Abstract
We study schedulability problems of timed systems with non-uniformly recurring computation tasks. Assume a set of real time tasks whose best and worst execution times, and deadlines are known. We use timed automata to describe the arrival patterns (and release times) of tasks. From the literature, it is known that the schedulability problem for a large class of such systems is decidable and can be checked efficiently.
In this paper, we provide a summary on what is decidable and what is undecidable in schedulability analysis using timed automata. Our main technical contribution is that the schedulability problem will be undecidable if these three conditions hold: (1) the execution times of tasks are intervals, (2) a task can announce its completion time, and (3) a task can preempt another task. We show that if one of the above three conditions is dropped, the problem will be decidable. Thus our result can be used as an indication in identifying classes of timed systems that can be analysed efficiently.
This work has been partially supported by the Swedish Research Council and the European Research Training Network GAMES.
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References
Abdeddaïm, Y.: Scheduling with Timed Automata. PhD thesis, Verimag (2002)
Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138(1), 3–34 (1995)
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Amnell, T., Fersman, E., Mokrushin, L., Pettersson, P., Yi, W.: Times - a tool for modelling and implementation of embedded systems. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 460–464. Springer, Heidelberg (2002)
Abdeddaïm, Y., Maler, O.: Job-shop scheduling using timed automata. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 478–492. Springer, Heidelberg (2001)
Abdeddaïm, Y., Maler, O.: Preemptive job-shop scheduling using stopwatch automata. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 113–126. Springer, Heidelberg (2002)
Cassez, F., Laroussinie, F.: Model-checking for hybrid systems by quotienting and constraints solving. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 373–388. Springer, Heidelberg (2000)
Corbett, J.: Modeling and analysis of real-time ada tasking programs. In: Proc. IEEE RTSS 1994, pp. 132–141 (1994)
Ericsson, C., Wall, A., Yi, W.: Timed automata as task models for event-driven systems. In: Proceedings of Nordic Workshop on Programming Theory (1998)
Fehnker, A.: Citius, Vilius, Melius - Guiding and Cost-Optimality in Model Checking of Timed and Hybrid Systems. PhD thesis, KU Nijmegen (2002)
Fersman, E., Mokrushin, L., Pettersson, P., Yi, W.: Schedulability analysis using two clocks. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 224–239. Springer, Heidelberg (2003)
Fersman, E., Pettersson, P., Yi, W.: Timed automata with asynchronous processes: Schedulability and decidability. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 67–82. Springer, Heidelberg (2002)
Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: HYTECH: A model checker for hybrid systems. International Journal on Software Tools for Technology Transfer 1(1-2), 123–133 (1997)
Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? Journal of Computer and System Sciences 57, 94–124 (1998)
Hune, T., Larsen, K.G., Pettersson, P.: Guided Synthesis of Control Programs using Uppaal. Nordic Journal of Computing 8(1), 43–64 (2001)
Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a Nutshell. Int. Journal on Software Tools for Technology Transfer 1(1-2), 134–152 (1997)
McManis, J., Varaiya, P.: Suspension automata: A decidable class of hybrid automata. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 105–117. Springer, Heidelberg (1994)
Waszniowski, L., Hanzálek, Z.: Analysis of real time operating system based applications. In: Larsen, K.G., Niebert, P. (eds.) FORMATS 2003. LNCS, vol. 2791, Springer, Heidelberg (2004)
Yovine, S.: Kronos: A verification tool for real-time systems. International Journal on Software Tools for Technology Transfer 1(1-2), 110–122 (1997)
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Krčál, P., Yi, W. (2004). Decidable and Undecidable Problems in Schedulability Analysis Using Timed Automata. In: Jensen, K., Podelski, A. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2004. Lecture Notes in Computer Science, vol 2988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24730-2_20
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DOI: https://doi.org/10.1007/978-3-540-24730-2_20
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