Mathematical Modeling and Statistical Evaluation of the Security–Performance Trade-Off in IoT Cloud Architectures: A Case Study of UBT Smart City

This paper presents a mathematical and statistical analysis of the security–performance trade-off in the context of the IoT Cloud architecture implemented at UBT Smart City. Through detailed modeling and real-world measurement data collected before and after the deployment of advanced security measures—such as VPN configuration, Network Security Groups (NSGs), Route Tables, and DDoS Protection—we quantify the impact of security on system performance. We propose a mathematical framework to evaluate the propagation delay of telemetry data through the system and employ queueing theory (M/M/1 model) to simulate the behavior of critical data processing services. Additionally, we perform hypothesis testing and statistical comparison to validate the significance of the observed performance changes. The results show an average delay increase of approximately 19% following the implementation of security mechanisms, highlighting the inevitable trade-off between enhanced security and operational speed. Finally, we introduce a multi-objective cost-delay function that can guide the selection of optimal security configurations by balancing latency and cost, providing a valuable tool for the future optimization of secure IoT infrastructures