A time-slotted multiple access wireless system with N transmitting nodes, each equipped with an energy harvesting (EH) device and a rechargeable battery of finite capacity, is studied. The energy arrival process at each node is modeled as an independent two-state Markov process, such that a node either harvests one unit of energy, or none, at each time slot (TS). The access point (AP) schedules a subset of K nodes to transmit over K orthogonal channels at each TS. The maximum total throughput is studied for a backlogged system without the knowledge of the EH processes and nodes' battery states at the AP. The problem is identified as a partially observable Markov decision process, and the optimal policy for the general model is studied numerically. Under certain assumptions regarding the EH processes and the battery sizes, the optimal scheduling policy is characterized explicitly, and is shown to be myopic.