SummaryThe cloud computing systems, such as the Internet of Things (IoT), are usually introduced with a three‐layer architecture (IoT‐Fog‐Cloud) for the task offloading that is a solution to compensate for resource constraints in these systems. Offloading at the right location is the most significant challenge in this field. It is more appropriate to offload tasks to fog than to cloud based on power and performance metrics, but its resources are more limited than the resources of the cloud. This paper tries to optimize these factors in the fog by specifying the number of usable servers in the fog. For this purpose, we model a fog computing system using the queueing theory. Furthermore, binary search and reinforcement learning algorithms are proposed to determine the minimum number of servers with the lowest power consumption. We evaluate the cost of the fog in different scenarios. By solving the model, we find that the proposed dispatching policy is very flexible and outperformed the known policies by up to 31% and in no case is it worse than either of them, and the overall offloading cost increases when fog rejects tasks with a high probability. Our offloading method is more effective than running all fog servers simultaneously, based on simulation results. It is evident from the similarities between the simulation results and those derived from the analytical method that the model and results are valid.