Time-Reversibility for Real-Time Scheduling on Multiprocessor Systems

The real-time systems community has widely studied real-time scheduling, focusing on how to guarantee schedulability (i.e., timely execution) of a set of real-time tasks. However, there still exist a number of task sets that are actually schedulable by a target scheduling algorithm, but proven schedulable by none of existing schedulability tests, especially on a multiprocessor. In this paper, we propose a new paradigm for real-time scheduling, called time-reversibility, which views real-time scheduling under a change in the sign of time, and present how to utilize the paradigm for schedulability improvement. To this end, we first define the notion of a time-reversed scheduling algorithm and a time-reversible schedulability test; for example, the time-reversed scheduling algorithm against Earliest Deadline First (EDF) is Latest Release-time First (LRF). Then, we develop time-reversibility theories for schedulability improvement, which utilizes the definitions so as to compose schedulability. Finally, we generalize the definitions and theories to job-level dynamic-priority scheduling in which the priority of a job may vary with time, such as Earliest Deadline first until Zero Laxity (EDZL). Specifically, we accommodate time-varying job parameters to the time-reversibility definitions, and adapt the time-reversibility theories for the additional necessary deadline-miss conditions specialized for a class of job-level dynamic-priority scheduling algorithms. As case studies, we demonstrate that the time-reversibility theories help to find up to 13.6 percent additional EDF- and EDZL-schedulable task sets.