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Abstract—Virtual Network Functions (VNFs) are software implementation of middleboxes (MBs) (e.g., firewalls and proxy servers) that provide performance and security guarantees for virtual machine (VM) cloud applications. In this paper, we study a new VM flow migration problem for dynamic VNF-enabled cloud data centers (VDCs). The goal is to migrate the VM flows in the dynamic VDCs to minimize the total network traffic while load-balancing VNFs with limited processing capabilities. We refer to the problem as FMDV: flow migration in dynamic VDCs. We propose an optimal and efficient minimum cost flow-based flow migration algorithm and two benefit-based efficient heuristic algorithms to solve the FMDV. Via extensive simulations, we show that our algorithms are effective in mitigating dynamic cloud traffic while achieving load balance among VNFs. In particular, all our algorithms reduce dynamic network traffic in all cases and our optimal algorithm always achieves the best traffic-mitigation effect, reducing the network traffic by up to 28% compared to the case without flow migration.