Best-case response times and jitter analysis of real-time tasks with arbitrary deadlines

In this paper, we present and prove exact best-case response time and improved jitter analysis of real-time periodic tasks with activation jitter and arbitrary deadlines that are scheduled by means of fixed-priority pre-emptive scheduling. We illustrate the analysis by means of examples. Apart from having a value on its own whenever timing constraints include lower bounds on response times of a system to events, our novel analysis also allows for an improvement of existing end-to-end response time analysis in distributed systems, i.e. where the finalization of one task on a processor activates another task on another processor. Best-case and worst-case analysis for tasks with constrained deadlines have a dual nature. We present various witnesses of non-duality of best-case and worst-case analysis for tasks with arbitrary deadlines, illustrating that both our novel best-case analysis and its proof are not straightforward extensions of existing work.