The Internet of Healthcare Things (IoHT) consists of a wide variety of resource-restricted, heterogeneous, IoT-enabled, wearable/non-wearable medical equipment (things) that connect over the internet to transform traditional healthcare into a smart, connected, proactive, patient-centric healthcare system. The pivotal functions of the 6LoWPAN protocol stack enable comprehensive integration of such networks from wearable wireless sensor networks (W-WSN) to IoHT, as TCP/IP does not suffice the requirements of IoHT networks. As a result, the congestion in the IoHT network increases with a growing number of devices, resulting in loss of critical medical information due to buffer loss and channel loss, which is unacceptable. In this paper, we explored different applications of patient-centric IoHT architectures to draw a realistic resource-limited topological layout of IoHT for congestion estimation. After critically reviewing existing congestion schemes for 6LoWPANs, we proposed an effective buffer-loss estimation model based on the Queuing Theory to determine the number of packets lost at the node’s buffer. The buffer is modeled as an M/M/1/K Markov Chain Queue. The M/M/1/K Queue equilibrium equation is used to establish a relationship between the probabilities of the buffer being empty or completely filled. We derived the expressions for total buffer-loss probability and expected mean packet delay for the resource-constraint IoHT network. Furthermore, to validate the buffer-loss estimation, an analytical model is used to compare buffer-loss probabilities, the number of packets dropped at leaf/intermediate nodes and the number of packets successfully received at the local sink node. The results show a close correlation between both the models on varying values of the number of leaf nodes, buffer size, offered packet load and available channel capacity. Thus, in resource-restrictive IoHT, the proposed model performs better than two related works.