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Automated analysis of real-time scheduling using graph games

Published: 08 April 2013 Publication History

Abstract

In this paper, we introduce the powerful framework of graph games for the analysis of real-time scheduling with firm deadlines. We introduce a novel instance of a partial-observation game that is suitable for this purpose, and prove decidability of all the involved decision problems. We derive a graph game that allows the automated computation of the competitive ratio (along with an optimal witness algorithm for the competitive ratio) and establish an NP-completeness proof for the graph game problem. For a given on-line algorithm, we present polynomial time solution for computing (i) the worst-case utility; (ii) the worst-case utility ratio w.r.t. a clairvoyant off-line algorithm; and (iii) the competitive ratio. A major strength of the proposed approach lies in its flexibility w.r.t. incorporating additional constraints on the adversary and/or the algorithm, including limited maximum or average load, finiteness of periods of overload, etc., which are easily added by means of additional instances of standard objective functions for graph games.

References

[1]
K. Altisen, G. Gößler, and J. Sifakis. Scheduler modeling based on the controller synthesis paradigm. Real-Time Systems, 23(1--2):55--84, 2002.
[2]
H. Aydin, R. Melhem, D. Mossé, and P. Mejıa-Alvarez. Power-aware scheduling for periodic real-time tasks. IEEE Trans. Comput., 53(5):584--600, May 2004.
[3]
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. Real-Time Syst., 4:125--144, May 1992.
[4]
S. Baruah and J. R. Haritsa. Scheduling for overload in real-time systems. IEEE Trans. Comput., 46:1034--1039, September 1997.
[5]
S. Baruah and M. E. Hickey. Competitive on-line scheduling of imprecise computations. IEEE Trans. Comp., 47:1027--1032, 1998.
[6]
A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge Univ. Press, 1998.
[7]
L. Brim, J. Chaloupka, L. Doyen, R. Gentilini, and J-F. Raskin. Faster algorithms for mean-payoff games. FMSD, 38:97--118, 2011.
[8]
K. Chatterjee, L. Doyen, T. A. Henzinger, and J-F. Raskin. Generalized mean-payoff and energy games. In FSTTCS, pages 505--516, 2010.
[9]
V. Devadas, F. Li, and H. Aydin. Competitive analysis of online real-time scheduling algorithms under hard energy constraint. Real-Time Syst., 46(1):88--120, September 2010.
[10]
A. Ehrenfeucht and J. Mycielski. Positional strategies for mean payoff games. Int. J. of Game Theory, 8:109--113, 1979.
[11]
R. M. Karp. A characterization of the minimum cycle mean in a digraph. Discr. Math., 23:309--311, 1978.
[12]
E. Kopczynski. Half-positional determinacy of infinite games. In ICALP (2), pages 336--347, 2006.
[13]
E. Koutsoupias. Scheduling without payments. In SAGT pages 143--153, 2011.
[14]
G. Koren and D. Shasha. D over: An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM J. on Comp., 24:318--339, 1995.
[15]
D. A. Martin. Borel determinacy. Annals of Math., 102:363--371, 1975.
[16]
N. Nisan, T. Roughgarden, E. Tardos, and V. Vazirani. Algorithmic Game Theory. Cambridge Univ. Press, New York, NY, USA, 2007.
[17]
M. A. Palis. Competitive algorithms for fine-grain real-time scheduling. RTSS, pages 129--138, 2004.
[18]
C. H. Papadimitriou. Computational Complexity. Addison-Wesley, 1993.
[19]
R. Rajkumar, C. Lee, J. Lehoczky, and D. Siewiorek. A resource allocation model for qos management. In RTSS, pages 298 --307, 1997.
[20]
L. S. Shapley. Stochastic games. PNAS USA, 39:1095--1100, 1953.
[21]
Y. Velner. The complexity of mean-payoff automaton expression. In ICALP, 2012.
[22]
U. Zwick and M. Paterson. The complexity of mean payoff games on graphs. TCS, 158:343--359, 1996.

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    cover image ACM Conferences
    HSCC '13: Proceedings of the 16th international conference on Hybrid systems: computation and control
    April 2013
    378 pages
    ISBN:9781450315678
    DOI:10.1145/2461328
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    Published: 08 April 2013

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    Author Tags

    1. competitive analysis
    2. game theory
    3. real-time scheduling

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    HSCC '13: Computation and Control
    April 8 - 11, 2013
    Pennsylvania, Philadelphia, USA

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    HSCC '13 Paper Acceptance Rate 40 of 86 submissions, 47%;
    Overall Acceptance Rate 153 of 373 submissions, 41%

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    • (2021)Adapting to the Behavior of Environments with Bounded MemoryElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.346.4346(52-66)Online publication date: 16-Sep-2021
    • (2020)Precedence-Aware Automated Competitive Analysis of Real-Time SchedulingIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2020.301280339:11(3981-3992)Online publication date: Nov-2020
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    • (2018)Automated competitive analysis of real-time scheduling with graph gamesReal-Time Systems10.1007/s11241-017-9293-454:1(166-207)Online publication date: 1-Jan-2018
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    • (2014)A Framework for Automated Competitive Analysis of On-line Scheduling of Firm-Deadline Tasks2014 IEEE Real-Time Systems Symposium10.1109/RTSS.2014.9(118-127)Online publication date: Dec-2014
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