The efficient buffer space management in intermittently connected Internet of Things (IC-IoT) is of great importance for data delivery performance guarantee in such networks. This article considers two typical buffer space management policies for IC-IoT, i.e., buffer-space sharing (BS) and buffer-space allocation (BA). The BS policy allows the buffer space of each device to be fully shared by the exogenous packets and the packets from other devices, while the BA policy divides the buffer space into the source buffer and relay buffer for storing the two kinds of packets separately. With the help of the queueing theory and Markov chain theory, we develop a theoretical framework to capture the sophisticated queueing processes for the buffer space under either BS or BA policy, which enables the limiting distribution of the buffer occupation state to be determined. We then provide theoretical modeling for throughput and expected end-to-end delay to evaluate the fundamental performance of the IC-IoT under the BS and BA policies. Finally, extensive simulation and numerical results are presented to validate theoretical models and to demonstrate the effects of BS and BA policies on the IC-IoT performance.