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

By Institute of Electrical and Electronics Engineers

ISBN-10: 0769533493

ISBN-13: 9780769533490

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This is represented by the n Inequality (5)’s of the LP in Figure 4. The following two lemmas formally assert that the problem of obtaining a feasible solution4 to the LP in Figure 4 is equivalent to the problem of obtaining a schedule for the workload on the n processors. • The n variables {α1 , α2 , . . , αn }, with αi denoting the fraction of the workload to be assigned to the i’th processor; • The n variables {s1 , s2 , . . , sn }, with si denoting the time-instant at which the head node begins transmitting data to the i’th processor; and Lemma 1 Given feasible solution to the LP in Figure 4 that assigns value ξo to the variable ξ, we can construct a schedule for a workload of size σwith completion-time ξo .

This is the later of its ready time and the time at which Pi has finished receiving data (and the head-node is thus able to commence datatransmission to Pi+1 ). This computation of si+1 is done in line 6. Lines 7 and 8 update the values of the fraction of the workload that has already been allocated, and the index of the processor to be considered next. Properties. It should be evident that the schedule generated by this algorithm is both correct — the job will indeed complete by its deadline on the computed number of processors, according to the schedule that is implicitly determined by the algorithm, and optimal — the number of processors used is the minimum possible.

Rn upon which to execute it, what is the earliest time at which σ can complete execution? 2, the approach in [9] is via the abstraction of heterogeneous clusters — clusters in which all n processors become available at the same instant but different processors may have different computing capacities. Specifically, the algorithm in [9] assumes that all n processors become available at time-instant rn and the i’th processor Pi takes Cpi × x time to process x units of data, where the Cpi ’s are as given in Equation 4 (reproduced below): ξ(σ, n) Cpi = ξ(σ, n) + rn − ri Cm α1 σ + Cp1 α1 σ = Cm (α1 + α2 )σ + Cp2 α2 Solving, we obtain the values α1 = 101/162 and α2 = 61/162.

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