A computer-implemented method of allocating power to computing machines, the method comprising: receiving, at a computing allocation system (610; 706) and from a plurality of computing machines (602, 604, 606; 702, 704, 706), electronic communications (612, 712) wherein each electronic communication includes: i) a power value that represents a first request for a first power allotment that is expected to be used by a computing machine during a predetermined period of time; and ii) one or more first priority values that represent priorities of one or more tasks expected to be executed by the computing machine during the predetermined period of time; determining, at the computing allocation system, using a scoring function, a plurality of scores associated with the plurality of computing machines, using the priority values for the plurality of computing machines as inputs to the scoring function; granting, with the computing allocation system and to the plurality of computing machines, power allotments for the plurality of computing machines in accordance with determined scores for the plurality of computing machines; sending an electronic communications (626, 734) to the plurality of computing machines, the communications formatted to cause particular ones of the plurality of computing machines to take a power allotment in accordance with their granted allotments; maintaining, at the computing allocation system, an electronic reserve list of computing machines that are each operating below a respective power limit assigned to the respective computing machine; and sending a subsequent communications (732, 738) to the plurality of computing machines from the electronic reserve list, the subsequent communications providing a new power limit for particular ones of the computing machines, the new power limit being lower than the power limit previously assigned to particular ones of the computing machines wherein a difference between the power limit previously assigned to a particular computing machine and a new power limit for the particular computing machine is substantially equal to a power allotment granted to a computing machine associated with a top score of the scores; wherein the computing allocation system controls power allocation to a plurality of computing machines repeatedly at a periodic frequency. receiving, at a computing allocation system (610; 706) and from a plurality of computing machines (602, 604, 606; 702, 704, 706), electronic communications (612, 712) wherein each electronic communication includes: i) a power value that represents a first request for a first power allotment that is expected to be used by a computing machine during a predetermined period of time; and ii) one or more first priority values that represent priorities of one or more tasks expected to be executed by the computing machine during the predetermined period of time; determining, at the computing allocation system, using a scoring function, a plurality of scores associated with the plurality of computing machines, using the priority values for the plurality of computing machines as inputs to the scoring function; granting, with the computing allocation system and to the plurality of computing machines, power allotments for the plurality of computing machines in accordance with determined scores for the plurality of computing machines; sending an electronic communications (626, 734) to the plurality of computing machines, the communications formatted to cause particular ones of the plurality of computing machines to take a power allotment in accordance with their granted allotments; maintaining, at the computing allocation system, an electronic reserve list of computing machines that are each operating below a respective power limit assigned to the respective computing machine; and sending a subsequent communications (732, 738) to the plurality of computing machines from the electronic reserve list, the subsequent communications providing a new power limit for particular ones of the computing machines, the new power limit being lower than the power limit previously assigned to particular ones of the computing machines wherein a difference between the power limit previously assigned to a particular computing machine and a new power limit for the particular computing machine is substantially equal to a power allotment granted to a computing machine associated with a top score of the scores; wherein the computing allocation system controls power allocation to a plurality of computing machines repeatedly at a periodic frequency.