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A bandwidth allocation scheme for compositional real-time systems with periodic resources

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Abstract

Allocation of bandwidth among components is a fundamental problem in compositional real-time systems. State-of-the-art algorithms for bandwidth allocation use either exponential-time or pseudo-polynomial-time techniques for exact allocation, or linear-time, utilization-based techniques which may over-provision bandwidth. In this paper, we propose research into a third possible approach: parametric approximation algorithms for bandwidth allocation in compositional real-time systems. We develop a fully-polynomial-time approximation scheme (FPTAS) for allocating bandwidth for sporadic task systems scheduled by earliest-deadline first (EDF) upon an Explicit-Deadline Periodic (EDP) resource. Our algorithm takes, as parameters, the task system and an accuracy parameter ϵ>0, and returns a bandwidth which is guaranteed to be at most a factor (1+ϵ) more than the optimal minimum bandwidth required to successfully schedule the task system. Furthermore, the algorithm has time complexity that is polynomial in the number of tasks and 1/ϵ.

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Notes

  1. Note the component-level scheduling algorithm may differ from the system-level scheduling algorithm. Furthermore, many compositional frameworks permit components to be composed of sub-components.

  2. We abuse terminology slightly and allow (Π,Θ,Δ) describe both the resource Ω and an interface for C.

  3. Observe this is not a restriction on the number of hierarchical levels for our results. Subcomponents may also be represented by sporadic tasks, and our results will apply without change.

  4. Please note that we are permitting over-capacity periodic resources for the sake of comparison only. Our goal is to show that the value returned by application of Theorem 2 (when such value exists) is bounded by a constant factor from the optimal Θ ∗. Showing that a solution for the relaxed problem (where over-capacity is permitted) is bounded by constant factor from optimal will imply the same for the original problem, where over-capacity periodic resources are disallowed.

  5. Relative error is defined as follows: \(\frac{\varTheta-\varTheta^{*}}{\varTheta^{*}}\). In this case, the exact capacity is Θ ∗ and the estimated capacity Θ is either the sufficient capacity \(\bar{\varTheta}\) or approximate capacity \(\widehat {\varTheta}\).

References

  • Albers K, Slomka F (2004) An event stream driven approximation for the analysis of real-time systems. In: Proceedings of the EuroMicro conference on real-time systems. IEEE Computer Society Press, Catania, pp 187–195

    Chapter  Google Scholar 

  • Albers K, Bodmann F, Slomka F (2008) Advanced hierarchical event-stream model. In: Proceedings of the EuroMicro conference on real-time systems. IEEE Computer Society, Prague, pp 211–220

    Chapter  Google Scholar 

  • Almeida L, Pedreiras P (2004) Scheduling within temporal partitions: response-time analysis and server design. In: EMSOFT ’04: Proceedings of the 4th ACM international conference on embedded software. ACM, New York, pp 95–103. DOI:http://doi.acm.org/10.1145/1017753.1017772

    Chapter  Google Scholar 

  • Baruah S, Howell R, Rosier L (1990) Algorithms and complexity concerning the preemptive scheduling of periodic, real-time tasks on one processor. Real-Time Systems: The International Journal of Time-Critical Computing 2:301–324

    Google Scholar 

  • Baruah S, Mok A, Rosier L (1990) Preemptively scheduling hard-real-time sporadic tasks on one processor. In: Proceedings of the 11th real-time systems symposium. IEEE Computer Society Press, Orlando, pp 182–190

    Chapter  Google Scholar 

  • Baruah S, Howell R, Rosier L (1993) Feasibility problems for recurring tasks on one processor. Theor Comput Sci 118(1):3–20

    Article  MathSciNet  MATH  Google Scholar 

  • Baruah S, Chen D, Gorinsky S, Mok A (1999) Generalized multiframe tasks. Time-Critical Comput Syst 17(1):5–22

    Google Scholar 

  • Bini E, Buttazzo G (2004) Biasing effects in schedulability measures. In: Proceedings of the 16th EuroMicro conference on real-time systems. IEEE Computer Society, Los Alamitos, pp 196–203

    Chapter  Google Scholar 

  • Davis RI, Burns A (2005) Hierarchical fixed priority pre-emptive scheduling. In: Proceedings of the IEEE real-time systems symposium. IEEE Computer Society, Miami, pp 389–398

    Google Scholar 

  • de Alfaro L, Henzinger TA (2001a) Interface automata. In: Proceedings of the ninth annual symposium on foundations of software engineering (FSE). ACM Press, Vienna, pp 109–120

    Google Scholar 

  • de Alfaro L, Henzinger TA (2001b) Interface theories for component-based design. In: EMSOFT ’01: Proceedings of the first international workshop on embedded software. Springer, London, pp 148–165

    Google Scholar 

  • Deng Z, Liu J (1997) Scheduling real-time applications in an open environment. In: Proceedings of the eighteenth real-time systems symposium. IEEE Computer Society Press, San Francisco, pp 308–319

    Chapter  Google Scholar 

  • Easwaran A (2007) Compositional schedulability analysis supporting associativity, optimality, dependency and concurrency. PhD dissertation, University of Pennsylvania, Department of Computer and Information Science

  • Easwaran A, Anand M, Lee I (2007) Compositional analysis framework using EDP resource models. In: Proceedings of the IEEE real-time systems symposium. IEEE Computer Society, Tuscon, pp 129–138

    Google Scholar 

  • Eisenbrand F, RothvoßT (2010) EDF-schedulability of synchronous periodic task systems is coNP-hard. In: Proceedings of the annual ACM-SIAM symposium on discrete algorithms

    Google Scholar 

  • Feng XA, Mok A (2002) A model of hierarchical real-time virtual resources. In: Proceedings of the IEEE real-time systems symposium. IEEE Computer Society, Los Alamitos, pp 26–35

    Google Scholar 

  • Fisher N (2008) Approximation algorithms for compositional real-time systems: Trading bandwidth for speed-of-analysis. In: Proceedings of the workshop on compositional theory and technology for real-time embedded systems. IEEE Computer Society Press, Barcelona

    Google Scholar 

  • Fisher N (2009) An FPTAS for interface selection in the periodic resource model. In: Proceedings of the 17th international conference on real-time and network systems. Paris, France

    Google Scholar 

  • Fisher N, Dewan F (2009) Approximate bandwidth allocation for compositional real-time systems. In: Proceedings of the 21st EuroMicro conference on real-time systems. IEEE Computer Society Press, Dublin

    Google Scholar 

  • Henzinger TA, Matic S (2006) An interface algebra for real-time components. In: RTAS ’06: Proceedings of the 12th IEEE real-time and embedded technology and applications symposium. IEEE Computer Society, Washington, DC, pp 253–266

    Chapter  Google Scholar 

  • Kuo TW, Li CH (1998) A fixed priority driven open environment for real-time applications. In: Proceedings of the IEEE real-time systems symposium. IEEE Computer Society Press, Madrid, pp 256–267

    Google Scholar 

  • Lehoczky J, Sha L, Ding Y (1989) The rate monotonic scheduling algorithm: Exact characterization and average case behavior. In: Proceedings of the real-time systems symposium—1989. IEEE Computer Society Press, Santa Monica, pp 166–171

    Google Scholar 

  • Lipari G, Baruah S (2000) Efficient scheduling of real-time multi-task applications in dynamic systems. In: Proceedings of the real-time technology and applications symposium. IEEE Computer Society Press, Washington, pp 166–175

    Chapter  Google Scholar 

  • Lipari G, Bini E (2003) Resource partitioning among real-time applications. In: Proceedings of the EuroMicro conference on real-time systems. IEEE Computer Society, Porto, pp 151–160

    Chapter  Google Scholar 

  • Lipari G, Carpenter J, Baruah S (2000) A framework for achieving inter-application isolation in multiprogrammed, hard real-time environments. In: Proceedings of the real-time systems symposium. IEEE Computer Society Press, Orlando, pp 217–226

    Google Scholar 

  • Mok AK (1983) Fundamental design problems of distributed systems for the hard-real-time environment. PhD thesis, Laboratory for Computer Science, Massachusetts Institute of Technology. Available as Technical Report No MIT/LCS/TR-297

  • Mok A (1988) Task management techniques for enforcing ED scheduling on a periodic task set. In: Proc. 5th IEEE workshop on real-time software and operating systems. Washington DC, pp 42–46

    Google Scholar 

  • Mok A, Feng X, Chen D (2001) Resource partition for real-time systems. In: 7th IEEE real-time technology and applications symposium (RTAS ’01). IEEE Press, New York, pp 75–84

    Chapter  Google Scholar 

  • Rajkumar R, Juvva K, Molano A, Oikawa S (2001) Resource kernels: a resource-centric approach to real-time and multimedia systems. In: Readings in multimedia computing and networking. Morgan Kaufmann, San Francisco, pp 476–490

    Google Scholar 

  • Regehr J, Stankovic JA (2001) HLS: A framework for composing soft real-time schedulers. In: Proceedings of the 22nd IEEE real-time systems symposium (RTSS 2001). London, UK, pp 3–14

    Chapter  Google Scholar 

  • Saewong S, Rajkumar R, Lehoczky JP, Klein MH (2002) Analysis of hierarchical fixed-priority scheduling. In: Proceedings of the EuroMicro conference on real-time systems. IEEE Computer Society Press, Vienna, pp 173–181

    Google Scholar 

  • Shin I, Lee I (2003) Periodic resource model for compositional real-time guarantees. In: Proceedings of the IEEE real-time systems symposium. IEEE Computer Society, Los Alamitos, pp 2–13

    Google Scholar 

  • Shin I, Lee I (2004) Compositional real-time scheduling framework. In: Proceedings of the IEEE real-time systems symposium. IEEE Computer Society, Los Alamitos, pp 57–67

    Google Scholar 

  • Shin I, Lee I (2008) Compositional real-time scheduling framework with periodic model. ACM Trans Embed Comput Syst 7(3):30:1–30:39

    Article  Google Scholar 

  • Shin I, Easwaran A, Lee I (2008) Hierarchical scheduling framework for virtual clustering of multiprocessors. In: Proceedings of the EuroMicro conference on real-time systems. IEEE Computer Society Press, Prague, pp 181–190

    Chapter  Google Scholar 

  • Thiele L, Chakraborty S, Naedele M (2000) Real-time calculus for scheduling hard real-time systems. In: Proceedings of IEEE international symposium on circuits and systems (ISCAS) Geneva, Switzerland, pp 101–104

    Google Scholar 

  • Thiele L, Wandeler E, Stoimenov N (2006) Real-time interfaces for composing real-time systems. In: Proceedings of the 6th ACM and IEEE international conference on embedded software (EMSOFT), pp 34–43

    Chapter  Google Scholar 

  • Vazirani VV (2001) Approximation algorithms. Springer, Berlin

    Google Scholar 

  • Wandeler E, Thiele L (2005) Real-time interfaces for interface-based design of real-time systems with fixed priority scheduling. In: EMSOFT ’05: Proceedings of the 5th ACM international conference on Embedded software. ACM, New York, pp 80–89. DOI:http://doi.acm.org/10.1145/1086228.1086246

    Chapter  Google Scholar 

  • Wandeler E, Thiele L (2006) Interface-based design of real-time systems with hierarchical scheduling. In: IEEE real time technology and applications symposium, San Jose, CA, pp 243–252

    Google Scholar 

Download references

Acknowledgements

We are sincerely thankful to the reviewers for the detailed comments, corrections, and insightful directions which helped us to improve the quality of the article. This research has been supported in part by a National Science Foundation CAREER Award (CNS-0953585) and a grant from Wayne State University’s Office of Vice President of Research.

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  1. Department of Computer Science, Wayne State University, 5057 Woodward Avenue, Suite 3010, Detroit, MI, USA

    Nathan Fisher & Farhana Dewan

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  1. Nathan Fisher
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  2. Farhana Dewan
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Correspondence to Nathan Fisher.

Additional information

A preliminary version of this work has been published in 21st Euromicro Conference on Real-Time Systems, 2009, pages 87–96 (Fisher and Dewan 2009).

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Fisher, N., Dewan, F. A bandwidth allocation scheme for compositional real-time systems with periodic resources. Real-Time Syst 48, 223–263 (2012). https://doi.org/10.1007/s11241-011-9144-7

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