Task automata: Schedulability, decidability and undecidability

We present a model, task automata, for real time systems with non-uniformly recurring computation tasks. It is an extended version of timed automata with asynchronous processes that are computation tasks generated (or triggered) by timed events. Compared with classical task models for real time syst...

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Vydáno v:	Information and computation Ročník 205; číslo 8; s. 1149 - 1172
Hlavní autoři:	Fersman, Elena, Krcal, Pavel, Pettersson, Paul, Yi, Wang
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	San Diego, CA Elsevier Inc 2007 Elsevier
Témata:	Algebraic topology Applied sciences Computer science Computer science; control theory; systems Computer systems performance. Reliability Datavetenskap Exact sciences and technology Information technology Informationsteknik Language theory and syntactical analysis Mathematics Miscellaneous Modeling and verification Real time systems Schedulability analysis Sciences and techniques of general use Software TECHNOLOGY TEKNIKVETENSKAP Theoretical computing Timed automata Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Real time systems Schedulability analysis Modeling and verification Timed automata Asynchronous Bounded automaton Decidability Computer theory Asynchronous automaton Constraint Check Scheduling Real time Real time system Completion Subtraction Influence Strategy Time interval Timing Execution time
ISSN:	0890-5401, 1090-2651, 1090-2651
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Abstract	We present a model, task automata, for real time systems with non-uniformly recurring computation tasks. It is an extended version of timed automata with asynchronous processes that are computation tasks generated (or triggered) by timed events. Compared with classical task models for real time systems, task automata may be used to describe tasks (1) that are generated non-deterministically according to timing constraints in timed automata, (2) that may have interval execution times representing the best case and the worst case execution times, and (3) whose completion times may influence the releases of task instances. We generalize the classical notion of schedulability to task automata. A task automaton is schedulable if there exists a scheduling strategy such that all possible sequences of events generated by the automaton are schedulable in the sense that all associated tasks can be computed within their deadlines. Our first technical result is that the schedulability for a given scheduling strategy can be checked algorithmically for the class of task automata when the best case and the worst case execution times of tasks are equal. The proof is based on a decidable class of suspension automata: timed automata with bounded subtraction in which clocks may be updated by subtractions within a bounded zone. We shall also study the borderline between decidable and undecidable cases. Our second technical result shows that the schedulability checking problem will be undecidable if the following three conditions hold: (1) the execution times of tasks are intervals, (2) the precise finishing time of a task instance may influence new task releases, and (3) a task is allowed to preempt another running task.
AbstractList	We present a model, task automata , for real time systems with non-uniformly recurring computation tasks. It is an extended version of timed automata with asynchronous processes that are computation tasks generated (or triggered) by timed events. Compared with classical task models for real time systems, task automata may be used to describe tasks (1) that are generated non-deterministically according to timing constraints in timed automata, (2) that may have interval execution times representing the best case and the worst case execution times, and (3) whose completion times may influence the releases of task instances. We generalize the classical notion of schedulability to task automata. A task automaton is schedulable if there exists a scheduling strategy such that all possible sequences of events generated by the automaton are schedulable in the sense that all associated tasks can be computed within their deadlines. Our first technical result is that the schedulability for a given scheduling strategy can be checked algorithmically for the class of task automata when the best case and the worst case execution times of tasks are equal. The proof is based on a decidable class of suspension automata: timed automata with bounded subtraction in which clocks may be updated by subtractions within a bounded zone. We shall also study the borderline between decidable and undecidable cases. Our second technical result shows that the schedulability checking problem will be undecidable if the following three conditions hold: (1) the execution times of tasks are intervals, (2) the precise finishing time of a task instance may influence new task releases, and (3) a task is allowed to preempt another running task. We present a model, task automata, for real time systems with non-uniformly recurring computation tasks. It is an extended version of timed automata with asynchronous processes that are computation tasks generated (or triggered) by timed events. Compared with classical task models for real time systems, task automata may be used to describe tasks (1) that are generated non-deterministically according to timing constraints in timed automata, (2) that may have interval execution times representing the best case and the worst case execution times, and (3) whose completion times may influence the releases of task instances. We generalize the classical notion of schedulability to task automata. A task automaton is schedulable if there exists a scheduling strategy such that all possible sequences of events generated by the automaton are schedulable in the sense that all associated tasks can be computed within their deadlines. Our first technical result is that the schedulability for a given scheduling strategy can be checked algorithmically for the class of task automata when the best case and the worst case execution times of tasks are equal. The proof is based on a decidable class of suspension automata: timed automata with bounded subtraction in which clocks may be updated by subtractions within a bounded zone. We shall also study the borderline between decidable and undecidable cases. Our second technical result shows that the schedulability checking problem will be undecidable if the following three conditions hold: (1) the execution times of tasks are intervals, (2) the precise finishing time of a task instance may influence new task releases, and (3) a task is allowed to preempt another running task.
Author	Krcal, Pavel Pettersson, Paul Fersman, Elena Yi, Wang
Author_xml	– sequence: 1 givenname: Elena surname: Fersman fullname: Fersman, Elena email: elena.fersman@ericsson.com – sequence: 2 givenname: Pavel surname: Krcal fullname: Krcal, Pavel email: pavelk@it.uu.se – sequence: 3 givenname: Paul surname: Pettersson fullname: Pettersson, Paul email: paupet@it.uu.se, Paul.Pettersson@mdh.se – sequence: 4 givenname: Wang surname: Yi fullname: Yi, Wang email: yi@it.uu.se
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Keywords	Real time systems Schedulability analysis Modeling and verification Timed automata Asynchronous Bounded automaton Decidability Computer theory Asynchronous automaton Constraint Check Scheduling Real time Real time system Completion Subtraction Influence Strategy Time interval Timing Execution time
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Snippet	We present a model, task automata, for real time systems with non-uniformly recurring computation tasks. It is an extended version of timed automata with... We present a model, task automata , for real time systems with non-uniformly recurring computation tasks. It is an extended version of timed automata with... We present a model, task automata, for real time systems with non-uniformly recurring computation tasks. It is an extended version of timed automata with...
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Title	Task automata: Schedulability, decidability and undecidability
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