Section: Research Program

The Algorithm-Architecture Adequation methodology and Real-Time Scheduling

Participants : Liliana Cucu, Dumitru Potop-Butucaru, Yves Sorel.

The Algorithm-Architecture Adequation (AAA) methodology relies on distributed real-time schedulability and optimization theories to map efficiently an algorithm model to an architecture model.

The algorithm model which describes the functional specifications of the applications, is an extension of the well known data-flow model from Dennis [16]. It is a directed acyclic hyper-graph (DAG) that we call “conditioned factorized data dependence graph”, whose vertices are functions and hyper-edges are directed “data or control dependences” between functions. The data dependences define a partial order on the functions execution. The basic data-flow model was extended in three directions: first infinite (resp. finite) repetition of a sub-graph pattern in order to specify the reactive aspect of real-time systems (resp. in order to specify the finite repetition of a sub-graph consuming different data similar to a loop in imperative languages), second “state” when data dependences are necessary between different infinite repetitions of the sub-graph pattern introducing cycles which must be avoided by introducing specific vertices called “delays” (similar to z −n in automatic control), third “conditioning” of a function by a control dependence similar to conditional control structure in imperative languages, allowing the execution of alternative subgraphs. Delays combined with conditioning allow the programmer to specify automata necessary for describing “mode changes”.

The architecture model which describes the non functional specifications is, in the simplest case, a directed graph whose vertices are of two types: “processor” (one sequencer of functions, several sequencers of communications and distributed or shared memories) and “medium” (multiplexers and demultiplexers), and whose edges are directed connections. With such model it is possible to describe classic heterogeneous distributed, parallel and multiprocessor platforms as well as the most recent multi/manycore platforms. The worst case times mentioned previously are estimated according to this model.

The implementation model is a graph obtained by applying an external composition law such that an architecture graph operates on an algorithm graph to give an algorithm graph while taking advantage of timing characteristics, basically periods, deadlines and WCETs. This resulting algorithm graph is built by performing spatial and timing allocations (distribution and scheduling) of algorithm graph functions on architecture graph resources, and of dependences between functions on communication media. In that context "Adequation" means to search, in the solution space of implementation graphs, one implementation graph which verifies real-time constraints and, in addition, minimizes some criteria. These criteria consists in the total execution time of the algorithm executed on the architecture, the number of computing or communication resources, etc. Below, we describe distributed real-time schedulability analyses and optimization techniques suited for that purposes.

We address two main issues: uniprocessor and multiprocessor real-time scheduling for which some real-time constraints are of high criticality, i.e. they must be satisfied otherwise dramatic consequences occur.

In the case of uniprocessor real-time scheduling, besides the usual deadline constraint, often equal to the period of each task, i.e. a function with timing characteristics, we take into consideration dependences beetween tasks, and possibly several latencies. The latter are “end-to-end” constraints that may have complex relationships. Dealing with multiple real-time constraints raises the complexity of the scheduling problems. Moreover, costs of the Real-Time Operating System (RTOS) and of preemptions lead to, at least, a waste of resources due to their approximation in the WCET (Worst Execution Time) of each task, as proposed by Liu and Layland in their seminal article [18]. This is the reason why we first studied non-preemptive real-time scheduling with dependences, periodicities, and latencies constraints. Although a bad approximation of costs of the RTOS and of preemptions, may have dramatic consequences on real-time scheduling, there are only few researches on this topic. Thus, we investigated preemptive real-time scheduling while taking into account its cost which is very difficult to determine because it varies according to the instance (job) of each task. This latter is integrated in the schedulability conditions, and in the corresponding scheduling algorithms we propose. More generally, we integrate in schedulability analyses costs of the RTOS and of preemptions.

In the case of multiprocessor real-time scheduling, we chose to study first the “partitioned approach”, rather than the “global approach”, since the latter uses task migrations whose cost is prohibitive for current commercial processors, even for the more recent many/multicore. The partitioned approach enables us to reuse the results obtained in the uniprocessor case in order to derive solutions for the multiprocessor case. We consider also the semi-partitioned approach which allows only some migrations in order to minimize their costs. In addition, to satisfy the multiple real-time constraints mentioned in the uniprocessor case, we have to minimize the total execution time (makespan) since we deal with automatic control applications involving feedback loops. The complexity of such minimization problem increases because the cost of interprocessor communications (through buses in a multi-processor or routers in a manycore) must be taken into account. Furthermore, the domain of embedded systems leads to solving minimization resources problems. Since both optimization problems are NP-hard we develop exact algorithms (ILP, B & B, B & C) which are optimal for simple problems, and heuristics which are sub-optimal for realistic problems corresponding to industrial needs. Long time ago we proposed a very fast “greedy” heuristics whose results were regularly improved, and extended with local neighborhood heuristics, or used as initial solutions for metaheuristics.

Besides the spatial dimension (distributed) of the real-time scheduling problem, other important dimensions are the type of communication mechanisms (shared memory vs. message passing), or the source of control and synchronization (event-driven vs. time-triggered). We explore real-time scheduling on architectures corresponding to all combinations of the above dimensions. This is of particular impact in application domains such as railways and avionics.