Section: New Results

Multiprocessor Real-Time Scheduling

Participants : Mehdi Mezouak, Salah Eddine Saidi, Yves Sorel.

Always in the context of the master internship of Mehdi Mezouak, we studied the extension to multiprocessor of our offline time triggered scheduler. Since we chose the partitioned multiprocessor scheduling approach rather than the global one which is not suited to safety critical applications due to the prohibitive cost of task migrations, the uniprocessor schedulability analysis is easily extended. Indeed, the main modification consists, for every processor, in accounting for the cost of inter-processor communications and synchronizations due to data dependences when a producer task is allocated to a processor which is different from the one the corresponding consumer task is allocated to. Therefore, new scheduler calls are added to the scheduling table corresponding to instants when awaited data are available, i.e. produced and then transfered. Of course, there are as many scheduling tables, and thus schedulers, as there are processors, and these scheduling tables are supposed to share a unique global time. The implementation of this global time raises a complex problem since it is not possible to dispatch a unique physical clock to all the processors. Among various solutions, we chose to use a physical clock rather than a logical one like in the Lamport's timestamp approach since we are interested in safety critical real-time. In addition, we chose the Berkeley's algorithm based on a master-slave approach where the clock server is maintained by one of the processor of the multiprocessor. This algorithm is more robust to failures than other algorithms based on an external clock server. Finally, using the measurement system mentioned previously, we measured accurately the cost of inter-processor communications according to the number of transfered data, in the case of an ethernet network that we experimented last year to connect several LPC4080 microcontroller boards.

During the second year of the PhD thesis of Salah Eddine Saidi, we continued to study the parallelization on multi-core of FMI-based co-simulation of numerical models, that is increasingly used for the design of Cyber-Physical Systems. Such model developed according to the FMI standard is defined by a number of C functions, called “operations”, for computing its variables (inputs, outputs, state) and data dependences between these variables. Each model has an associated integration step and exchanges data with the other models according to its communication step which can be larger or equal to its integration step. These models are represented by a dataflow graph of operations [35] that is compliant with the conditioned repetitive dataflow model of our AAA methodology for functional specification. Our work mainly focused on two aspects. First, we proposed a graph transformation algorithm in order to allow handling multi-rate co-simulation, i.e. where connected models have different communication steps. This algorithm is based on the concept of graph unfolding similarly to the unrolling algorithm of our AAA methodology. The new graph is represented over the hyper-step which is equal to the least common multiple of the communication steps of all the models. Each operation is repeated in the graph according to the ratio between the hyper-step and its communication step. Then, rather than adding edges connecting all the repetitions of dependent operations, specific rules are used to define the repetitions that have to be connected by edges. These rules ensure correct data exchange between the operations as requested in the context of simulation. Second, some FMI functions called to compute model variables may not be “thread-safe”, i.e. they cannot be executed in parallel as they may share some resource (e.g. variables). Consequently, if two or more operations belonging to the same model are executed on different cores, a mechanism that ensures these operations are executed in strictly disjoint time intervals must be set up. We proposed an acyclic orientation heuristic to solve this problem. This heuristic adds non directed edges between the operations that belong to the same model, and then assigns directions to these edges with the aim of minimizing the critical path of the resulting graph and subject to the constraint that no cycle is generated in the graph.