Bounding execution resources for the task scheduling problem in cyber-physical systems

In designing and analyzing real-time systems, the central problem resides in finding a feasible schedule for a given task set, if one exists. A lot of research effort has been carried out in approaching the various aspects of task scheduling. While most results have been achieved for preemptive scheduling, the non-preemptive case has still room for improvement, due to its complexity. In addition, the widespread usage of cyber-physical systems (CPS) is putting real-time scheduling in the position to deal with new challenges, as additional (and sometimes particular) requirements are raised by such systems. This paper, which continues the previous work of the authors, introduces a new lower bound on the number of processing units that allows a feasible schedule of a task set for both preemptive and non-preemptive scheduling. As a specific CPS issue, the necessity of moving the processing units in space, which incurs additional time requirements, is considered. The single-instance case is first discussed, then the results are extended to the periodic case.