Section: Research Program

Scheduling Theory

Based on sound formalization of time and CPS architectures, real-time scheduling theory provides tools for predicting the timing behavior 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.

The literature about real-time scheduling (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. Scheduling of data-flow graphs has also been extensively studied in the past decades.

A milestone in this prospect is the development of abstract affine scheduling techniques (Buffer minimization in EDF scheduling of data-flow graphs. A. Bouakaz and J.-P. Talpin. LCTES, ACM, 2013.). It consists, first, of approximating task communication patterns (e.g. between Safety-Critical Java threads) using cyclo-static data-flow graphs and affine functions. Then, it uses state of the art ILP techniques to find optimal schedules and to concretize them as real-time schedules in the program implementations (ADFG for the synthesis of hard real-time applications. A. Bouakaz, J.-P. Talpin, J. Vitek. ACSD, IEEE, June 2012.) (Design of SCJ Level 1 Applications Using Affine Abstract Clocks. A. Bouakaz and J.-P. Talpin. SCOPES, ACM, 2013.).

Abstract scheduling, or the use of abstraction and refinement techniques in scheduling borrowed to the theory of abstract interpretation (La vérification de programmes par interprétation abstraite. P. Cousot. Séminaire au Collège de France, 2008.) is a promising development toward tooled methodologies to orchestrate thousands of heterogeneous hardware/software blocks on modern CPS architectures (just consider modern cars or aircrafts). It is an issue that simply defies the state of the art and known bounds of complexity theory in the field, and consequently requires a particular address.

To develop the underlying theory of this promising research topic, we first need to deepen the theoretical foundation to establish links between scheduling analysis and abstract interpretation. A theory of time systems would offer the ideal framework to pursue this development. It amounts to representing scheduling constraints, inferred from programs, as types or contract properties. It allows to formalize the target time model of the scheduler (the architecture, its middle-ware, its real-time system) and defines the basic concepts to verify assumptions made in one with promises offered by the other: contract verification or, in this case, synthesis.