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A multiple server setting is considered, where each server has tunable speed,and increasing the speed incurs an energy cost. Jobs arrive to a single queue,and each job has two types of sub-tasks, map and reduce, and a {\bf precedence}constraint among them: any reduce task of a job can only be processed once allthe map tasks of the job have been completed. In addition to the schedulingproblem, i.e., which task to execute on which server, with tunable speed, anadditional decision variable is the choice of speed for each server, so as tominimize a linear combination of the sum of the flow times of jobs/tasks andthe total energy cost. The precedence constraints present new challenges forthe speed scaling problem with multiple servers, namely that the number oftasks that can be executed at any time may be small but the total number ofoutstanding tasks might be quite large. We present simple speed scalingalgorithms that are shown to have competitive ratios, that depend on the powercost function, and/or the ratio of the size of the largest task and theshortest reduce task, but not on the number of jobs, or the number of servers.

Speed Scaling On Parallel Servers with MapReduce Type Precedence Constraints