A single-hop network where a fusion center (FC) collects data from a set of energy harvesting nodes is considered. If a node that is scheduled has data and sufficient energy, it makes a successful transmission. Otherwise, the channel allocated to the node remains idle. The goal is to make efficient use of channel resources in order to either (1) use all the energy that is harvested by nodes, or (2) stabilize all data buffers. In the absence of feedback from nodes about hullers or battery states, or prior knowledge of the statistics of energy harvest and data arrival processes, this is a Restless Multi-Armed Bandit (RMAB) problem. Despite the hardness of RMAB problems in general, a simple randomized policy achieves near opthnality for this problem under a broad class of arrival processes for unlimited battery capacity. Moreover, there is almost no loss of optimality under a reasonable-sized finite battery assumption.