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The classic Earliest Deadline First (EDF) algorithm is widely studied and used due to its simplicity and strong theoretical performance, but has not been rigorously analyzed for systems where jobs may execute critical sections protected by shared locks. Analyzing such systems is often challenging due to unpredictable delays caused by contention. In this paper, we propose a straightforward generalization of EDF, called EDF-Block. In this generalization, the critical sections are executed non-preemptively, but scheduling and lock acquisition priorities are based on EDF. We establish lower bounds on the speed augmentation required for any non-clairvoyant scheduler (EDF-Block is an example of non-clairvoyant schedulers) and for EDF-Block, showing that EDF-Block requires at least 4.11× speed augmentation for jobs and 4× for tasks. We then provide an upper bound analysis, demonstrating that EDF-Block requires speedup of at most 6 to schedule all feasible job and task sets. 

The Conditional DAG (CDAG) task model is used for modeling multiprocessor real-time systems containing conditional expressions for which outcomes are not known prior to their evaluation. Feasibility analysis for CDAG tasks upon multiprocessor platforms is shown to be complete for the complexity classpspace; assumingnp≠pspace, this result rules out the use of Integer Linear Programming solvers for solving this problem efficiently. It is further shown that there can be no pseudo-polynomial time algorithm that solves this problem unlessp=pspace.