An Interval Algebra for Multiprocessor Resource Allocation

This paper presents an interval algebra created specifically to evaluate timing properties of multiprocessor systems. It models the application load as intervals, and considers allocation and scheduling as algebraic operations over those intervals, aiming to analyse the impact of resource allocation decisions on application response times or schedulability. The theoretical background is introduced informally, followed by the description of a reference implementation of the interval algebra in C++, aiming to appeal to the design practitioner rather than the formalist. Examples of the usage of the proposed algebra are also provided, showing its applicability to the performance evaluation of industrial systems implemented over bus-based and Network-on-Chip multiprocessor platforms. A particular design flow is highlighted, where the interval algebra is used as a fitness function in a genetic algorithm tailored to optimise resource allocation in hard real-time multiprocessors.