  We consider energy minimization for data-intensive applications run on large
number of servers, for given performance guarantees. We consider a system,
where each incoming application is sent to a set of servers, and is considered
to be completed if a subset of them finish serving it. We consider a simple
case when each server core has two speed levels, where the higher speed can be
achieved by higher power for each core independently. The core selects one of
the two speeds probabilistically for each incoming application request. We
model arrival of application requests by a Poisson process, and random service
time at the server with independent exponential random variables. Our model and
analysis generalizes to today's state-of-the-art in CPU energy management where
each core can independently select a speed level from a set of supported speeds
and corresponding voltages. The performance metrics under consideration are the
mean number of applications in the system and the average energy expenditure.
We first provide a tight approximation to study this previously intractable
problem and derive closed form approximate expressions for the performance
metrics when service times are exponentially distributed. Next, we study the
trade-off between the approximate mean number of applications and energy
expenditure in terms of the switching probability.
