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Speed scaling for a tandem server setting is considered, where there is aseries of servers, and each job has to be processed by each of the servers insequence. Servers have a variable speed, their power consumption being a convexincreasing function of the speed. We consider the worst case setting as well asthe stochastic setting. In the worst case setting, the jobs are assumed to beof unit size with arbitrary (possibly adversarially determined) arrivalinstants. For this problem, we devise an online speed scaling algorithm that isconstant competitive with respect to the optimal offline algorithm that hasnon-causal information. The proposed algorithm, at all times, uses the samespeed on all active servers, such that the total power consumption equals thenumber of outstanding jobs. In the stochastic setting, we consider a moregeneral tandem network, with a parallel bank of servers at each stage. In thissetting, we show that random routing with a simple gated static speed selectionis constant competitive. In both cases, the competitive ratio depends only onthe power functions, and is independent of the workload and the number ofservers.

Speed Scaling with Tandem Servers