This paper develops and evaluates an accumulate-then-transmit framework for multi-user scheduling in a full-duplex (FD) wireless-powered Internet-of-Things system, consisting of multiple energy harvesting (EH) IoT devices (IoDs) and one FD hybrid access point (HAP). All IoDs have no embedded energy supply and thus need to perform EH before transmitting their data to the HAP. Thanks to its FD capability, the HAP can simultaneously receive data uplink and broadcast energy-bearing signals downlink to charge IoDs. The instantaneous channel information is assumed unavailable throughout this paper. To maximize the system average throughput, we design a new throughput-oriented scheduling scheme, in which a single IoD with the maximum weighted residual energy is selected to transmit information to the HAP, while the other IoDs harvest and accumulate energy from the signals broadcast by the HAP. However, similar to most of the existing throughput-oriented schemes, the proposed throughout-oriented scheme also leads to unfair inter-user throughput because IoDs with better channel performance will be granted more transmission opportunities. To strike a balance between the system throughput and user fairness, we then propose a fairness-oriented scheduling scheme based on the normalized accumulated energy. To evaluate the system performance, we model the dynamic charging/discharging processes of each IoD as a finite-state Markov Chain. Analytical expressions of the system outage probability and average throughput are derived over Rician fading channels for both proposed schemes. Simulation results validate the performance analysis and demonstrate the performance superiority of both proposed schemes over the existing schemes.