Abstract-Various industrial control applications have stringent end-to-end latency requirements in the order of a few milliseconds. Software-defined networking (SDN) is a promising solution in order to meet these stringent requirements under varying traffic patterns, as it enables the flexible management of flows across the network. Thus, SDN allows to ensure that traffic flows use congestion-free paths, reducing the delay to forwarding and processing delays at the SDN nodes. However, accommodating new flows at runtime is under such a setting challenging as it may require the migration of existing flows, without interrupting ongoing traffic. In this paper, we consider the problem of dynamic flow migration and propose a polynomial time algorithm that can find a solution if direct flow migration is feasible. We furthermore propose an algorithm for computing both direct and indirect flow migration and prove its correctness. Numerical results obtained on a FatTree network topology show that flow migration is typically necessary for networks with a moderate number of flows, while direct flow migration is feasible in around 60% of the cases.