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Unformatted text preview: period, there is at least one job
available, i.e., for each t, there is at least one i with Ai ≤ t and Di ≥ t. In period t, the processor allocates its eﬀort across the n jobs as θt , where 1T θt = 1, θt 0. Here
θti (the ith component of θt ) gives the fraction of the processor eﬀort devoted to job i in period t.
Respecting the availability and deadline constraints requires that θti = 0 for t < Ai or t > Di . To
complete the jobs we must have
t =A i θti st ≥ Wi , 140 i = 1, . . . , n. (a) Formulate the problem of choosing the speeds s1 , . . . , sT , and the allocations θ1 , . . . , θT , in
order to minimize the total energy E , as a convex optimization problem. The problem data
are S min , S max , R, φ, and the job data, Ai , Di , Wi , i = 1, . . . , n. Be sure to justify any change
of variables, or introduction of new variables, that you use in your formulation.
(b) Carry out your method on the problem instance described in proc_sched_data.m, with
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- Fall '13
- The Aeneid