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We consider garbage collection (GC) in dynamic real-time systems. We consider the time-based GC approach of running the collector as a separate, concurrent thread, and focus on real-time scheduling to obtain assurances on mutator timing behavior, while ensuring that memory is never exhausted. We present a scheduling algorithm called GCUA. The algorithm considers mutator activities that are subject to time/utility function time constraints, variable execution time demands, the unimodal arbitrary arrival model that allows a strong adversary, and resource overloads. We establish several properties of GCUA including probabilistically-satisfied utility lower bounds for each mutator activity, a lower bound on the system-wide total accrued utility, bounded sensitivity for the assurances to variations in mutator execution time demand estimates, and no memory exhaustion at all times. Our simulation experiments validate our analytical results and confirm the algorithm's effectiveness and superiority.