systems Design and Analysis 3rd Edition John Wiley and Sons Hoboken NJ.
Lee W. Y. Hong S. J. and Kim J. (2003). On-line scheduling of scalable real-time tasks on multiprocessor systems Journal of Parallel and Distributed Computing63(12): 1315–1324.
Lehoczky J.P. and Sha L. (1986). Performance of real-time bus scheduling algorithms ’86 ACM SIGMETRICS Joint International Conference on Computer Performance Modeling Measurement and Evaluation New York NY USA pp. 44–53.
Lehoczky J.P. Sha L. and Ding Y. (1989). The rate monotonic scheduling algorithm: Exact characterization and average case behavior Proceedings of the IEEE Real-Time Systems Symposium Santa Monica CA USA pp. 166–171.
Leung J.Y.T. and Whitehead J. (1982). On the complexity of fixed-priority scheduling of periodic Performance Evaluation2(4): 237–250.
Liu C.L. and Layland J.W. (1973). Scheduling algorithms for multiprogramming in a hard real-time environment Journal of the ACM20(1): 40–61.
Liu J.W.S. (2000). Real Time Systems Prentice Hall New York NY.
Min-Allah N. Yong-Ji W. Jian-Sheng X. and Jiu-Xiang L. (2007). Revisiting fixed priority techniques in T.W. Kuo et al. (Eds.) Proceedings of Embedded and Ubiquitous Computing Lecture Notes in Computer Science Vol. 4808 Springer Berlin/Heidelberg pp. 134–145.
Min-Allah N. Khan S.U. and Yongji W. (2010). Optimal task execution times for periodic tasks using nonlinear constrained optimization Journal of Supercomputing59(3): 1–19.
Min-Allah N. and Khan S.U. (2011). A hybrid test for faster feasibility analysis of periodic tasks International Journal of Innovative Computing Information and Control7(10): 5689–5698.
Orozco J. Cayssials R. Santos J. and Santos R. (1998). On the minimum number of priority levels required for the rate monotonic scheduling of real-time systems Proceedings of the 10th Euromicro Workshop on Real Time Systems Berlin Germany.
Patan M. (2012). Distributed scheduling of sensor networks for identification of spatio-temporal processes International Journal of Applied Mathematics and Computer Science22(2): 299–311 DOI: 10.2478/v10006-012-0022-9.
Santos J. Gastaminza M. L. Orozco J. Picardi D. and Alimenti O. (1991). Priorities and protocols in real-time LANs Computer Communications14(9): 507–514.
Sha L. and Goodenough J.B. (1988). Real-time scheduling theory and ADA CMU/SEI-88-TR-33 Software Engineering Institute Carnegie-Mellon University Piittsburgh PA.
Sha L. Sprunt B. and Lehoczky J.P. (1989). Aperiodic task scheduling for hard real-time systems Journal of Real-Time Systems1(1): 27–69.
Sheng J. Wang Y. Liu J. Zeng H. and Min-Allah N. (2007). A static priority assignment algorithm with least number of priority levels Journal of Software18(7): 1844–1854.
Sjodin M. and Hansson H. (1998). Improved response-time analysis calculations Proceedings of the 19th IEEE Real-Time Systems Symposium Madrid Spain pp. 399–409.
Tindell K.W. Bums A. and Wellings A.J. (1994). An extendible approach for analyzing fixed priority hard real-time tasks Real-Time Systems Journal6(2):133–151.
Xuelian B. Yuhai Y. and Shiyao J. (2003). Optimal fixed priority assignment with limited priority levels Proceedings of the Advanced Parallel Programming Technologies Xiamen China pp. 194–203.
Xu J. and Parnas D. (1990). Scheduling processes with release times deadlines precedence and exclusion relations IEEE Transactions on Software Engineering16(3): 360–369.