In this paper, we consider a multiple-access channel, where multiple users equipped with energy harvesting batteries communicate to an access point. To avoid consuming extra energy on competition for the channel, the users are supposed to share the channel via time division multiple access (TDMA). In many existing works, it is commonly assumed that the users' energy harvesting processes and storage status are known to all the users before transmissions. In practice, such knowledge may not be readily available. To avoid excessive overhead for real-time information exchange, we consider the scenario where the users schedule their individual transmissions according to the users' statistical energy harvesting profiles. We first study the optimal transmission scheme in the case where each node has an infinite-capacity battery. By optimization theory, we show that, to maximize the average system throughput, all the users should transmit at an identical optimal power, which solely depends on the energy harvesting rate per time slot. We then study the equal-power TDMA scheme in the case where each node is equipped with a battery of finite capacity. The system is formulated as a polling system consisting of multiple energy queues and one server. By the Markov chain modeling method, we derive the performance of equal-power TDMA in this case, in terms of the energy loss ratio and average system throughput. In addition, we develop an algorithm to efficiently compute the optimal transmission power in the finite-capacity battery case. We also consider an equal-time TDMA scheme, which assigns equal-length subslots to each user, and analyze its system performance. It is found that equal-power TDMA always outperforms equal-time TDMA in the infinite-capacity battery case, whereas equal-time TDMA exhibits compatible or even slightly better performance in some scenarios when the batteries have finite capacities.