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We consider Discrete Event Systems involving tasks with real-time constraints and seek to control processing times so as to minimize a cost function subject to each task meeting its own constraint. When tasks are processed over a single stage, it has been shown that there are structural properties of the optimal state trajectory that lead to very efficient solutions of such problems. When tasks are processed over multiple stages and are subject to end-to-end real-time constraints, thesedoi:10.1109/tac.2008.2009572 fatcat:crat4z3ijvd7xjey4ehrzakpcu