  An important fundamental problem in green communications and networking is
the operation of servers (routers or base stations) with sleeping mechanism to
optimize energy-delay tradeoffs. This problem is very challenging when
considering realistic bursty, non-Poisson traffic. We prove for the first time
the optimal structure of such a sleep mechanism for multiple servers when the
arrival of jobs is modeled by a bursty Markov-modulated Poisson process (MMPP).
It is shown that the optimal operation, which determines the number of active
(or sleeping) servers dynamically, is hysteretic and monotone, and hence it is
a queue-threshold-based policy. This work settles a conjecture in the
literature that the optimal sleeping mechanism for a single server with
interrupted Poisson arrival process, which can be treated as a special case of
MMPP, is queue-threshold-based. The exact thresholds are given by numerically
solving the Markov decision process.
