<p>Fog computing has emerged as a promising computing infrastructure, bridging the gap between centralized cloud services and the data generation layer. The resource constrained nature of fog computing layer necessitates an effective and efficient resource management strategies to maximize the resource utilization and enhance overall performance. Efficient resource management in fog–cloud computing environments presents substantial challenges, especially due to the heterogeneity of devices, and dynamicity involved in the workloads. To address and overcome the aforementioned challenges, this article proposes an adaptive queueing models which improve the system performance and scalability. It introduces an analytical framework based on a multi-server finite queue model (M/M/r/K). The multi-server queue model facilitates service collaboration among all available fog nodes, enabling efficient processing of IoT tasks submitted by users. It presents a detailed system architecture and mathematical model for the proposed three-layer fog-cloud computing system, which includes IoT devices, fog computing nodes, and cloud servers. Experimental results demonstrate the effectiveness of the proposed model through various performance metrics and graphical representations, highlighting the variability of arithmetic outputs under different conditions. The present research underscores the potential of adaptive queueing models in optimizing IoT application performance in fog-cloud computing environments, paving the way for more robust and scalable resource management strategies. The experimental output demonstrates that increasing the buffer size reduces the blocking probability by up to 95% in light traffic, while delay handling improves by 400–550% and the immediate service probability drops by nearly 100% under heavy load conditions, providing clear guidance for effective buffer sizing in latency-sensitive applications.</p>