Pascal Richard

A Response-Time Bound in Fixed-Priority Scheduling with Arbitrary Deadlines

Since worst case response times must be determined repeatedly during the interactive design of real-time application systems, repeated exact computation of such response times would slow down the design process considerably. In this research, we identify three desirable properties of estimates of the exact response times: continuity with respect to system parameters, efficient computability, and approximability. We derive a technique possessing these properties for estimating the worst-case response time of sporadic task systems that are scheduled using fixed priorities upon a preemptive uniprocessor.

Negative results for scheduling independent hard real-time tasks with self-suspensions

In most real-time systems, tasks use remote operations that are executed upon dedicated processors. External operations introduce self-suspension delays in the behavior of tasks. This paper presents several negative results concerning scheduling independent hard real-time tasks with self-suspensions. Our main objective is to show that well-known scheduling policies such as fixed-priority or earliest deadline first are not efficient to schedule such task systems. We prove the scheduling problem to be NP-hard in the strong sense, even for synchronous task systems with implicit deadlines. We also show that scheduling anomalies can occur at run-time: reducing the execution requirement or the suspension delay of a task can lead the task system to be infeasible under EDF. Lastly, we present negative results on the worst-case performances of well-known scheduling algorithms (EDFy RM, DM, LLF, SRPTF) to maximize tasks completed by their deadlines.

Referential Horizontal Partitioning Selection Problem in Data Warehouses: Hardness Study and Selection Algorithms

Horizontal Partitioning has been largely adopted by the database community, where it took a significant part in the physical design process. Actually, it is supported by most commercial database systems (DBMS), where a native Data Definition Language for decomposing tables/materialized views using various modes is proposed. In traditional databases, horizontal partitioning has been largely studied, where several fragmentation algorithms were proposed to partition tables in isolation. In the relational data warehouse environment, horizontal partitioning consists in decomposing the whole warehouse schema into sub schemas, where each schema contains fragments of dimension and fact tables. Dimension tables are fragmented using the primary partitioning mode, whereas the fact table is divided using referential mode. In this article, the authors first focus on the evolution of horizontal partitioning in commercial DBMS motivated by decision support applications. Secondly, they give a formalization of the referential fragmentation schema selection problem in the data warehouse and they study its hardness to select an optimal solution. Due to its high complexity, they develop two algorithms: hill climbing and simulated annealing with several variants to select a near optimal partitioning schema. Finally, extensive experimental studies are conducted using the data set of APB1 benchmark to compare the quality the proposed algorithms using a mathematical cost model. Based on these experiments, some recommendations are given to advise database administrator for well using horizontal partitioning.

Optimistic problems in the trajectory approach in FIFO context

AFDX (Avionics Full Duplex Switched Ethernet) is a network designed for safety-critical applications in avionics systems. The flow analysis is mandatory for the certification. The end-to-end (ETE) delay upper bound has to be computed and hence guaranteed. Different approaches have been proposed to compute ETE delay upper bound such as the Network Calculus and the trajectory method. Both methods are deemed to introduce some pessimism in the computations. We only focus next on the trajectory approach. This paper shows that the original trajectory approach is flawed and can compute an optimistic ETE. We present a counter-example and discuss the sources of optimism that must be considered to revise the trajectory method.

Data Partitioning in Data Warehouses: Hardness Study, Heuristics and ORACLE Validation

Horizontal data partitioning is a non redundant optimization technique used in designing data warehouses. Most of todays commercial database systems offer native data definition language support for defining horizontal partitions of a table. Two types of horizontal partitioning are available: primary and derived horizontal fragmentations. In the first type, a table is decomposed into a set of fragments based on its own attributes, whereas in the second type, a table is fragmented based on partitioning schemes of other tables. In this paper, we first show hardness to select an optimal partitioning schema of a relational data warehouse. Due to its high complexity, we develop a hill climbing algorithm to select a near optimal solution. Finally, we conduct extensive experimental studies to compare the proposed algorithm with the existing ones using a mathematical cost model. The generated fragmentation schemes by these algorithms are validated on Oracle 10g using data set of APB1 benchmark.

Allocating and scheduling tasks in multiple fieldbus real-time systems

We consider real-time systems connected via several fieldbuses. Validating such systems consists of proving that tasks meet their end-to-end deadlines. Tasks are scheduled on processors by fixed-priority schedulers. We propose an automatic method for allocating tasks on processors and assigning priorities to tasks so that every deadline is met. Allocation and scheduling are simultaneously achieved. We do not limit the search space to a specific priority rule (such as rate monotonic or deadline monotonic). Feasible schedules are validated by a holistic analysis. Numerical results of the method are lastly presented on a real-size application. Our tool will be a beneficial help to design real-time distributed systems.

Dynamic priority scheduling of periodic tasks with extended precedences

The software architecture of a critical embedded control system generally consists of a set of multi-periodic communicating tasks. In order to be able to describe such a system, we define the notion of semaphore precedence constraint, which supports multi-rate communications that follow regular repetitive patterns. We propose a feasibility test for EDF and we study three implementations, for periodic task sets related by such extended precedences on monoprocessor architectures.

Approximation techniques for response-time analysis of static-priority tasks

We consider sporadic tasks with static priorities and constrained deadlines to be executed upon a uniprocessor platform. Pseudo-polynomial time algorithms are known for computing worst-case response times for this task model. Some applications require to evaluate efficiently upper bounds of response times. For this purpose, we propose parametric algorithms that allow to make a tradeoff between quality of results and computational effort according to an input accuracy parameter. In this paper, we present a parametric polynomial-time algorithm for computing upper bounds of worst-case response times, that is based on an improved fptas (Fully Polynomial Time Approximation Scheme). Then, we show that our bound does not achieve constant error bound in comparison with the exact worst-case response time. However, using the resource augmentation technique, we obtain a performance guarantee that allows to define a compromise between our response-time bound and processor capacity requirements. The algorithm average behavior is then analyzed through numerical experimentations.

On-line scheduling of real-time distributed computers with complex communication constraints

We consider the scheduling of periodic tasks running on distributed computers. Every execution of a task must meet its deadline. Response time analysis of the tasks is used to prove the schedulability of hard real-time distributed systems according to the on-line priority rules that schedule the processors and the network. Its main advantage is to take into account the precedence dependencies of the schedules of the tasks on the processors and the messages sent on the network(s). Past works have addressed the issue of tasks related by asynchronous communication constraints with the senders and the receivers working at the same rate. We study more general relations among tasks when the rates of dependent tasks are not equal. We call such relations generalized communication constraints. Usually distributed systems are scheduled using a synchronization protocol and an on-line scheduling algorithm by processor. We present a graph theoretical approach to this schedulability analysis. Our algorithm transforms complex communication relations into classical ones, so that the classical scheduling analysis can be fully applied. That transformation is independent of the architecture of the distributed systems and no assumption is made on the synchronization protocol considered.

Parametric Polynomial-Time Algorithms for Computing Response-Time Bounds for Static-Priority Tasks with Release Jitters

Feasibility analysis algorithms are based on particular metrics such as processor utilization, load factor, processor demand, response-times, etc. The design of efficient algorithms for computing these metrics is a major issue in real-time scheduling theory. In this paper we propose two FPTASs (fully-polynomial time approximation schemes) for checking feasibility of static-priority tasks subjected to release jitters executed upon a uniprocessor platform. We then use these FPTASs for computing two upper bounds of worst-case response-times. Lastly, we show that these bounds do not achieve constant error bounds in comparison with values computed by an exact worst-case response-time analysis (performed in pseudo-polynomial time), and we present numerical experiments.