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This paper presents a necessary and sufficient schedulability condition for determining whether a task will satisfy its period and precedences constraints when some tasks have already been scheduled. Tasks we are dealing with are non-preemptive and the periods considered here are strict. 1 Introduction Hard Real-Time preserves temporal and functional feasibility. Hard real-time system scheduling has been concerned with providing guarantees for temporal feasibility of task execution in all anticipated situations.

Goddard. Real-time divisible load scheduling for cluster computing. Technical Report UNL-CSE-2006-0016, Department of Computer Science and Engineering, The University of Nebraska at Lincoln, 2006. Proof Sketch: It immediately follows from Lemma 1 and Lemma 2 that the smallest value of ξ satisfying the LP in Figure 4 is exactly the desired earliest completion time. As a parenthetical side-note, we observe that this LP is easily modified to compute the earliest completion time upon more general heterogeneous platforms as well, in which there may be a different Cmi and a different Cpi associated with the data-communication and computing capacity of each processor Pi .

By assigning a workload σαi to the i’th processor, it immediately follows from the construction of the LP that the total workload is assigned to the n processors. Furthermore ξo , the value of ξ in the feasible solution, clearly represents an upper bound on the completion time of the schedule. The constraints that must be satisfied by these variables are as follows: 1. , the αi ’s must sum to 1. This is represented by Inequality (1) of the LP in Figure 4. Lemma 2 Given a schedule for a workload of size σ with completion-time ξ1 that there is a feasible solution to the LP in Figure 4 that assigns the variable ξ the value ξ1 .

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