In connection with the global decarbonization program until 2050, the transition to clean green energy, the growth of the Internet of Things (IoT) number, and energy distribution and control across the load are being raised. The relevance of the work is confirmed that there has been significant growth of the industrial IoT for years, significantly changing the mechanism of industrial enterprise management programs. The object of the research is the IoT device control system for efficient energy distribution using a Queuing Theory, namely the Teletraffic Theory. The novelty of the work is that the Teletraffic Theory, which deals with the mathematical modeling and analysis of traffic patterns in communication networks, can be explicitly applied to IoT device control. The authors developed a mathematical model of IoT control using the Teletraffic Theory and, based on it, created a simulation model of a network router and a transition schedule in the "GPSS World" software. The obtained results of the work were 16 states and a balance equation in which all probabilities were found. Probabilities were used to calculate nodes and network characteristics. 100,000 requests from IoT devices coming to two routers were simulated. The study results showed that the first node's load is 63.2 % with an average processing time per transaction of M=1.436 sec., and the load of the second node is 32 % with M=0.914 sec. The created network router model worked with minimal losses during transactions. Accordingly, the IoT control system developed in this study has shown its effectiveness and is applicable for practical use in controlling IoT devices in Smart Grid. It is planned to research the possibility of using Teletraffic Theory in energy distribution control systems in Smart Grids