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Documents authored by von der Brüggen, Georg

Document
DOI: 10.4230/LIPIcs.ECRTS.2025.17
Theoretical Foundations of Utility Accrual for Real-Time Systems

Authors: Jian-Jia Chen, Junjie Shi, Mario Günzel, Georg von der Brüggen, Kuan-Hsun Chen, and Peter Bella

Published in: LIPIcs, Volume 335, 37th Euromicro Conference on Real-Time Systems (ECRTS 2025)

Abstract
Providing guaranteed quantification of properties of soft real-time systems is important in practice to ensure that a system performs correctly most of the time. We study utility accrual for real-time systems, in which the utility of a real-time job is defined as a time utility function with respect to its response time. Essentially, we answer the fundamental questions: Does the utility accrual of a periodic real-time task in the long run converge to a single value? If yes, to which value? We first show that concrete problem instances exist where evaluating the utility accrual by simulating the scheduling algorithm or conducting scheduling experiments in a long run is erroneous. Afterwards, we show how to construct a Markov chain to model the interactions between the scheduling policy, the probabilistic workload of a periodic real-time task, the service provided by the system to serve the task, and the effect on the utility accrual. For such a Markov chain, we also provide the theoretical fundamentals to determine whether the utility accrual converges in the long run and the derivation of the utility accrual if it converges.
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Jian-Jia Chen, Junjie Shi, Mario Günzel, Georg von der Brüggen, Kuan-Hsun Chen, and Peter Bella. Theoretical Foundations of Utility Accrual for Real-Time Systems. In 37th Euromicro Conference on Real-Time Systems (ECRTS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 335, pp. 17:1-17:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ECRTS.2025.17,
  author =	{Chen, Jian-Jia and Shi, Junjie and G\"{u}nzel, Mario and von der Br\"{u}ggen, Georg and Chen, Kuan-Hsun and Bella, Peter},
  title =	{{Theoretical Foundations of Utility Accrual for Real-Time Systems}},
  booktitle =	{37th Euromicro Conference on Real-Time Systems (ECRTS 2025)},
  pages =	{17:1--17:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-377-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{335},
  editor =	{Mancuso, Renato},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2025.17},
  URN =		{urn:nbn:de:0030-drops-235950},
  doi =		{10.4230/LIPIcs.ECRTS.2025.17},
  annote =	{Keywords: Soft Real-Time Systems, Utility Accrual, Markov Chains, Dismiss Points}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2024.4
Tighter Worst-Case Response Time Bounds for Jitter-Based Self-Suspension Analysis

Authors: Mario Günzel, Georg von der Brüggen, and Jian-Jia Chen

Published in: LIPIcs, Volume 298, 36th Euromicro Conference on Real-Time Systems (ECRTS 2024)

Abstract
Tasks are called self-suspending if they can yield their ready state (specifically, releasing the processor while having highest priority) despite being incomplete, for instance, to offload computation to an external device or when waiting on access rights for shared resources or data. This self-suspending behavior requires special treatment when applying analytical results to compute worst-case response time bounds. One typical treatment is modeling self-suspension as release jitter in a so-called jitter-based analysis. The state of the art, when considering task-level fixed-priority scheduling, individually quantifies the jitter term of each higher-priority task by its worst-case response time minus its worst-case execution time. This work tightens the jitter term by taking the execution behavior of the other higher-priority tasks into account. Our improved jitter-based analysis analytically dominates the previous jitter-based analysis. Moreover, an evaluation for synthetically generated sporadic tasks demonstrates that this jitter term results in tighter worst-case response time bounds for self-suspending tasks. We observe an improvement for up to 55.89 % of the tasksets compared to the previous jitter-based analysis.
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Mario Günzel, Georg von der Brüggen, and Jian-Jia Chen. Tighter Worst-Case Response Time Bounds for Jitter-Based Self-Suspension Analysis. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gunzel_et_al:LIPIcs.ECRTS.2024.4,
  author =	{G\"{u}nzel, Mario and von der Br\"{u}ggen, Georg and Chen, Jian-Jia},
  title =	{{Tighter Worst-Case Response Time Bounds for Jitter-Based Self-Suspension Analysis}},
  booktitle =	{36th Euromicro Conference on Real-Time Systems (ECRTS 2024)},
  pages =	{4:1--4:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-324-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{298},
  editor =	{Pellizzoni, Rodolfo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2024.4},
  URN =		{urn:nbn:de:0030-drops-203074},
  doi =		{10.4230/LIPIcs.ECRTS.2024.4},
  annote =	{Keywords: Worst-Case Response Time, WCRT, Jitter, Self-Suspension, Analysis}
}
Document
DOI: 10.4230/DagRep.13.8.71
Functionally Safe Multi-Core Systems (Dagstuhl Seminar 23341)

Authors: Georg von der Brüggen, Ian Gray, and Catherine Nemitz

Published in: Dagstuhl Reports, Volume 13, Issue 8 (2024)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23341 "Functionally Safe Multi-Core Systems". The seminar took place at a time when there is significant debate and disagreement in both academia and industry on how future safety-critical systems can be developed, certified, and deployed. This process is increasingly complex, as on the one hand, modern systems must provide more services while, on the other hand, analysing such systems becomes significantly more challenging in a multi-core scenario than it was in the single-core era. It is therefore a vital question to determine how the same level of certainty can be provided in the future. The seminar brought together experts from academia and industry for the three major layers involved in safety-critical systems: application, middleware, and platform. They discussed the different perspectives, which problems are deemed specifically important, and potential solutions. One main focus when organizing the seminar was to not only present the different positions but also to provide space for lengthy discussion and disagreement.
Cite as

Georg von der Brüggen, Ian Gray, and Catherine Nemitz. Functionally Safe Multi-Core Systems (Dagstuhl Seminar 23341). In Dagstuhl Reports, Volume 13, Issue 8, pp. 71-90, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{vonderbruggen_et_al:DagRep.13.8.71,
  author =	{von der Br\"{u}ggen, Georg and Gray, Ian and Nemitz, Catherine},
  title =	{{Functionally Safe Multi-Core Systems (Dagstuhl Seminar 23341)}},
  pages =	{71--90},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{8},
  editor =	{von der Br\"{u}ggen, Georg and Gray, Ian and Nemitz, Catherine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.8.71},
  URN =		{urn:nbn:de:0030-drops-198135},
  doi =		{10.4230/DagRep.13.8.71},
  annote =	{Keywords: eda and micro-architectures, middleware, multi-core, safety-critical applications}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2023.10
On the Equivalence of Maximum Reaction Time and Maximum Data Age for Cause-Effect Chains

Authors: Mario Günzel, Harun Teper, Kuan-Hsun Chen, Georg von der Brüggen, and Jian-Jia Chen

Published in: LIPIcs, Volume 262, 35th Euromicro Conference on Real-Time Systems (ECRTS 2023)

Abstract
Real-time systems require a formal guarantee of timing-constraints, not only for individual tasks but also for data-propagation. The timing behavior of data-propagation paths in a given system is typically described by its maximum reaction time and its maximum data age. This paper shows that they are equivalent. To reach this conclusion, partitioned job chains are introduced, which consist of one immediate forward and one immediate backward job chain. Such partitioned job chains are proven to describe maximum reaction time and maximum data age in a universal manner. This universal description does not only show the equivalence of maximum reaction time and maximum data age, but can also be exploited to speed up the computation of such significantly. In particular, the speed-up for synthesized task sets based on automotive benchmarks can be up to 1600. Since only very few non-restrictive assumptions are made, the equivalence of maximum data age and maximum reaction time holds for almost any scheduling mechanism and even for tasks which do not adhere to the typical periodic or sporadic task model. This observation is supported by a simulation of a ROS2 navigation system.
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Mario Günzel, Harun Teper, Kuan-Hsun Chen, Georg von der Brüggen, and Jian-Jia Chen. On the Equivalence of Maximum Reaction Time and Maximum Data Age for Cause-Effect Chains. In 35th Euromicro Conference on Real-Time Systems (ECRTS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 262, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gunzel_et_al:LIPIcs.ECRTS.2023.10,
  author =	{G\"{u}nzel, Mario and Teper, Harun and Chen, Kuan-Hsun and von der Br\"{u}ggen, Georg and Chen, Jian-Jia},
  title =	{{On the Equivalence of Maximum Reaction Time and Maximum Data Age for Cause-Effect Chains}},
  booktitle =	{35th Euromicro Conference on Real-Time Systems (ECRTS 2023)},
  pages =	{10:1--10:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-280-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{262},
  editor =	{Papadopoulos, Alessandro V.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2023.10},
  URN =		{urn:nbn:de:0030-drops-180392},
  doi =		{10.4230/LIPIcs.ECRTS.2023.10},
  annote =	{Keywords: End-to-End, Timing Analysis, Maximum Data Age, Maximum Reaction Time, Cause-Effect Chain, Robot Operating Systems 2 (ROS2)}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2021.10
Hard Real-Time Stationary GANG-Scheduling

Authors: Niklas Ueter, Mario Günzel, Georg von der Brüggen, and Jian-Jia Chen

Published in: LIPIcs, Volume 196, 33rd Euromicro Conference on Real-Time Systems (ECRTS 2021)

Abstract
The scheduling of parallel real-time tasks enables the efficient utilization of modern multiprocessor platforms for systems with real-time constrains. In this situation, the gang task model, in which each parallel sub-job has to be executed simultaneously, has shown significant performance benefits due to reduced context switches and more efficient intra-task synchronization. In this paper, we provide the first schedulability analysis for sporadic constrained-deadline gang task systems and propose a novel stationary gang scheduling algorithm. We show that the schedulability problem of gang task sets can be reduced to the uniprocessor self-suspension schedulability problem. Furthermore, we provide a class of partitioning algorithms to find a stationary gang assignment and show that it bounds the worst-case interference of each task. To demonstrate the effectiveness of our proposed approach, we evaluate it for implicit-deadline systems using randomized task sets under different settings, showing that our approach outperforms the state-of-the-art.
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Niklas Ueter, Mario Günzel, Georg von der Brüggen, and Jian-Jia Chen. Hard Real-Time Stationary GANG-Scheduling. In 33rd Euromicro Conference on Real-Time Systems (ECRTS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 196, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ueter_et_al:LIPIcs.ECRTS.2021.10,
  author =	{Ueter, Niklas and G\"{u}nzel, Mario and von der Br\"{u}ggen, Georg and Chen, Jian-Jia},
  title =	{{Hard Real-Time Stationary GANG-Scheduling}},
  booktitle =	{33rd Euromicro Conference on Real-Time Systems (ECRTS 2021)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-192-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{196},
  editor =	{Brandenburg, Bj\"{o}rn B.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2021.10},
  URN =		{urn:nbn:de:0030-drops-139410},
  doi =		{10.4230/LIPIcs.ECRTS.2021.10},
  annote =	{Keywords: Real-Time Systems, Gang Scheduling, Parallel Computing, Scheduling Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2020.18
Offloading Safety- and Mission-Critical Tasks via Unreliable Connections

Authors: Lea Schönberger, Georg von der Brüggen, Kuan-Hsun Chen, Benjamin Sliwa, Hazem Youssef, Aswin Karthik Ramachandran Venkatapathy, Christian Wietfeld, Michael ten Hompel, and Jian-Jia Chen

Published in: LIPIcs, Volume 165, 32nd Euromicro Conference on Real-Time Systems (ECRTS 2020)

Abstract
For many cyber-physical systems, e.g., IoT systems and autonomous vehicles, offloading workload to auxiliary processing units has become crucial. However, since this approach highly depends on network connectivity and responsiveness, typically only non-critical tasks are offloaded, which have less strict timing requirements than critical tasks. In this work, we provide two protocols allowing to offload critical and non-critical tasks likewise, while providing different service levels for non-critical tasks in the event of an unsuccessful offloading operation, depending on the respective system requirements. We analyze the worst-case timing behavior of the local cyber-physical system and, based on these analyses, we provide a sufficient schedulability test for each of the proposed protocols. In the course of comprehensive experiments, we show that our protocols have reasonable acceptance ratios under the provided schedulability tests. Moreover, we demonstrate that the system behavior under our proposed protocols is strongly dependent on probability of unsuccessful offloading operations, the percentage of critical tasks in the system, and the amount of offloaded workload.
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Lea Schönberger, Georg von der Brüggen, Kuan-Hsun Chen, Benjamin Sliwa, Hazem Youssef, Aswin Karthik Ramachandran Venkatapathy, Christian Wietfeld, Michael ten Hompel, and Jian-Jia Chen. Offloading Safety- and Mission-Critical Tasks via Unreliable Connections. In 32nd Euromicro Conference on Real-Time Systems (ECRTS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 165, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{schonberger_et_al:LIPIcs.ECRTS.2020.18,
  author =	{Sch\"{o}nberger, Lea and von der Br\"{u}ggen, Georg and Chen, Kuan-Hsun and Sliwa, Benjamin and Youssef, Hazem and Ramachandran Venkatapathy, Aswin Karthik and Wietfeld, Christian and ten Hompel, Michael and Chen, Jian-Jia},
  title =	{{Offloading Safety- and Mission-Critical Tasks via Unreliable Connections}},
  booktitle =	{32nd Euromicro Conference on Real-Time Systems (ECRTS 2020)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-152-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{165},
  editor =	{V\"{o}lp, Marcus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2020.18},
  URN =		{urn:nbn:de:0030-drops-123811},
  doi =		{10.4230/LIPIcs.ECRTS.2020.18},
  annote =	{Keywords: internet of things, cyber-physical systems, real-time, mixed-criticality, self-suspension, computation offloading, scheduling, communication}
}
Document
Artifact
DOI: 10.4230/DARTS.5.1.6
Scheduling Self-Suspending Tasks: New and Old Results (Artifact)

Authors: Jian-Jia Chen, Tobias Hahn, Ruben Hoeksma, Nicole Megow, and Georg von der Brüggen

Published in: DARTS, Volume 5, Issue 1, Special Issue of the 31st Euromicro Conference on Real-Time Systems (ECRTS 2019)

Abstract
In computing systems, a job may suspend itself (before it finishes its execution) when it has to wait for certain results from other (usually external) activities. For real-time systems, such self-suspension behavior has been shown to induce performance degradation. Hence, the researchers in the real-time systems community have devoted themselves to the design and analysis of scheduling algorithms that can alleviate the performance penalty due to self-suspension behavior. As self-suspension and delegation of parts of a job to non-bottleneck resources is pretty natural in many applications, researchers in the operations research (OR) community have also explored scheduling algorithms for systems with such suspension behavior, called the master-slave problem in the OR community. This paper first reviews the results for the master-slave problem in the OR literature and explains their impact on several long-standing problems for scheduling self-suspending real-time tasks. For frame-based periodic real-time tasks, in which the periods of all tasks are identical and all jobs related to one frame are released synchronously, we explore different approximation metrics with respect to resource augmentation factors under different scenarios for both uniprocessor and multiprocessor systems, and demonstrate that different approximation metrics can create different levels of difficulty for the approximation. Our experimental results show that such more carefully designed schedules can significantly outperform the state-of-the-art.
Cite as

Jian-Jia Chen, Tobias Hahn, Ruben Hoeksma, Nicole Megow, and Georg von der Brüggen. Scheduling Self-Suspending Tasks: New and Old Results (Artifact). In Special Issue of the 31st Euromicro Conference on Real-Time Systems (ECRTS 2019). Dagstuhl Artifacts Series (DARTS), Volume 5, Issue 1, pp. 6:1-6:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Article{chen_et_al:DARTS.5.1.6,
  author =	{Chen, Jian-Jia and Hahn, Tobias and Hoeksma, Ruben and Megow, Nicole and von der Br\"{u}ggen, Georg},
  title =	{{Scheduling Self-Suspending Tasks: New and Old Results}},
  pages =	{6:1--6:3},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2019},
  volume =	{5},
  number =	{1},
  editor =	{Chen, Jian-Jia and Hahn, Tobias and Hoeksma, Ruben and Megow, Nicole and von der Br\"{u}ggen, Georg},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.5.1.6},
  URN =		{urn:nbn:de:0030-drops-107349},
  doi =		{10.4230/DARTS.5.1.6},
  annote =	{Keywords: Self-suspension, master-slave problem, computational complexity, speedup factors}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2019.16
Scheduling Self-Suspending Tasks: New and Old Results

Authors: Jian-Jia Chen, Tobias Hahn, Ruben Hoeksma, Nicole Megow, and Georg von der Brüggen

Published in: LIPIcs, Volume 133, 31st Euromicro Conference on Real-Time Systems (ECRTS 2019)

Abstract
In computing systems, a job may suspend itself (before it finishes its execution) when it has to wait for certain results from other (usually external) activities. For real-time systems, such self-suspension behavior has been shown to induce performance degradation. Hence, the researchers in the real-time systems community have devoted themselves to the design and analysis of scheduling algorithms that can alleviate the performance penalty due to self-suspension behavior. As self-suspension and delegation of parts of a job to non-bottleneck resources is pretty natural in many applications, researchers in the operations research (OR) community have also explored scheduling algorithms for systems with such suspension behavior, called the master-slave problem in the OR community. This paper first reviews the results for the master-slave problem in the OR literature and explains their impact on several long-standing problems for scheduling self-suspending real-time tasks. For frame-based periodic real-time tasks, in which the periods of all tasks are identical and all jobs related to one frame are released synchronously, we explore different approximation metrics with respect to resource augmentation factors under different scenarios for both uniprocessor and multiprocessor systems, and demonstrate that different approximation metrics can create different levels of difficulty for the approximation. Our experimental results show that such more carefully designed schedules can significantly outperform the state-of-the-art.
Cite as

Jian-Jia Chen, Tobias Hahn, Ruben Hoeksma, Nicole Megow, and Georg von der Brüggen. Scheduling Self-Suspending Tasks: New and Old Results. In 31st Euromicro Conference on Real-Time Systems (ECRTS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 133, pp. 16:1-16:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chen_et_al:LIPIcs.ECRTS.2019.16,
  author =	{Chen, Jian-Jia and Hahn, Tobias and Hoeksma, Ruben and Megow, Nicole and von der Br\"{u}ggen, Georg},
  title =	{{Scheduling Self-Suspending Tasks: New and Old Results}},
  booktitle =	{31st Euromicro Conference on Real-Time Systems (ECRTS 2019)},
  pages =	{16:1--16:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-110-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{133},
  editor =	{Quinton, Sophie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2019.16},
  URN =		{urn:nbn:de:0030-drops-107532},
  doi =		{10.4230/LIPIcs.ECRTS.2019.16},
  annote =	{Keywords: Self-suspension, master-slave problem, computational complexity, speedup factors}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.71
Packing Sporadic Real-Time Tasks on Identical Multiprocessor Systems

Authors: Jian-Jia Chen, Nikhil Bansal, Samarjit Chakraborty, and Georg von der Brüggen

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are statically assigned onto processors while ensuring that all timing constraints are met. The decision version of the problem, which is to check whether the deadline constraints of tasks can be satisfied on a given number of identical processors, has been known NP-complete in the strong sense. Several studies on this problem are based on approximations involving resource augmentation, i.e., speeding up individual processors. This paper studies another type of resource augmentation by allocating additional processors, a topic that has not been explored until recently. We provide polynomial-time algorithms and analysis, in which the approximation factors are dependent upon the input instances. Specifically, the factors are related to the maximum ratio of the period to the relative deadline of a task in the given task set. We also show that these algorithms unfortunately cannot achieve a constant approximation factor for general cases. Furthermore, we prove that the problem does not admit any asymptotic polynomial-time approximation scheme (APTAS) unless P=NP when the task set has constrained deadlines, i.e., the relative deadline of a task is no more than the period of the task.
Cite as

Jian-Jia Chen, Nikhil Bansal, Samarjit Chakraborty, and Georg von der Brüggen. Packing Sporadic Real-Time Tasks on Identical Multiprocessor Systems. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 71:1-71:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chen_et_al:LIPIcs.ISAAC.2018.71,
  author =	{Chen, Jian-Jia and Bansal, Nikhil and Chakraborty, Samarjit and von der Br\"{u}ggen, Georg},
  title =	{{Packing Sporadic Real-Time Tasks on Identical Multiprocessor Systems}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{71:1--71:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.71},
  URN =		{urn:nbn:de:0030-drops-100198},
  doi =		{10.4230/LIPIcs.ISAAC.2018.71},
  annote =	{Keywords: multiprocessor partitioned scheduling, approximation factors}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2018.6
Efficiently Approximating the Probability of Deadline Misses in Real-Time Systems

Authors: Georg von der Brüggen, Nico Piatkowski, Kuan-Hsun Chen, Jian-Jia Chen, and Katharina Morik

Published in: LIPIcs, Volume 106, 30th Euromicro Conference on Real-Time Systems (ECRTS 2018)

Abstract
This paper explores the probability of deadline misses for a set of constrained-deadline sporadic soft real-time tasks on uniprocessor platforms. We explore two directions to evaluate the probability whether a job of the task under analysis can finish its execution at (or before) a testing time point t. One approach is based on analytical upper bounds that can be efficiently computed in polynomial time at the price of precision loss for each testing point, derived from the well-known Hoeffding's inequality and the well-known Bernstein's inequality. Another approach convolutes the probability efficiently over multinomial distributions, exploiting a series of state space reduction techniques, i.e., pruning without any loss of precision, and approximations via unifying equivalent classes with a bounded loss of precision. We demonstrate the effectiveness of our approaches in a series of evaluations. Distinct from the convolution-based methods in the literature, which suffer from the high computation demand and are applicable only to task sets with a few tasks, our approaches can scale reasonably without losing much precision in terms of the derived probability of deadline misses.
Cite as

Georg von der Brüggen, Nico Piatkowski, Kuan-Hsun Chen, Jian-Jia Chen, and Katharina Morik. Efficiently Approximating the Probability of Deadline Misses in Real-Time Systems. In 30th Euromicro Conference on Real-Time Systems (ECRTS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 106, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{vonderbruggen_et_al:LIPIcs.ECRTS.2018.6,
  author =	{von der Br\"{u}ggen, Georg and Piatkowski, Nico and Chen, Kuan-Hsun and Chen, Jian-Jia and Morik, Katharina},
  title =	{{Efficiently Approximating the Probability of Deadline Misses in Real-Time Systems}},
  booktitle =	{30th Euromicro Conference on Real-Time Systems (ECRTS 2018)},
  pages =	{6:1--6:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-075-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{106},
  editor =	{Altmeyer, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2018.6},
  URN =		{urn:nbn:de:0030-drops-89978},
  doi =		{10.4230/LIPIcs.ECRTS.2018.6},
  annote =	{Keywords: deadline miss probability, multinomial-based approach, analytical bound}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2018.8
Push Forward: Global Fixed-Priority Scheduling of Arbitrary-Deadline Sporadic Task Systems

Authors: Jian-Jia Chen, Georg von der Brüggen, and Niklas Ueter

Published in: LIPIcs, Volume 106, 30th Euromicro Conference on Real-Time Systems (ECRTS 2018)

Abstract
The sporadic task model is often used to analyze recurrent execution of tasks in real-time systems. A sporadic task defines an infinite sequence of task instances, also called jobs, that arrive under the minimum inter-arrival time constraint. To ensure the system safety, timeliness has to be guaranteed in addition to functional correctness, i.e., all jobs of all tasks have to be finished before the job deadlines. We focus on analyzing arbitrary-deadline task sets on a homogeneous (identical) multiprocessor system under any given global fixed-priority scheduling approach and provide a series of schedulability tests with different tradeoffs between their time complexity and their accuracy. Under the arbitrary-deadline setting, the relative deadline of a task can be longer than the minimum inter-arrival time of the jobs of the task. We show that global deadline-monotonic (DM) scheduling has a speedup bound of 3-1/M against any optimal scheduling algorithms, where M is the number of identical processors, and prove that this bound is asymptotically tight.
Cite as

Jian-Jia Chen, Georg von der Brüggen, and Niklas Ueter. Push Forward: Global Fixed-Priority Scheduling of Arbitrary-Deadline Sporadic Task Systems. In 30th Euromicro Conference on Real-Time Systems (ECRTS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 106, pp. 8:1-8:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chen_et_al:LIPIcs.ECRTS.2018.8,
  author =	{Chen, Jian-Jia and von der Br\"{u}ggen, Georg and Ueter, Niklas},
  title =	{{Push Forward: Global Fixed-Priority Scheduling of Arbitrary-Deadline Sporadic Task Systems}},
  booktitle =	{30th Euromicro Conference on Real-Time Systems (ECRTS 2018)},
  pages =	{8:1--8:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-075-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{106},
  editor =	{Altmeyer, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2018.8},
  URN =		{urn:nbn:de:0030-drops-89965},
  doi =		{10.4230/LIPIcs.ECRTS.2018.8},
  annote =	{Keywords: global fixed-priority scheduling, schedulability analyses, speedup bounds}
}
Document
DOI: 10.4230/DARTS.4.2.6
Evaluations of Push Forward: Global Fixed-Priority Scheduling of Arbitrary-Deadline Sporadic Task Systems (Artifact)

Authors: Jian-Jia Chen, Georg von der Brüggen, and Niklas Ueter

Published in: DARTS, Volume 4, Issue 2, Special Issue of the 30th Euromicro Conference on Real-Time Systems (ECRTS 2018)

Abstract
This artifact provides the experimental details and implementations of all the facilitated schedulability tests used in the reported acceptance ratio based evaluations as documented in the related paper "Push Forward: Global Fixed-Priority Scheduling of Arbitrary-Deadline Sporadic Task Systems".
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Jian-Jia Chen, Georg von der Brüggen, and Niklas Ueter. Evaluations of Push Forward: Global Fixed-Priority Scheduling of Arbitrary-Deadline Sporadic Task Systems (Artifact). In Special Issue of the 30th Euromicro Conference on Real-Time Systems (ECRTS 2018). Dagstuhl Artifacts Series (DARTS), Volume 4, Issue 2, pp. 6:1-6:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Article{chen_et_al:DARTS.4.2.6,
  author =	{Chen, Jian-Jia and von der Br\"{u}ggen, Georg and Ueter, Niklas},
  title =	{{Evaluations of Push Forward: Global Fixed-Priority Scheduling of Arbitrary-Deadline Sporadic Task Systems (Artifact)}},
  pages =	{6:1--6:5},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2018},
  volume =	{4},
  number =	{2},
  editor =	{Chen, Jian-Jia and von der Br\"{u}ggen, Georg and Ueter, Niklas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.4.2.6},
  URN =		{urn:nbn:de:0030-drops-89746},
  doi =		{10.4230/DARTS.4.2.6},
  annote =	{Keywords: global fixed-priority scheduling, schedulability analyses, speedup bounds}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2017.9
On the Pitfalls of Resource Augmentation Factors and Utilization Bounds in Real-Time Scheduling

Authors: Jian-Jia Chen, Georg von der Brüggen, Wen-Hung Huang, and Robert I. Davis

Published in: LIPIcs, Volume 76, 29th Euromicro Conference on Real-Time Systems (ECRTS 2017)

Abstract
In this paper, we take a careful look at speedup factors, utilization bounds, and capacity augmentation bounds. These three metrics have been widely adopted in real-time scheduling research as the de facto standard theoretical tools for assessing scheduling algorithms and schedulability tests. Despite that, it is not always clear how researchers and designers should interpret or use these metrics. In studying this area, we found a number of surprising results, and related to them, ways in which the metrics may be misinterpreted or misunderstood. In this paper, we provide a perspective on the use of these metrics, guiding researchers on their meaning and interpretation, and helping to avoid pitfalls in their use. Finally, we propose and demonstrate the use of parametric augmentation functions as a means of providing nuanced information that may be more relevant in practical settings.
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Jian-Jia Chen, Georg von der Brüggen, Wen-Hung Huang, and Robert I. Davis. On the Pitfalls of Resource Augmentation Factors and Utilization Bounds in Real-Time Scheduling. In 29th Euromicro Conference on Real-Time Systems (ECRTS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 76, pp. 9:1-9:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.ECRTS.2017.9,
  author =	{Chen, Jian-Jia and von der Br\"{u}ggen, Georg and Huang, Wen-Hung and Davis, Robert I.},
  title =	{{On the Pitfalls of Resource Augmentation Factors and Utilization Bounds in Real-Time Scheduling}},
  booktitle =	{29th Euromicro Conference on Real-Time Systems (ECRTS 2017)},
  pages =	{9:1--9:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-037-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{76},
  editor =	{Bertogna, Marko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2017.9},
  URN =		{urn:nbn:de:0030-drops-71619},
  doi =		{10.4230/LIPIcs.ECRTS.2017.9},
  annote =	{Keywords: Real-time systems, speedup factors, utilization bounds, capacity augmentation bounds}
}
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