In the auto_pid mode, we use a PID controller to calculate the sleep time for the DefragmenterTask. 

The sleep time can vary between defragmenter_auto_min_sleep (default: 0.6s) and 

defragmenter_auto_max_sleep (default: 10s). We calculate the output of the PID controller and subtract that from the max sleep time.

The input to the PID controller is the current scoredFragmentation. The PID controller internally uses an "error value" which is the difference between the input and the set point (scoredFragmentation, default 7%). The error is essentially how far away we are from the target fragmentation of 7%. 

The PID controller has 3 terms, of which we use 2 (one is set to 0):

• The proportional term, which is the error multiplied by a constant factor P

• The integral term (an accumulation of all errors, multiplied by a constant factor I)

The PID controller output is recalculated every defragmenter_auto_pid_dt (default: 30 seconds). 

The P is currently set to 0.3. For 30% scored fragmentation, we'd get an proportional term 0.3 x 0.3 = 0.09s of sleep reduction. So even at 30% fragmentation, the PID controller would start running every 9.91s, and any other adjustment to sleep time would come from the integral term (accumulated over time). 

This might not be the ideal behaviour in cases of bulk expiration/deletion workloads where we get a sudden increase in memory fragmentation and we might want a more immediate, proportional, response.