The traditional Vestal's model of Mixed-Criticality (MC) systems was recently extended to Imprecise Mixed-Critical task model (IMC) to guarantee some minimum level of (degraded) service to the low-critical tasks even after the system switches to the high-critical behavior. This paper extends the IMC task model by associating specific Quality-of-Service (QoS) values with the low-critical tasks and proposes a fluid-based scheduling algorithm, called MCFQ, for such task model. The MCFQ algorithm allows some low-critical tasks to provide full service even during the high-critical behavior so that the QoS of the overall system is increased. To the best of our knowledge MCFQ is the first algorithm for IMC task sets considering multiprocessor platform and QoS values. By extending the recently proposed MC-Fluid and MCF fluid-based multiprocessor scheduling algorithms for IMC task model, empirical results show that MCFQ algorithm can significantly improve the QoS of the system in comparison to that of both MC-Fluid and MCF. In addition, the schedulability performance of MCFQ is very close to the optimal MC-Fluid algorithm. Finally, we prove that the MCFQ algorithm has a speedup bound of 4/3, which is optimal for IMC tasks.
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