Fog computing brings computing infrastructure to the edge of the network. This enables resource-greedy real-time mobile applications by offloading them to the fog, which provides enough computing resources and reduces the response time in comparison with cloud computing-based solutions. In the paper, we analyze the two-parameter offloading mechanism that takes into account both the computing complexity and the data size to be transferred in case of offloading. We derive the cumulative distribution function of the response time in terms of Laplace-Stieltjes Transform. It is used for the analysis of the probability that the response time exceeds a predefined threshold, which is specified based on the type of application. © Springer Nature Switzerland AG 2020.