Section: Research Program

Time Scheduling

Cyber-physical systems are reactive systems whose correctness not only depends on a deterministic behavior but also on timing predictability. The timing parameters of a CPS are requirements that arise from the system’s specification (e.g. minimum throughput, maximum latency, deadlines) or timing properties of the physical and cyber-parts that restrict the CPS implementation. The design of a CPS must ensure that these timing requirements will be met, even in the worst-case scenario, through the different components and their timing properties.

Scheduling theory

Real-time scheduling theory provides tools for predicting the timing behaviour of a CPS which consists of many interacting software and hardware components. Expressing parallelism among software components is a crucial aspect of the design process of a CPS. It allows for efficient partition and exploitation of available resources. In the real-time scheduling theory literature, many models of computation have been proposed to express such parallelism, for instance:

• Set of independent periodic, sporadic, or aperiodic tasks where each real-time task is generally characterised with some timing parameters: deadline, period, first start time, jitter, etc. The periodic and sporadic task models (Scheduling algorithms for multiprogramming in a hard-real-time environment. C. L. Liu and J. W. Layland. Journal of the ACM 20(1), 1973.) are very well studied task models since they allow to analytically reason about the timing behaviour of tasks. More expressive task models (The digraph real-time task model. M. Stigge, P. Ekberg, N. Guan, and W. Yi. Real-Time and Embedded Technology and Applications Symposium. IEEE, 2011.) such as the multi-frame and the recurring real-time task models have also emerged.

• Task graph models (Task graph scheduling using timed automata. Y. Abdeddaïm, A. Kerbaa, and O. Maler. International Symposium on Parallel and Distributed Processing. IEEE, 2003.) where precedence constraints among real-time tasks may exist.

• Data-flow graph models such as synchronous data-flow (SDF (Synchronous data-flow. E. A. Lee and D. G. Messerschmitt. Proceedings of the IEEE, 1987.)) and cyclo-static dataflow (CSDF (Cycle-static dataflow. G. Blisen, M. Engels, R. Lauwereins, and J. Peperstraete. Transactions on Signal Processing). IEEE, 1996.) models where the set of tasks (also called actors) communicate with each other through FIFO channels. When it fires, an actor consumes a predefined number of tokens from its inputs and produces a predefined number of tokens on its outputs. The scheduling problem is hence more complex since data dependencies must be satisfied.

The literature about real-time scheduling of sets of independent real-time tasks (A survey of hard real-time scheduling for multiprocessor systems. R. I. Davis and A. Burns. ACM Computing Survey 43(4), 2011.) provides very mature schedulability tests regarding many scheduling strategies, preemptive or non-preemptive scheduling, uniprocessor or multiprocessor scheduling, etc. Historically, real-time systems where scheduled by cyclic executives (i.e. static scheduling). However, since this approach produces rigid and difficult to maintain systems and handles only periodic tasks, the research community has proposed many dynamic scheduling algorithms, which can be classified as fixed-priority scheduling (e.g. rate-monotonic scheduling, deadline monotonic scheduling) and dynamic priority scheduling (e.g. earliest-deadline first scheduling, least laxity scheduling). Multiprocessor scheduling can be further classified as partitioned scheduling (each task is allocated to a processor and no migration is allowed), global scheduling (a single job can migrate to and execute on different processors), or hybrid.

Scheduling of data-flow graphs has also been extensively studied in the past decades. Static-periodic scheduling is the main scheduling approach, which consists in infinitely repeating a firing sequence of actors. This problem has been addressed with respect to many performance criteria: throughput maximisation (Throughput analysis of synchronous data-flow graphs. Ghamarian, A.H. et al. Application of Concurrency to System Design. IEEE, 2006), latency minimisation (Latency minimization for synchronous data flow graphs. A. H. Ghamarian, et al. Conference on Digital System Design Architectures, Methods and Tools. Euromicro, 2007.), buffer minimisation (Minimal memory schedules for data-flow networks. M. Cubric and P. Panangaden. International Conference on Concurrency Theory. Springer, 1993.), code size minimisation (Looped schedules for dataflow descriptions of multirate signal processing algorithms. S. S. Bhattacharyya and E. A. Lee. Journal of Formal Methods in System Design. Kluwer, 1994.), etc. Recently, real-time dynamic scheduling (fixed-priority and earliest-deadline first scheduling) of data-flow graphs has been addressed where actors are mapped to periodic real-time tasks and existing schedulability tests are adapted to synthesise the timing characteristics of actors (Affine data-flow graphs for the synthesis of hard real-time applications. A. Bouakaz, J.-P. Talpin, and J. Vitek. International Conference on Application of Concurrency to System Design. IEEE Press, 2012.) (Hard-real-time scheduling of data-dependent tasks in embedded streaming applications. M. Bamakhrama and T. Stefanov. International Conference on Embedded Software. ACM, 2011.)