2023Activity reportProject-TeamKOPERNIC

3.1 Worst case execution time estimation of a program

The temporal study of real-time systems is based on the estimation of the bounds for their temporal parameters and more precisely the WCET of a program executed on a given processor. The main analyses for estimating WCETs are static analyses  36, dynamic analyses  20, also called measurement-based analyses, and finally hybrid analyses that combine the two previous ones  36.

The Kopernic approach for solving the WCET estimation problem is based on (i) the identification of the impact of variability factors on the execution of a program on a processor and (ii) the proposition of compositional rules allowing to integrate the impact of each factor within a WCET estimation. Historically, the real-time community had illustrated the distribution of execution times for programs as heavy-tailed ones as intuitively the large values of execution times of programs are agreed to have a low probability of appearance. For instance Tia et al. are the first underlining this intuition within a paper introducing execution times described by probability distributions within a single core schedulability analysis 35. Since 35, a low probability is associated to large values of execution times of a program executed on a single core processor. It is, finally, in 2000 that the group of Alan Burns, within the thesis of Stewart Edgar  21, formalizes this property as a conjecture indicating that a maximal bound on the execution times of a program may be estimated by the Extreme Value Theory  24. No mathematical definition of what represents this bound for the execution time of a program has been proposed at that time. Two years later, a first attempt to define this bound has been done by Bernat et al.  17, but the proposed definition is extending the static WCET understanding as a combination of execution times of basic blocks of a program. Extremely pessimistic, the definition remains intuitive, without associating a mathematical description. After 2013, several publications from Liliana Cucu-Grosjean's group at Inria Nancy introduce a mathematical definition of a probabilistic worst-case execution time, respectively, probabilistic worst-case response time, as an appropriate formalization for a correct application of the Extreme Value Theory to the real-time problems 2, 1, 5.

We identify the following open research problems related to the first research axis:

1. the generalization of modes analysis to multi-dimensional, each dimension representing a program when several programs cooperate;
2. the proposition of a rules set for building programs that are time predictable for the internal architecture of a given single core and, then, of a multicore processor;
3. modeling the impact of processor features on the energy consumption to better consider both worst case execution time and schedulability analyses considered within the third research axis of this proposal.

3.2 Building measurement-based benchmarks

The real-time community is facing the lack of benchmarks adapted to measurement-based analyses. Existing benchmarks for the estimation of WCET  33, 25, 22 have been used to estimate WCETs mainly for static analyses. They contain very simple programs and are not accompanied by a measurement protocol. They do not take into account functional dependencies between programs, mainly due to shared global variables which, of course, influence their execution times. Furthermore, current benchmarks do not take into account interferences due to the competition for resources, e.g., the memory shared by the different cores in a multicore. On the other hand, measurement-based analyses require execution times measured while executing programs on embedded processors, similar to those used in the embedded systems industry. For example, the mobile phone industry uses multicore based on non predictable cores with complex internal architecture, such as those of the ARM Cortex-A family. In a near future, these multicore will be found in critical embedded systems found in application domains such as avionics, autonomous cars, railway, etc., in which the team is deeply involved. This increases dramatically the complexity of measurement-based analyses compared to analyses performed on general purpose personal computers as they are currently performed.

We understand by measurement-based benchmarks a 3-uple composed by a program, a processor and a measurement protocol. The associated measurement protocols should detail the variation of the input variables (associated to sensors) of these benchmarks and their impact on the output variables (associated to actuators), as well as the variation of the processor states.

Proposing reproducibility and representativity properties that measurement-based benchmarks should follow is the strength of this research axis 7. We understand by the reproducibility, the property of a measurement protocol to provide the same ordered set of execution times for a fixed pair (program, processor). We understand by the representativity, the existence of a (sufficiently small) number of values for the input variables allowing a measurement protocol to provide an ordered set of execution times that ensure a convergence for the Extreme Value Index estimators.

Within this research axis we identify the following open problems:

1. proving reproducibility and representativity properties while extending current benchmarks from predictable unicore processors (e.g., ARM Cortex-M4) to non predictable ones (e.g., ARM Cortex-A53 or Cortex-A7);
2. proving reproducibility and representativity properties while extending unicore benchmarks to multicore processors. In this context, we face the supplementary difficulty of defining the principles that an operating system should satisfy in order to ensure a real-time behaviour.

3.3 Scheduling of graph tasks on different resources within an energy budget

Following the model-driven approach, the functional description of the cyber part of the CPS, is performed as a graph of dependent functions, e.g., a block diagram of functions in Simulink, the most widely used modeling/simulation tool in industry. Of course, a program is associated to every function. Since the graph of dependent programs becomes a set of dependent tasks when real-time constraints must be taken into account, we are facing the problem of verifying the schedulability of such dependent task sets when it is executed on a multicore processor.

Directed Acyclic Graphs (DAG) are widely used to model different types of dependent task sets. The typical model consists of a set of independent tasks where every task is described by a DAG of dependent sub-tasks with the same period inherited from the period of each task  16. In such DAG, the sub-tasks are vertices and edges are dependencies between sub-tasks. This model is well suited to represent, for example, the engine controller of a car described with Simulink. The multicore schedulability analysis may be of two types, global or partitionned. To reduce interference and interactions between sub-tasks, we focus on partitioned scheduling where each sub-task is assigned to a given core  23, 6, 8.

In order to propose a general DAG task model, we identify the following open research problems:

1. solving the schedulability problem where probabilistic DAG tasks are executed on predictable and non predictable processors, and such that some tasks communicate through predictable networks, e.g., inside a multicore or a manycore processor, and non-predictable networks, e.g., between these processors through internet. Within this general schedulability problem; we consider five main classes of scheduling algorithms that we adapt to solve probabilistic DAG task scheduling problems. We compare the new algorithms with respect to their energy-consumption in order to propose new versions with a decreased energy consumption by integrating variation of frequencies for processor features like CPU or memory accesses.
2. the validation of the proposed framework on our multicore drone case study. To answer to the challenging objective of proposing time predictable platforms for drones, we currently migrate the PX4-RT programs on heterogeneous architectures. This includes an implementation of the scheduling algorithms detailed within this research axis within current operating system, NuttX2.

4.1 Avionics

Time critical solutions in this context are based on temporal and spatial isolation of the programs and the understanding of multicore interferences is crucial. Our contributions belong mainly to the solutions space for the objective [O1] identified previously.

4.2 Railway

Time critical solutions in this context concern both the proposition of an appropriate scheduler and associated schedulability analyses. Our contributions belong to the solutions space of problems dealt within objectives [O1] and [O2] identified previously.

4.3 Autonomous cars

Time critical solutions in this context concern the interaction between programs executed on multicore processors and messages transmitted through wireless communication channels. Our contributions belong to the solutions space of all three classes of problems dealt within all three Kopernic objectives identified previously.

4.4 Drones

As it is the case of autonomous cars, there is an interaction between programs and messages, suggesting that our contributions in this context belong to the solutions space of all three classes of problems dealt within the objectives identified previously.

5.1 Impact of research results

The Kopernic members provide theoretical means to decrease both the processor utilization and the energy consumption. Such gain is estimated within $30\%$ to $60\%$ utilization gain for existing architectures or energy consumption for new architectures by decreasing the number of necessary cores.

6.1 Awards

Liliana Cucu-Grosjean and Adriana Gogonel have been nominated among the 100 most innovative French inventors of the year 2023 by the newpaper La Tribune (France). Liliana Cucu-Grosjean has been nominated among the 100 most influent Romanian in 2023 by the newpaper Newsweek (Romania). StatInf, a spin-off of the Kopernic team has been awarded within the TechForFuture contest in Paris at the category "Industrie du Futur"

6.2 Keynotes

Liliana Cucu-Grosjean has gave a keynote entitled "Probabilities – a means to gain time and space when designing CPS" at the 2023 edition of the Hipeac conference

6.3 Nominations

Liliana Cucu-Grosjean has been nominated to run for the election and have been elected vice-chair of the IEEE Technical Community on Real-Time Systems (TCRTS). She has started her office on January, 1st of 2024 as the first female vice-chair of this IEEE committee after more than 40 years of existence. According to the IEEE TCRTS rules, she becomes chair of this committee on January, 1st, 2026 for a period of two years.

7.1 New software

7.2 Open data

The Kopernic members contribute to the effort of reproducing research results and numerical evaluation by proposing dynamic benchmarks for statistical analysis of measured execution times, memory accesses and other traces obtained during the Hardware in the Loop execution of the open source programs PX4-RT. A set of measurements obtained from the execution of the PX4-RT programs on the Pixhawk board are shared with the community under the name of KDBench, a.k.a, Kopernic Dynamic Benchmarks. The data related to KDBench are available at https://­team.­inria.­fr/­kopernic/­kdbench/ and the contact person is Liliana Cucu-Grosjean.

8.1 Worst case execution time estimation of a program

Participants: Slim Ben Amor, Rihab Bennour, Liliana Cucu-Grosjean, Adriana Gogonel, Kossivi Kougblenou, Marwan Wehaiba El Khazen.

We consider WCET statistical estimators that are based on the utilization of the Extreme Value Theory  24. Compared to existing methods  36, our results require the execution of the program under study on the targeted processor or at least a cycle-accurate simulator of this processor. We concentrate on the separation of hardware and software impacts 9, where the correct application of the Extreme Value Theory brings an important support 10.

The originality of this year results concerns the migration from the WCET estimation to the estimation of the worst-case energy consumption 12. More precisely, we propose a new statistical model introducing the impact of both software and hardware events on the estimation of worst-case energy consumption of programs on embedded processors. In order to achieve this purpose, we build a framework to better understand the representativeness of measurements with respect to both software and hardware events. During this year, we test this framework on both execution times and energy consumption data for existing benchmarks as a first step towards a complete statistical worst-case energy consumption model. We denote by WCEC the worst-case energy consumption of a program.

Different execution profiles for the Dec program

Another original aspect of this work is the definition of critical paths in the context of worst-case statistical estimations. Indeed, while a static analysis calculates a worst-case value based on a critical path, in statistical-based estimators we define a similar concept of critical paths. For a program $A$ executed on a processor $\Pi$ and a measurement protocol $ℳ$, we obtain an ordered sequences of paths ${\left(P_j\right)}_j$ and of execution times or energy consumption values denoted by $V^{*}$, depending on the choice of target variable (WCET or WCEC).

The Worst-Case Execution Time of a program $A$ is defined as its largest execution time for any valid execution scenario $S$, while the probabilistic worst-case execution time (pWCET) ${𝒞}_{𝒯}$ of a program is an upper bound on all possible probabilistic execution times ${{𝒞}_{𝒯}}_i$ for all possible execution scenarios $S_i,\forall i\ge 1$ (Each scenario $S_i$ thus defines a probability distribution of execution times ${{𝒞}_{𝒯}}_i$). The relation $⪰$ describes the relation between the probabilistic execution times (pET) of a program and its pWCET, ${𝒞}_{𝒯}⪰{{𝒞}_{𝒯}}_i$, $\forall i$, defined as follows. One writes ${𝒞}_{𝒯}⪰{{𝒞}_{𝒯}}_i$ or ${𝒞}_{𝒯}$ is said to be worse than ${{𝒞}_{𝒯}}_i$ if its complementary cumulative distribution function (survival function 1-CDF) has a higher or equal probability associated to each possible value, i.e., $P({𝒞}_{𝒯}\ge c)\ge P({{𝒞}_{𝒯}}_i\ge c)$, $\forall c$ and $\forall i\ge 1$.

Based on the previous (p)WCET definitions, we may define the analogous concepts of the worst case energy consumption (WCEC) and of the probabilistic WCEC (pWCEC) of a program as follows. A Worst-Case Energy Consumption of a program is its largest energy consumption during the execution of that program for any valid execution scenario, while the probabilistic worst-case energy consumption ${𝒞}_{ℰ}$ of a program is an upper bound on all possible probabilistic energy consumption profiles ${{𝒞}_{ℰ}}_i$ for all possible execution scenarios $S_i,\forall i\ge 1$. The relation $⪰$ describes, as with pETs, the relation between the probabilistic energy consumption (pEC) of a program and its pWCEC, such that ${𝒞}_{ℰ}⪰{{𝒞}_{ℰ}}_i$, $\forall i$. We say that a path $P_j$ of a program $A$ is critical with respect to a pWCET estimation of $A$ if, at least, one measurement of the execution of that path appears within the set of measurements building the pWCET estimate of $A$. Similarly, we define critical paths wrt the pWCEC estimation. A path $P_j$ of a program $A$ is critical with respect to a pWCEC estimation of $A$ if, at least, one measurement of the energy consumption associated to the execution of that path appears within the set of measurements building the pWCEC estimate of $A$. For instance, in Figure 2, we illustrate for the program $Dec$  25 executed on an ARM microcontroller, by two colors different measured energy consumption, where points with the same color identify paths that are equivalent with respect to the worst-case energy consumption estimation.

8.2 Building measurement-based benchmarks: KDBench

Participants: Slim Ben Amor, Rihab Bennour, Masum Bin Alam, Liliana Cucu-Grosjean, Ismail Hawila, Yves Sorel, Marwan Wehaiba El Khazen.

KDBench, our measurement-based benchmarks, are obtained by modifying open-source programs of the autopilot PX4 designed to control a wide range of air, land, sea and underwater drones. More precisely, the studied programs are executed on a standard Pixhawk drone board based on a predictable single core processor ARM Cortex-M4 and during the CEOS project we have transformed this set of programs into a set of dependent tasks that satisfies real-time constraints, leading to a new version of PX4, called PX4-RT. As usual, the set of dependent real-time tasks is defined by a data dependency graph. An interested reader may refer to the web page of the Kopernic team at The KDBench website.

During this year, the data associated to the KDBench has been collected from 3 flights according to different scenarios, where we vary from one scenario to another the periods of programs. We consider 4 different scenarios per flight and we obtain 12 sets of collected data, 4 sets for each flight. Moreover, different data are extracted from the benchmark after the flight completes.

We collect data from three different flight that we generate by using the QGroundControl software which provides planning for MAVlink enabled drones. The three flights are described as follows:

1. during the first flight short_flight, the drone follows a simple line trajectory and the duration of the flight is 23s,
2. for the second medium_flight we choose a flight with a sudden change of the drone orientation, in addition to other waypoints where we change the altitude. The duration of this flight is around $43s$,
3. the third long_flight has more waypoints than the second flight and its duration is 2min 48s.

More precisely, we have considered the execution of 9 real-time tasks (or programs) of PX4-RT. Their list is detailed in the table below together with their periods of activation. In the first line of this table, tasks are ordered according to their priority from the highest priority (on the left of the table) to the lowest priority (on the right of the table). For instance, the task Sensors has the highest priority while Commander has the lowest priority. The last 4 lines of this table contain the periods of activation of each task within the 4 considered measuring flight scenarios, where the periods $T_i$ are indexed according to the scenario number $i$.

8.3 Scheduling of graph tasks on different resources within an energy budget

Participants: Slim Ben Amor, Liliana Cucu-Grosjean, Ismail Hawila, Kossivi Kougblenou, Yves Sorel, Kevin Zagalo.

Due to widespread of multicore processors on embedded and real-time systems, we concentrate our work on the study of the schedulability of graph tasks on such processors. We consider preemptive (both global and partitionned) fixed-priority scheduling policies. We monitor, when possible, the energy consumption required to meet deadlines as a metric comparing the efficiency of scheduling policies.

Given the difficulty of our scheduling problem, we have considered the single processor case for of independent tasks for which a feasibility interval has been proved 11, 14. To this problem we have added the precedence constraints and we study the specific case of control real-time tasks as an important mean to understand how probabilities may be associated to the inter-arrival times between consecutive instances of the same program or task as well as understanding the motivation for precedence constraints between tasks and/or their instances.

With respect to the proposition of a new task model merging scheduling and WCET concerns for real-time control systems, our purpose is that this new task model fulfills the following expectations:

1. the data and/or precedence constraints between different control tasks as well as non-control tasks are considered;
2. the impact of data constraints on the execution times of control tasks is considered;
3. the impact of period variation between dependent control tasks is considered.

Data and precedence constraints represented by a DAG-based task model for KDBench programs

Such expectations applied to the PX4-RT programs require to indicate the appropriate precendence constraints. In Figure 3, we represent by continuous lines edges that depict precedence constraints between tasks and by dotted lines edges that depict the data constraints for the PX4-RT program 13.

9.1 CIFRE Grant funded by StatInf

Participants: Liliana Cucu-Grosjean, Adriana Gogonel, Marwan Wehaiba El Khazen.

A CIFRE agreement between the Kopernic team and the start-up StatInf has started on October 1st, 2020. Its funding is related to study the evolution of WCET models to consider the energy consumption according to Kopernic research objectives.

9.2 CIFRE Grant funded by StatInf

Participants: Liliana Cucu-Grosjean, Slim Ben Amor, Ismail Hawila, Yves Sorel.

A CIFRE agreement between the Kopernic team and the start-up StatInf has started on October 1st, 2022. Its funding is related to study the relation between the control theory robustness and the schedulability problem using probabilistic descriptions according to Kopernic research objectives.

10.1 International initiatives

10.2 International research visitors

10.3 National initiatives

11.1 Promoting scientific activities

11.2 Teaching - Supervision - Juries

11.3 Popularization

12.1 Major publications

• 1 patentL.Liliana Cucu-Grosjean and A.Adriana Gogonel. Simulation Device.FR2016/050504FranceMarch 2016, URL: https://hal.archives-ouvertes.fr/hal-01666599back to text
• 2 inproceedingsL.Liliana Cucu-Grosjean, L.Luca Santinelli, M.Michael Houston, C.Code Lo, T.Tullio Vardanega, L.Leonidas Kosmidis, J.Jaume Abella, E.Enrico Mezzetti, E.Eduardo Quiñones and F. J.Francisco J. Cazorla. Measurement-Based Probabilistic Timing Analysis for Multi-path Programs.the 24th Euromicro Conference on Real-Time Systems, ECRTS2012, 91--101back to text
• 3 articleR.Robert Davis and L.Liliana Cucu-Grosjean. A Survey of Probabilistic Schedulability Analysis Techniques for Real-Time Systems.Leibniz Transactions on Embedded Systems612019, 53HALDOIback to text
• 4 articleR.Robert Davis and L.Liliana Cucu-Grosjean. A Survey of Probabilistic Timing Analysis Techniques for Real-Time Systems.Leibniz Transactions on Embedded Systems612019, 60HALDOIback to text
• 5 patentA.Adriana Gogonel and L.Liliana Cucu-Grosjean. Dispositif de caractérisation et/ou de modélisation de temps d'exécution pire-cas.1000408053FranceJune 2017, URL: https://hal.archives-ouvertes.fr/hal-01666535back to text
• 6 inproceedingsT.T. Kloda, A.A. Bertout and Y.Y. Sorel. Latency analysis for data chains of real-time periodic tasks. the 23rd IEEE International Conference on Emerging Technologies and Factory Automation, ETFA'18September 2018back to text
• 7 articleC.Cristian Maxim, A.Adriana Gogonel, I. M.Irina Mariuca Asavoae, M.Mihail Asavoae and L.Liliana Cucu-Grosjean. Reproducibility and representativity: mandatory properties for the compositionality of measurement-based WCET estimation approaches.SIGBED Review1432017, 24--31back to text
• 8 inproceedingsS. E.S. E. Saidi, N.N. Pernet and Y.Y. Sorel. Scheduling Real-time HiL Co-simulation of Cyber-Physical Systems on Multi-core Architectures. the 24th IEEE International Conference on Embedded and Real-Time Computing Systems and ApplicationsAugust 2018back to text

12.2 Publications of the year

12.3 Cited publications

• 15 bookR.R. Baheti and H.H. Gill. Cyber-physical systems.IEEE2011back to text
• 16 inproceedingsS.S. Baruah, V.V. Bonifaci, A.A. Marchetti-Spaccamela, L.L. Stougie and A.A. Wiese. A Generalized Parallel Task Model for Recurrent Real-time Processes.2012 IEEE 33rd Real-Time Systems Symposium (RTSS)2012, 63-72back to text
• 17 inproceedingsG.Guillem Bernat, A.Antoine Colin and S. M.Stefan M. Petters. WCET Analysis of Probabilistic Hard Real-Time System.Proceedings of the 23rd IEEE Real-Time Systems Symposium (RTSS'02)IEEE Computer Society2002, 279--288back to text
• 18 inproceedingsT.T. Bourke, J.-L.J.-L. Colaço, B.B. Pagano, C.C. Pasteur and M.M. Pouzet. A Synchronous-Based Code Generator for Explicit Hybrid Systems Languages.Compiler Construction - 24th International Conference, CC, Joint with ETAPS2015, 69--88back to text
• 19 inproceedingsL.L. Cucu. Preliminary results for introducing dependent random variables in stochastic feasiblity analysis on CAN.the WIP session of the 7th IEEE International Workshop on Factory Communication Systems (WFCS)2008back to text
• 20 articleR. I.R. I. Davis and L.L. Cucu-Grosjean. A Survey of Probabilistic Timing Analysis Techniques for Real-Time Systems.LITES612019, 03:1--03:60back to text
• 21 inproceedingsS.S. Edgar and A.A. Burns. Statistical Analysis of WCET for Scheduling.the 22nd IEEE Real-Time Systems Symposium (RTSS)2001, 215--225back to text
• 22 inproceedingsH.H. Falk, S.S. Altmeyer, P.P. Hellinckx, B.B. Lisper, W.W. Puffitsch, C.C. Rochange, M.M. Schoeberl, R. B.R. B. Sorensen, P.P. Wägemann and S.S. Wegener. TACLeBench: A Benchmark Collection to Support Worst-Case Execution Time Research.16th International Workshop on Worst-Case Execution Time Analysis (WCET)55OASICS2016, 2:1--2:10back to text
• 23 inproceedingsJ.Jose Fonseca, G.Geoffrey Nelissen, V.Vincent Nelis and L.Luís Pinho. Response time analysis of sporadic DAG tasks under partitioned scheduling.11th IEEE Symposium on Industrial Embedded Systems (SIES)05 2016, 1-10back to text
• 24 articleS. J.S. J. Gil, I.I. Bate, G.G. Lima, L.L. Santinelli, A.A. Gogonel and L.L. Cucu-Grosjean. Open Challenges for Probabilistic Measurement-Based Worst-Case Execution Time.Embedded Systems Letters932017, 69--72back to textback to text
• 25 inproceedingsJ.J. Gustafsson, A.A. Betts, A.A. Ermedahl and B.B. Lisper. The Mälardalen WCET Benchmarks: Past, Present And Future.10th International Workshop on Worst-Case Execution Time Analysis (WCET)15OASICS2010, 136--146back to textback to text
• 26 articleE.E. Lee. Computing Needs Time.Communications of ACM5252009back to text
• 27 bookE.E. Lee and S.S. Seshia. Introduction to embedded systems - a cyber-physical systems approach.MIT Press2017back to text
• 28 inproceedingsJ.J.P. Lehoczky. Real-Time Queueing Theory.the 10th IEEE Real-Time Systems Symposium (RTSS)1996back to text
• 29 bookS. B.S. Baruah M. Bertogna and G.G. Buttazzo. Multiprocessor Scheduling for Real-Time Systems.Springer2015back to text
• 30 inproceedingsD.D. Maxim, O.O. Buffet, L.L. Santinelli, L.L. Cucu-Grosjean and R. I.R. I. Davis. Optimal Priority Assignment Algorithms for Probabilistic Real-Time Systems.the 19th International Conference on Real-Time and Network Systems (RTNS)2011back to text
• 31 inproceedingsD.D. Maxim and L.L. Cucu-Grosjean. Response Time Analysis for Fixed-Priority Tasks with Multiple Probabilistic Parameters.the IEEE Real-Time Systems Symposium (RTSS)2013back to text
• 32 inproceedingsF.F. Ndoye and Y.Y. Sorel. Monoprocessor Real-Time Scheduling of Data Dependent Tasks with Exact Preemption Cost for Embedded Systems.the 16th IEEE International Conference on Computational Science and Engieering (CSE)2013back to text
• 33 inproceedingsF.F. Nemer, H.H. Cassé, P.P. Sainrat, J. P.J. P. Bahsoun and M. D.M. D. Michiel. PapaBench: a Free Real-Time Benchmark.6th Intl. Workshop on Worst-Case Execution Time (WCET) Analysis4OASICS2006back to text
• 34 inproceedingsS. E.S. E. Saidi, N.N. Pernet and Y.Y. Sorel. Automatic Parallelization of Multi-Rate FMI-based Co-Simulation On Multi-core.the Symposium on Theory of Modeling & Simulation: DEVS Integrative M&S Symposium2017back to text
• 35 inproceedingsT.T.S. Tia, Z.Z. Deng, M.M. Shankar, M.M. Storch, J.J. Sun, L.L.C. Wu and J.J.S Liu. Probabilistic Performance Guarantee for Real-Time Tasks with Varying Computation Times.IEEE Real-Time and Embedded Technology and Applications Symposium1995back to textback to text
• 36 articleR.R. Wilhelm, J.J. Engblom, A.A. Ermedahl, N.N. Holsti, S.S. Thesing, D.D. Whalley, G.Bernat, C.C. Ferdinand, R.Heckmann, T.T. Mitra, F.F. Mueller, I.I. Puaut, P.P. Puschner, G.G. Staschulat and P.P. Stenströem. The worst-case execution time problem: overview of methods and survey of tools.Trans. on Embedded Computing Systems732008, 1-53back to textback to textback to textback to text