Numerically efficient probabilistic guarantees for resource reservations

Manica, Nicola; Palopoli, Luigi; Abeni, Luca

doi:10.1109/etfa.2012.6489566

Cited by 8 publications

(6 citation statements)

References 18 publications

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“…If we set ∆ = 1, we obtain a close approximation of the actual behaviour of the task. If we set ∆ = Q s , we recover the conservative model used in our previous work [28]. As shown in Figure 3, very different trade-offs between computation time and accuracy of the probability result from different choices of ∆.…”

Section: Discussionmentioning

confidence: 99%

An Analytical Solution for Probabilistic Guarantees of Reservation Based Soft Real-Time Systems

Palopoli

Fontanelli

Abeni

et al. 2016

IEEE Trans. Parallel Distrib. Syst.

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We show a methodology for the computation of the probability of deadline miss for a periodic real-time task scheduled by a resource reservation algorithm. We propose a modelling technique for the system that reduces the computation of such a probability to that of the steady state probability of an infinite state Discrete Time Markov Chain with a periodic structure. This structure is exploited to develop an efficient numeric solution where different accuracy/computation time trade-offs can be obtained by operating on the granularity of the model. More importantly we offer a closed form conservative bound for the probability of a deadline miss. Our experiments reveal that the bound remains reasonably close to the experimental probability in one real-time application of practical interest. When this bound is used for the optimisation of the overall Quality of Service for a set of tasks sharing the CPU, it produces a good sub-optimal solution in a small amount of time

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Section: Discussionmentioning

confidence: 99%

An Analytical Solution for Probabilistic Guarantees of Reservation Based Soft Real-Time Systems

Palopoli

Fontanelli

Abeni

et al. 2016

IEEE Trans. Parallel Distrib. Syst.

Self Cite

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“…Much of the recent literature has reached the conclusion that such analysis can be conveniently reduced to the study of the steady state solution of a particular class of discrete‐time Markov chains (DTMC), called quasi‐birth‐death process (QBDP) . This result holds both for fixed‐priority scheduling and for resource reservations, and it allowed us to use some of the most efficient numeric and analytic algorithms as a basis for the implementation of the system analysis. Moreover, the resulting DTMC is a conservative approximation of the system, leading to a pessimistic result in the probabilistic analysis, as proved in the works of Diaz et al and Palopoli et al…”

Section: The Prosit Toolmentioning

confidence: 99%

Section: Algorithms: Analysis and Synthesismentioning

confidence: 99%

“…The analysis is significantly simpler if we adopt a resource reservation scheduler, 3 in which each task executes as if on a dedicated computer and can be analyzed independently of the other tasks (the temporal isolation property). This radical simplification makes the model easy to construct and to analyze and brought different authors to develop efficient numerical methods 20,21 or analytic bounds. 6,22,23 Importantly, in all the articles cited so far, the computation time is assumed to be independent and identically distributed (i.i.d).…”

Section: Related Workmentioning

confidence: 99%

“…This model is easily generalized to the case of aperiodic tasks, making the conservative simplification that the activation of each job is considered only at the beginning of a reservation period. 21 Let c min and c max be the minimum and the maximum computation time. Since the computation time range in the bounded set { c min , … , c max } , the value of v j will be lower bounded by c min .…”

Section: Resource Reservationsmentioning

confidence: 99%

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The PROSIT tool: Toward the optimal design of probabilistic soft real‐time systems

et al. 2018

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Summary In recent years, series of important achievements have paved the way for the introduction of probabilistic analysis in the area of soft real‐time systems design. In this article, we present an extensible design tool, called PROSIT, which facilitates the access to this technology for a potentially large number of researchers and industrial practitioners. The tool enables the probabilistic analysis of the temporal performance of a real‐time task under fixed‐priority and resource reservations scheduling algorithms. For resource reservations, the tool also offers an automatic procedure for the synthesis of scheduling parameters that optimize a quality metric related to the probabilistic behavior of the tasks.

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Efficiently bounding deadline miss probabilities of Markov chain real-time tasks

Friebe,

Marković,

Papadopoulos

et al. 2024

Real-Time Syst

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In real-time systems analysis, probabilistic models, particularly Markov chains, have proven effective for tasks with dependent executions. This paper improves upon an approach utilizing Gaussian emission distributions within a Markov task execution model that analyzes bounds on deadline miss probabilities for tasks in a reservation-based server. Our method distinctly addresses the issue of runtime complexity, prevalent in existing methods, by employing a state merging technique. This not only maintains computational efficiency but also retains the accuracy of the deadline-miss probability estimations to a significant degree. The efficacy of this approach is demonstrated through the timing behavior analysis of a Kalman filter controlling a Furuta pendulum, comparing the derived deadline miss probability bounds against various benchmarks, including real-time Linux server metrics. Our results confirm that the proposed method effectively upper-bounds the actual deadline miss probabilities, showcasing a significant improvement in computational efficiency without significantly sacrificing accuracy.

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Numerically efficient probabilistic guarantees for resource reservations

Cited by 8 publications

References 18 publications

An Analytical Solution for Probabilistic Guarantees of Reservation Based Soft Real-Time Systems

An Analytical Solution for Probabilistic Guarantees of Reservation Based Soft Real-Time Systems

The PROSIT tool: Toward the optimal design of probabilistic soft real‐time systems

Efficiently bounding deadline miss probabilities of Markov chain real-time tasks

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