Systems, apparatuses, methods, and software that implement power budget allocation optimization algorithms in multi-processor systems, such as server farms. The algorithms are derived from a queuing theoretic model that minimizes the mean response time of the system to the jobs in the workload while accounting for a variety of factors. These factors include, but are not necessarily limited to, the type of power (frequency) scaling mechanism(s) available within the processors in the system, the power-to-frequency relationship(s) of the processors for the scaling mechanism(s) available, whether or not the system is an open or closed loop system, the arrival rate of jobs incoming into the system, the number of jobs within the system, and the type of workload being processed.