This article considers an Industrial Internet of Things (IIoT) scenario, where wireless devices embedded with sensors are deployed over an industrial machine, and transmit the measured data to a final gateway (GW) using Terahertz (THz) frequencies. To mitigate the path loss of such high frequencies, the GW is equipped with multiple radiating elements, thereby generating highly directive beams, while sensors have just one single radiating element for miniaturization purposes. In this scenario, we study the applicability of a slotted carrier sense multiple access with collision avoidance (CSMA/CA) from a mathematical perspective. The analytical model is validated via comparison with simulations, and the impact of different simplifying assumptions in shown. We also demonstrate the effectiveness of the CSMA/CA when compared to ALOHA, and we prove that propagation delays cannot be neglected at THz frequencies. © 2014 IEEE.