Optimal Sleeping Mechanism for Multiple Servers With MMPP-Based Bursty Traffic Arrival

A 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 that the optimal structure of such a sleeping 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 letter 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.