Optimal Operation of a Green Server with Bursty Traffic

To reduce the energy consumption of various information and communication systems, sleeping mechanism design is considered to be a key problem. Prior work has derived optimal single server sleeping policies only for non-bursty, memoryless Poisson arrivals. In this paper, for the first time, we derive the optimal sleep operation for a single server facing bursty traffic arrivals. Specifically, we model job arrivals as a discrete-time interrupted Bernoulli process (IBP) which models bursty traffic arrivals. Key factors including the switching and working energy consumption costs as well as a delay penalty are accounted for in our model. As the arrival process state (busy or quiet) cannot be directly observed by the server, we formulate the problem as a POMDP (partially observable Markov decision process), and show that it can be tractably solved as a belief-MDP by considering the time interval since the last observed arrival t. We prove that the optimal sleeping policy is hysteretic and the numerical results reveal that the optimal policy is a t-based two-threshold policy, where the sleeping thresholds change with t. The simulation results show that our policy outperforms the previously derived Poisson-optimal policy and that the system cost decreases with the burstiness of traffic.