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In this paper we consider the problem of mixed-criticality (MC) scheduling of implicit-deadline sporadic task systems on a homogenous multiprocessor platform. Focusing on dual-criticality systems, algorithms based on the fluid scheduling model have been proposed in the past. These algorithms use a dual-rate execution model for each high-criticality task depending on the system mode. Once the system switches to the high-criticality mode, the execution rates of such tasks are increased to meet their increased demand. Although these algorithms are speed-up optimal, they are unable to schedule several feasible dual-criticality task systems. This is because a single fixed execution rate for each high-criticality task after the mode switch is not efficient to handle the high variability in demand during the transition period immediately following the mode switch. This demand variability exists as long as the carry-over jobs of high-criticality tasks, that is jobs released before the mode switch, have not completed. Addressing this shortcoming, we propose a multi-rate fluid execution model for dual-criticality task systems in this paper. Under this model, high-criticality tasks are allocated varying execution rates in the transition period after the mode switch to efficiently handle the demand variability. We derive a sufficient schedulability test for the proposed model and show its dominance over the dual-rate fluid execution model. Further, we also present a speed-up optimal rate assignment strategy for the multi-rate model, and experimentally show that the proposed model outperforms all the existing MC scheduling algorithms with known speed-up bounds.