Abstract
Speed scaling for a network of servers represented by a directed acyclic graph is considered. Jobs arrive at a source server, with a specified destination server, and are defined to be complete once they are processed by all servers on any feasible path between the source and the corresponding destination. Each server has variable speed, with power consumption function P, a convex increasing function of the speed. The objective is to minimize the sum of the flow time (summed across jobs) and the energy consumed by all the servers, which depends on how jobs are routed, as well as how server speeds are set. Algorithms are derived for both the worst case and stochastic job arrivals setting, whose competitive ratio depends only on the power functions and path diversity in the network, but is independent of the workload.
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