Section: New Results

Principles of Probabilistic Composition

Participants : Slim Ben-Amor, Liliana Cucu, Adriana Gogonel, Cristian Maxim.

The statistical estimation of time parameters for real-time systems is proposed at two levels:

1. at program level and in this case we are dealing with timing analysis of programs that requires later appropriate probabilistic composition principles like reproducibility and representativity [3], [1]. For instance we have underlined in [14] the difficulties to ensure such properties for many-cores architectures.

   While we are proposing static analyses using worst-case bounds on the execution at instruction level for specialized architectures [2], we are interested also in proposing composition principles allowing to combine the timing impact of execution time variation factors, identified as a key open problem in the context of the timing analysis of programs while using the Extreme Value Theory [1]. Our composition solution is based on a Bayesian modeling that considers iteratively the inclusion of new factors while a representative measurement protocole is built [13] with respect to the reproducible Extreme Value Theory-based estimator that we have proposed.

2. at system level and in this case we are dealing with schedulability analysis of set of programs, a.k..a tasks, that requires appropriate composition principles like probabilistic independence while the dependence between tasks is taken into account. After proposing a first solution to the schedulability analysis of real-time probabilistic tasks in presence of precedence constraints on uniprocessor system [6], we explore the state of art of real-time scheduling on multiprocessor system and probabilistic real-time existing analysis. Our choice goes to partitioned multiprocessor scheduling to ensure the applicability of our previous results in the case of one processor. We have proposed a first optimal partitioning strategy based individual task utilization and we compare different tasks combinations that fit on a single processor following an utilization task ratio principle as partitioning choice. When assessing our method, a counter example of a possible optimality has appeared. Moreover this method has not an important improvement compared to existing partitioning strategies like best fit. Therefore we prepare the application of an existing solution to the bin packing problem [17] proposed in mathematics domain to partition real-time tasks on multiprocessor system in order to propose an appropriate probabilistic analysis.

   The exact schedulability analyses are often competing with statistical estimation of response time based on simulation and we propose such result in [9]. Such results allow to advance on the understanding of the notion of representativeness in the context of our problem that becomes today central in our community. The explosion of probabilistic schedulability analyses published in the last years have convinced us to join the book proposal of a Handbook on Real-Time Computing in order to integrate a comprehensive description of these analyses [4].