Fog computing (FC) brings a Cloud close to users and improves the quality of service and delay services. In this article, the convergence of FC and Software-Defined-Networking (SDN) has been proposed to implement complicated mechanisms of resource management. SDN has suited the practical standard for FC systems. The priority and differential flow space allocation have been applied to arrange this framework for the heterogeneous request in Machine-Type-Communications. The delay-sensitive flows are assigned to a configuration of priority queues on each Fog. Due to limited resources in the Fog, a promising solution is offloading flows to other Fogs through a decision-based SDN controller. The flow-based Fog nodes have been modeled according to the queueing theory, where polling priority algorithms have been applied to service the flows and to reduce the starvation problem in a multi-queueing model. It is observed that the percentage of delay-sensitive processed flows, the network consumption, and the average service time in the proposed mechanism are improved by about 80%, 65%, and 60%, respectively, compared to traditional Cloud computing. Therefore, the delay reductions based on the types of flows and task offloading is proposed.