Limiting the number of unexpected wakeups in a computer system implementing a power-saving preemptive wakeup method from historical data

Dynamically reducing power consumption by a processor in a computer system by determining a maximum number of times (token count) that the processor can incur a start-up delay after being placed into a low-power mode during a token period of time when executing a task for a token period of time. The processor may be placed into the low-power mode while executing the task in response to an idle indicator only if a current value of the token count assigned to the task is greater than zero. The current value of the token count is decremented each time the processor incurs a start-up delay in response to being awakened from the low-power mode. The current token count is reset to match the assigned token count at the end of each token period. Furthermore, wakeup may be anticipated to allow the processor to be awakened preemptively.