This paper focuses on the statistical analysis of an adaptive real-time feedback scheduling technique based on imprecise computation. We consider two-version tasks made of a mandatory and an optional part to be scheduled according to a feedback control rate-monotonic algorithm. A Proportional-Integral-Derivative (PID) control action provides the feedback strategy for deciding about the execution or rejection of the optional sub-tasks. By modelling the task execution times as random variables, we compute the probability density of the CPU utilization and derive conditions on PID parameters guaranteeing the stability of the overall system around a desired level of CPU utilization. This allows us to highlight the tasks statistics and the scheduling parameters that affect critically stability. The analysis is developed by first exploiting a number of simplifying assumptions that are progressively removed. The main results are also demonstrated through monte-carlo simulations of the scheduling algorithm.
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