Multiprocessor extensions to real-time calculus

Many embedded platforms consist of a heterogeneous collection of processing elements, memory modules, and communication subsystems. These components often implement different scheduling/arbitration policies, have different interfaces, and are supplied by different vendors. Hence, compositional techniques for modeling and analyzing such platforms are of interest. In prior work, the real-time calculus framework has proven to be very effective in this regard. However, real-time calculus has heretofore been limited to systems with uniprocessor processing elements, which is a serious impediment given the advent of multicore technologies. In this paper, a two-step approach is proposed that allows the power of real-time calculus to be applied in globally-scheduled multiprocessor systems: first, assuming that job response-time bounds are given, determine whether these bounds are met; second, using these bounds, determine the resulting residual processor supply and streams of job completion events using formalisms from real-time calculus. For this methodology to be applied in settings where response-time bounds are not specified, such bounds must be determined. Closed-form expressions for calculating such response-time bounds are presented for a large family of fixed-job-priority schedulers. We have also applied the developed analysis framework in a case study.