Speed Scaling with Multiple Servers Under A Sum Power Constraint
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The problem of scheduling jobs and choosing their respective speeds with multiple servers under a sum power constraint to minimize the flow time + energy is considered. This problem is a generalization of the flow time minimization problem with multiple unit-speed servers, when jobs can be parallelized, however, with a sub-linear, concave speedup function k^1/α, α>1 when allocated k servers, i.e., jobs experience diminishing returns from being allocated additional servers. When all jobs are available at time 0, we show that a very simple algorithm EQUI, that processes all available jobs at the same speed is (2-1/α) 2/(1-(1/α))-competitive, while in the general case, when jobs arrive over time, an LCFS based algorithm is shown to have a constant (dependent only on α) competitive ratio.
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