Open loop optimal control of base station activation for green networks

In recent years there has been an increasing awareness that the deployment as well as utilization of new information technology may have some negative ecological impact. This includes awareness to energy consumption which could have negative consequences on the environment. In recent years, it was suggested to increase energy saving by deactivating base stations during periods in which the traffic is expected to be low. In this paper we study the optimal deactivation policies, using recent tools from Multimodularity (which is the analog concept of convexity in optimization over integers). We consider two scenarios: In the first case, a central control derives the optimal open loop policies so as to maximize the expected throughput of the system given that at least a certain percentage of Base stations are deactivated (switched OFF). In the second case, we derive optimal open loop polices, which each base station can employ in a decentralized manner to minimize the average buffer occupancy cost when the fraction of time for which the BS station is deactivated (idle mode) is lower bounded. In both the cases, we show that the cost structure is Multimodular and characterize the structure of optimal policies.