Schedulability analysis of fixed-priority systems using timed automata

In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it i...

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Veröffentlicht in:	Theoretical computer science Jg. 354; H. 2; S. 301 - 317
Hauptverfasser:	Fersman, Elena, Mokrushin, Leonid, Pettersson, Paul, Yi, Wang
Format:	Journal Article Tagungsbericht
Sprache:	Englisch
Veröffentlicht:	Amsterdam Elsevier B.V 2006 Elsevier
Schlagworte:	Algorithmics. Computability. Computer arithmetics Applied sciences Automata. Abstract machines. Turing machines Computer science; control theory; systems Computer systems performance. Reliability Exact sciences and technology Modelling and verification Real time systems Schedulability analysis Software Theoretical computing Timed automata Real time systems Schedulability analysis Modelling and verification Timed automata Tool Automaton Computer theory Priority Scheduling Verification Modeling Timed system Real time system Reachability Arrival time Subtraction Response time Periodic system Execution time
ISSN:	0304-3975, 1879-2294, 1879-2294
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Abstract	In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it is shown that the general schedulability checking problem for such models is a reachability problem for a decidable class of timed automata extended with subtraction. Unfortunately, the number of clocks needed in the analysis is proportional to the maximal number of schedulable task instances associated with a model, which is in many cases huge. In this paper, we show that for fixed-priority scheduling strategy, the schedulability checking problem can be solved using standard timed automata with two extra clocks in addition to the clocks used in the original model to describe task arrival times. The analysis can be done in a similar manner to response time analysis in classic Rate-Monotonic Analysis (RMA). The result is further extended to systems with data-dependent control, in which the release time of a task may depend on the time-point at which other tasks finish their execution. For the case when the execution times of tasks are constants, we show that the schedulability problem can be solved using n + 1 extra clocks, where n is the number of tasks. The presented analysis techniques have been implemented in the Times tool. For systems with only periodic tasks, the performance of the tool is comparable with tools implementing the classic RMA technique based on equation-solving, without suffering from the exponential explosion in the number of tasks.
AbstractList	In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it is shown that the general schedulability checking problem for such models is a reachability problem for a decidable class of timed automata extended with subtraction. Unfortunately, the number of clocks needed in the analysis is proportional to the maximal number of schedulable task instances associated with a model, which is in many cases huge. In this paper, we show that for fixed-priority scheduling strategy, the schedulability checking problem can be solved using standard timed automata with two extra clocks in addition to the clocks used in the original model to describe task arrival times. The analysis can be done in a similar manner to response time analysis in classic Rate-Monotonic Analysis (RMA). The result is further extended to systems with data-dependent control, in which the release time of a task may depend on the time-point at which other tasks finish their execution. For the case when the execution times of tasks are constants, we show that the schedulability problem can be solved using n+1 extra clocks, where n is the number of tasks. The presented analysis techniques have been implemented in the Times tool. For systems with only periodic tasks, the performance of the tool is comparable with tools implementing the classic RMA technique based on equation-solving, without suffering from the exponential explosion in the number of tasks. In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it is shown that the general schedulability checking problem for such models is a reachability problem for a decidable class of timed automata extended with subtraction. Unfortunately, the number of clocks needed in the analysis is proportional to the maximal number of schedulable task instances associated with a model, which is in many cases huge. In this paper, we show that for fixed-priority scheduling strategy, the schedulability checking problem can be solved using standard timed automata with two extra clocks in addition to the clocks used in the original model to describe task arrival times. The analysis can be done in a similar manner to response time analysis in classic Rate-Monotonic Analysis (RMA). The result is further extended to systems with data-dependent control, in which the release time of a task may depend on the time-point at which other tasks finish their execution. For the case when the execution times of tasks are constants, we show that the schedulability problem can be solved using n+1n+1 extra clocks, where nn is the number of tasks. The presented analysis techniques have been implemented in the Times tool. For systems with only periodic tasks, the performance of the tool is comparable with tools implementing the classic RMA technique based on equation-solving, without suffering from the exponential explosion in the number of tasks. In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it is shown that the general schedulability checking problem for such models is a reachability problem for a decidable class of timed automata extended with subtraction. Unfortunately, the number of clocks needed in the analysis is proportional to the maximal number of schedulable task instances associated with a model, which is in many cases huge. In this paper, we show that for fixed-priority scheduling strategy, the schedulability checking problem can be solved using standard timed automata with two extra clocks in addition to the clocks used in the original model to describe task arrival times. The analysis can be done in a similar manner to response time analysis in classic Rate-Monotonic Analysis (RMA). The result is further extended to systems with data-dependent control, in which the release time of a task may depend on the time-point at which other tasks finish their execution. For the case when the execution times of tasks are constants, we show that the schedulability problem can be solved using n + 1 extra clocks, where n is the number of tasks. The presented analysis techniques have been implemented in the Times tool. For systems with only periodic tasks, the performance of the tool is comparable with tools implementing the classic RMA technique based on equation-solving, without suffering from the exponential explosion in the number of tasks.
Author	Mokrushin, Leonid Pettersson, Paul Fersman, Elena Yi, Wang
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Keywords	Real time systems Schedulability analysis Modelling and verification Timed automata Tool Automaton Computer theory Priority Scheduling Verification Modeling Timed system Real time system Reachability Arrival time Subtraction Response time Periodic system Execution time
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Snippet	In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax...
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SubjectTerms	Algorithmics. Computability. Computer arithmetics Applied sciences Automata. Abstract machines. Turing machines Computer science; control theory; systems Computer systems performance. Reliability Exact sciences and technology Modelling and verification Real time systems Schedulability analysis Software Theoretical computing Timed automata
Title	Schedulability analysis of fixed-priority systems using timed automata
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