The Industrial Internet of Things (IIoT) intends to speed up digital manufacturing transformation. As a crucial role, Industrial IoT aims to improve the performance and reliability of the processing of massive time-critical data continually generated by heterogeneous smart objects. To resolve these challenges, Industrial IoT incorporates the Fog computing paradigm to support intelligence near the Edge level as an additional alternative to Cloud computing. However, a Fog node allows dealing with only limited data processing, storage, and communications. Indeed, a heavy load processing task requires multiple Fog nodes to achieve its execution and may need an intelligent dynamic pooling of Cloud resources. In this paper, we propose PIAF (A Processing Intelligent Agent Running on Fog Infrastructure). An intelligent agent-based IIoT framework that runs on the Fog infrastructure to distribute the processing of time-critical data streams. We outline its several components and their interactions. Then, for this purpose, we model the PIAF framework using the Time Petri Nets modeling.