For simplicity of exposition, consider two performance levels of
the system from a pool of performance levels for a given user
delay. Let denote the user delay,
the system power
consumption for the higher performance level, and
that for
the lower one. The energy consumption for the system during the
user delay without DPM/DVS will be
Suppose we can predict the user delay perfectly, change the system
performance to the lower one after the system finishes responding,
and change it back to the higher one right before the next user
input. Let and
denote the performance level
transition power, and
and
denote the delay for
higher-to-lower and lower-to-higher transitions, respectively. We
also assume that
. Then the energy consumption
for the system during the user delay with such a performance-level
transition is given by
If the system changes the performance level upon a user input, we
can obtain the energy saving through a similar analysis as
If the delay models are used to predict as
and the system
is put into the low performance level if
and
put back into the high performance level right before the
predicted user delay elapses, we have
Given the two performance levels, the energy saving ratio is only
dependent on the user delay and prediction error. Comparing
with
, we can see that using predicted user delay is
actually more energy-efficient if
is large compared with
user delay prediction errors. Note that both
and
can be negative, which means energy consumption can be actually
increased if performance-level transition is not properly done.