The integration of computing containers into Internet of Things (IoT) systems created a lot of challenges and opportunities in the connected devices and cloud computing industries. In this paper, the author proposed a mathematical modeling method to analyze and optimize the deployment of computing containers into an IoT-based ecosystem. By implementing mathematical modeling techniques, such as queuing theory, optimization algorithms, and statistical analysis, we aim to address key concerns related to resource allocation, workload distribution, and performance optimization. Proposed models take the dynamic nature of an IoT system, considering factors such as real-time data streams and varying workloads for the satisfaction of scalability requirements. The author aids in identifying the optimal placement strategies for computing containers, ensuring efficient resource utilization and workload balancing across the IoT network.