Abstract
Liu and Layland discovered the famous utilization bound \(N(2^{ \frac{1} {N} } - 1)\) for fixed-priority scheduling on single-processor systems in the 1970s.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Under the algorithms in [157], a split subtask’s priority is artificially advanced to the highest level on its host processor, which breaks down the RMS priority order and thereby leads to a lower utilization bound.
References
C.L. Liu, J.W. Layland, Scheduling algorithms for multiprogramming in a hard-real-time environment. J. ACM 20(1), 46–61 (1973). doi:10.1145/321738.321743. http://doi.acm.org/10.1145/321738.321743
J. Carpenter, S. Funk, P. Holman, A. Srinivasan, J. Anderson, S. Baruah, A categorization of real-time multiprocessor scheduling problems and algorithms, in Handbook of Scheduling - Algorithms, Models, and Performance Analysis (2004). http://www.crcnetbase.com/doi/abs/10.1201/9780203489802.ch30
B. Andersson, S. Baruah, J. Jonsson, Static-priority scheduling on multiprocessors, in RTSS, 2001
B. Andersson, Global static priority preemptive multiprocessor scheduling with utilization bound 38%, in OPODIS, 2008
B. Andersson, J. Jonsson, The utilization bounds of partitioned and pfair static-priority scheduling on multiprocessors are 50%, in Euromicro Conference on Real-Time Systems (ECRTS), 2003
D. Oh, T.P. Baker, Utilization bounds for n-processor rate monotone scheduling with static processor assignment. Real-Time Syst. 15(2), 183–192. doi:10.1023/A:1008098013753. http://dx.doi.org/10.1023/A:1008098013753 (1998)
J. Anderson, V. Bud, U.C. Devi, An EDF-based scheduling algorithm for multiprocessor soft real-time systems, in ECRTS, 2005
B. Andersson, K. Bletsas, S. Baruah, Scheduling arbitrary-deadline sporadic task systems multiprocessors, in RTSS, 2008
S. Kato, N. Yamasaki, Portioned EDF-based scheduling on multiprocessors, in EMSOFT, 2008
J. Anderson, A. Srinivasan, Mixed pfair/erfair scheduling of asynchronous periodic tasks J. Comput. Syst. Sci. 68(1), 157–204 (2004). doi:10.1016/j.jcss.2003.08.002. http://dx.doi.org/10.1016/j.jcss.2003.08.002
S.K. Baruah, N.K. Cohen, C.G. Plaxton, D.A. Varvel, Proportionate progress: A notion of fairness in resource allocation. Algorithmica 15(6), 600–625 (1996). doi:10.1007/BF01940883. http://dx.doi.org/10.1007/BF01940883
U. Devi, J. Anderson, Tardiness bounds for global edf scheduling on a multiprocessor, in IEEE Real-Time Systems Symposium (RTSS), 2005
K. Lakshmanan, R. Rajkumar, J. Lehoczky, Partitioned fixed-priority preemptive scheduling for multi-core processors, in ECRTS, 2009
B. Andersson, E. Tovar, Multiprocessor scheduling with few preemptions, in RTCSA, 2006
B. Andersson, K. Bletsas, Sporadic multiprocessor scheduling with few preemptions, in Euromicro Conference on Real-Time Systems (ECRTS), 2008
S. Kato, N. Yamasaki, Real-time scheduling with task splitting on multiprocessors, in IEEE Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA), 2007
S. Kato, N. Yamasaki, Y. Ishikawa, Semi-partitioned scheduling of sporadic task systems on multiprocessors, in ECRTS, 2009
S. Kato,N. Yamasaki, Portioned static-priority scheduling on multiprocessors, in IPDPS, 2008
S. Kato, N. Yamasaki, Semi-partitioned fixed-priority scheduling on multiprocessors, in RTAS, 2009
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Guan, N. (2016). Liu and Layland’s Utilization Bound. In: Techniques for Building Timing-Predictable Embedded Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-27198-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-27198-9_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27196-5
Online ISBN: 978-3-319-27198-9
eBook Packages: EngineeringEngineering (R0)