Abstract
We use competitive analysis to study how to best use redundancy to achieve fault-tolerance in online real-time scheduling. We show that the optimal way to make use of spatial redundancy depends on a complex interaction of the benefits, execution times, release times, and latest start times of the jobs. We give a randomized online algorithm whose competitive ratio is \(O(\log \Phi log\Delta \tfrac{{log^2 n\log m}}{{\log \log m}})\) for transient faults. Here n is the number of jobs present in the system at any one time, m is the number of processors, Φ is the ratio of maximum value density of a job to the minimum value density of a job, and Δ the ratio of the longest possible execution time to the shortest possible execution time. We show that this bound is close to optimal by giving an \(\Omega (log\Delta \Phi (\tfrac{{logm}}{{loglogmloglog(m\Delta \Phi )}})^2 )\) lower bound on the competitive ratio of any randomized algorithm. In the case of permanent faults, there is a randomized online algorithm that has a competitive ratio of \(O(\log \Phi log\Delta \tfrac{{\log m}}{{\log \log m}})\). We also show a lower bound of \(\Omega (log\Delta \Phi \tfrac{{logm}}{{loglog(m\Delta \Phi )}})\) on the competitive ratio for interval scheduling with permanent faults.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. Bar-Noy, R. Canetti, S. Kutten, Y. Mansour, and B. Schieber, “Bandwidth Allocation with Preemption”, STOC, 1995.
S. Baxuah, J. Harita, and N. Sharma, “On-line scheduling to maximize task completions”, IEEE Real-time Systems Symposium, 1994.
S. Baruah, G. Koren, D. Mao, B. Mishra, A. Raghunathan, L. Rosier, D. Shasha, and F. Wang, “On the competitiveness of on-line real-time task scheduling”, Journal of Real-Time Systems, 4, 124–144, 1992.
S. Baruah, G. Koren, B. Mishra, A. Raghunathan, L. Rosier, and D. Shasha, “On-line scheduling in the presence of overload”, IEEE FOGS, 101–110, 1991.
U. Faigle and W. Nawijn, “Note on scheduling intervals online”, Discrete Applied Math., 58, 13–17, 1995.
B. Kalyanasundaram, and K. Pruhs, “Fault-tolerant scheduling”, STOC, 115–124, 1994.
B. Kalyanasundaram and K. Pruhs “Speed is as powerful as clairvoyance”, FOGS, 1995.
B. Kalyanasundaram and K. Pruhs “eal-time scheduling with fault-tolerance”, Technical report, Computer Science Dept. University of Pittsburgh.
G. Koren, and D. Shasha, “Dover:An optimal on-line scheduling algorithm for overloaded real-time system”, IEEE Real-time Systems Symposium, 290–299, 1992.
G. Koren and D. Shasha, “MOCA: A multiprocessor on-line competitive algorithm for real-time systems scheduling”, Theoretical Computer Science, 128, 75–97, 1994.
R. Lipton, and A. Tomkins, “Online interval scheduling”, SODA, 302–311, 1994.
J. Vytopil, Formal techniques in real-time and fault-tolerant systems, Kluwer Academic Publishers, 1993.
G. Woeginger, “On-line scheduling of jobs with fixed start and end time”, Theoretical Computer Science, 130, 5–16, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kalyanasundaram, B., Pruhs, K. (1997). Fault-tolerant real-time scheduling. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_23
Download citation
DOI: https://doi.org/10.1007/3-540-63397-9_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63397-6
Online ISBN: 978-3-540-69536-3
eBook Packages: Springer Book Archive