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Real-time dynamic workload consists of tasks that can arbitrarily join and leave the system at run-time. To avoid incurring deadline misses, tasks that request to join the system must pass an admission test, which has to cope with potential scheduling transients originated by the residual effect of the tasks that previously left the system. This phenomenon may require some tasks to suffer an admission delay before being accepted for execution. This paper focuses on uniprocessor earliest-deadline first (EDF) scheduling with constrained deadlines and explicitly considers methods for handling scheduling transients in the presence of dynamic real-time workload. A generalized analysis framework is first presented to overcome several limitations of the existing approaches (including the support for overlapping transients), and is then used to derive methods for computing bounds on the admission delays incurred by tasks. Building on such results, an on-line protocol is proposed to handle the admission control of a dynamic workload, which also comes with a variant that can execute in polynomial time to favor its practical application. Furthermore, the paper shows how the presented analysis can be used off-line for analyzing mode-changes among static task sets. Experimental results are finally presented to evaluate the proposed algorithms.