Exact Analysis of ZSRM Mixed-Criticality Scheduling of Sporadic Tasks

Zero-Slack Rate-Monotonic (ZSRM) is a family of mixed-criticality schedulers which are based on fixed-priority preemptive scheduling. One scheduler (which we call ZSRMS) [5] works as follows: a job J is suspended at time t if at time t there is a higher-criticality job J ′ that has not finished and t minus the arrival time of J ′ exceeds a pertask configurable parameter (which we call zero-slack offset). ZSRM-S has two advantages compared to other mixed-criticality schedulers: (i) adaptation is local; i.e., there is no system-wide mode change needed and (ii) resumption is simple and natural. ZSRM-S has one drawback [7]: a high-criticality job J ′ can suffer from interference from a low-criticality job J that resumed after being suspended by another high-criticality job J ′′ (carry-in). Therefore, a variant of ZSRM (which we call ZSRM-SE) has been proposed [6]; it uses an enforcement mechanism to avoid carry-in. With ZSRM-SE, if a high-criticality job causes a low-criticality job to suspend and the high-criticality job has performed more execution than a certain bound then the low-criticality job shall not resume. We consider constrained-deadline sporadic tasks scheduled by ZSRM-S and present an exact schedulability test which solves a Mixed-Integer Linear Program (MILP). We also present that result for ZSRM-SE.