Task offloading is one of the main concepts in fog computing which improves the system efficiency and decreases latency. Previously proposed models, such as exponential queue models, addressed the offloading models in a simple model. This study proposes a novel analytical model that examines batch queuing systems and the influence of batch size-dependent service time on system performance. Some of the system's properties are indicated using this model, and the correctness of the suggested model via numerical evaluations and simulations is shown. The evaluation results show that our proposed model provides acceptable accuracy and enables efficient task offloading, applied to fog computing systems.