Evaluation of the Age Latency of a Real-Time Communicating System Using the LET Paradigm

Automotive and avionics embedded systems are usually composed of several tasks that are subject to complex timing constraints. In this context, the LET paradigm was introduced to improve the determinism of a system of tasks that communicate data through shared variables. The age latency corresponds to the maximum time for the propagation of data in these systems. Its precise evaluation is an important and challenging question for the design of these systems. We consider in this paper a set of multi-periodic tasks that communicate data following the LET paradigm. Our main contribution is the development of mathematical and algorithmic tools to model precisely the dependency between tasks executions to experiment with an original methodology for computing the age latency of the system. These tools allow to handle the whole graph instead of particular chains and to extract automatically the critical parts of the graph. Experiments on randomly generated graphs indicate that systems with up to 90 periodic tasks and a hyperperiod bounded by 100 can be handled within a reasonable amount of time

Parameterized Complexity of a Parallel Machine Scheduling Problem

In this paper we consider the parameterized complexity of two versions of a parallel machine scheduling problem with precedence delays, unit processing times and time windows. In the first version - with exact delays - we assume that the delay between two jobs must be exactly respected, whereas in the second version - with minimum delays - the delay between two jobs is a lower bound on the time between them. Two parameters are considered for this analysis: the pathwidth of the interval graph induced by the time windows and the maximum precedence delay value. We prove that our problems are para-NP-complete with respect to any of the two parameters and fixed-parameter tractable parameterized by the pair of parameters

Optimal and fast throughput evaluation of CSDF

International audienceThe Synchronous Dataow Graph (SDFG) and Cyclo-Static Dataow Graph (CSDFG) are two well-known models, used practically by industry for many years, and for which there is a large number of analysis techniques. Yet, basic problems such as the throughput computation or the liveness evaluation are not well solved, and their complexity is still unknown. In this paper, we propose K-Iter, an iterative algorithm based on K-periodic scheduling to compute the throughput of a CSDFG. By using this technique, we are able to compute in less than a minute the throughput of industry applications for which no result was available before

Fast and Efficient Dataflow Graph Generation

International audienceDataflow modeling is a highly regarded method for the design of embedded systems. Measuring the performance of the associated analysis and compilation tools requires an efficient dataflow graph generator. This paper presents a new graph generator for Phased Computation Graphs (PCG), which augment Cyclo-Static Dataflow Graphs with both initial phases and thresholds. A sufficient condition of liveness is first extended to the PCG model. The determination of initial conditions minimizing the total amount of initial data in the channels and ensuring liveness can then be expressed using Integer Linear Programming. This contribution and other improvements of previous works are incorporated in Turbine, a new dataflow graph generator. Its effectiveness is demonstrated experimentally by comparing it to two existing generators, DFTools and SDF3

Minimizing makespan for a bipartite graph on a single processor with an integer precedence delay

International audienceWe consider the makespan minimization for a unit execution time task sequencing problem with a bipartite precedence delays graph and a positive precedence delay d. We prove that the associated decision problem is strongly NP-complete and we provide a non-trivial polynomial sub-case. We also give an approximation algorithm with ratio 32

Minimiser la durée d'un ordonnancement pour un graphe biparti sur un processeur avec un délai entier et des tâches de durée unitaire

We consider a set of tasks of unit execution times and a bipartite precedence delays graph with a positive precedence delay d: an arc (i,j) of this graph means that j can be executed at least d time units after the completion time of i. The problem is to sequence the tasks in order to minimize the makespan.Firstly, we prove that the associated decision problem is NP-complete. Then, we provide a non trivial polynomial time algorithm if the degree of every tasks from one of the two sets is 2. Lastly, we give an approximation algorithm with ratio 3/2.Nous considèrons un ensemble de tâches de durée unitaire et un graphe de delais de précédence biparti avec une valeur du delai d: tout arc (i,j) de ce graphe signifie que j doit être exécutée au moins d unités de temps après l'exécution de i. Le problème est alors de déterminer un ordonnancement des tâches sur un processeur de durée minimale.Dans un premier temps, nous montrons que le problème de décision associé est NP-complet. Puis, nous développons un algorithme polynomial non trivial dans le cas ou le degré de toutes les tâches de l'un des deux ensembles du graphe biparti est 2. Finalement, nous développons un algorithme approché de ratio de performance 3/2

Variants of the two machine flow-shop with precedence constraints

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A graph-based analysis of the cyclic scheduling problem with time constraints: schedulability and periodicity of the earliest schedule

International audienceWe consider in this paper a set of generic tasks constrained by a set of uniform precedence constraints corresponding to a natural generalization of the basic cyclic scheduling problem. The two parameters of any uniform constraint (namely the value and the height) between two tasks may be negative, which allows one to tackle a larger class of practical applications.We firstly study the structure and the existence of a periodic schedule. A necessary and sufficient condition for the existence of a schedule is then deduced. As there are no resource constraints, tasks following the earliest schedule have minimum average cycle times. The permanent state of the earliest schedule is characterized and we point out that the minimum average cycle times of tasks are equal for the earliest schedule and an optimal periodic schedule. An algorithm to check the existence of a schedule and to compute these minimum average cycle times using linear programming is lastly presented

Minimiser la durée d'un ordonnancement pour un graphe biparti sur un processeur avec un délai entier et des tâches de durée unitaire

We consider a set of tasks of unit execution times and a bipartite precedence delays graph with a positive precedence delay d: an arc (i,j) of this graph means that j can be executed at least d time units after the completion time of i. The problem is to sequence the tasks in order to minimize the makespan.Firstly, we prove that the associated decision problem is NP-complete. Then, we provide a non trivial polynomial time algorithm if the degree of every tasks from one of the two sets is 2. Lastly, we give an approximation algorithm with ratio 3/2.Nous considèrons un ensemble de tâches de durée unitaire et un graphe de delais de précédence biparti avec une valeur du delai d: tout arc (i,j) de ce graphe signifie que j doit être exécutée au moins d unités de temps après l'exécution de i. Le problème est alors de déterminer un ordonnancement des tâches sur un processeur de durée minimale.Dans un premier temps, nous montrons que le problème de décision associé est NP-complet. Puis, nous développons un algorithme polynomial non trivial dans le cas ou le degré de toutes les tâches de l'un des deux ensembles du graphe biparti est 2. Finalement, nous développons un algorithme approché de ratio de performance 3/2