Speed Scaling on Parallel Servers With MapReduce Type Precedence Constraints

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