14th IEEE International Conference on Embedded and Real-time by Institute of Electrical and Electronics Engineers

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Theorem 1 Computing the earliest completion time of a given divisible workload of size σ on a cluster with parameters Cm and Cp , and n identical processors with (nondecreasing) available times r1 , r2 , . . , rn , is equivalent to solving the linear programming problem given in Figure 4. [4] L. Khachiyan. A polynomial algorithm in linear programming. Dokklady Akademiia Nauk SSSR, 244:1093–1096, 1979. [5] X. Lin, Y. Lu, J. Deogun, and S. Goddard. Real-time divisible load scheduling for cluster computing.

Deadline-based scheduling of divisible real-time loads. In Proceedings of the ICSA International Conference on Parallel and Distributed Computing Systems, Las Vegas, Nevada, September 2007. ξ ← ξ1 [2] G. B. Dantzig. Linear Programming and Extensions. Princeton University Press, 1963. constitutes a feasible solution to the LP. We now present our main result in this section, demonstrating the equivalence of scheduling to minimize completion time to Linear Programming. [3] N. Karmakar. A new polynomial-time algorithm for linear programming.

USA Abstract In [6, 8], Lin et al. extended DLT to apply to divisible real-time jobs – divisible jobs with associated deadlines and the requirement that a job complete by its deadline in order to be useful. Among other results, they obtained elegant solutions to the following two problems: Recent research in real-time divisible load theory (RT-DLT) has addressed the problem of distributing arbitrarily parallelizable real-time workloads among processors which become available at different instants in the future.

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