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  1. Virtual Network Functions (VNFs) are software implementation of middleboxes (MBs) (e.g., firewalls) that provide performance and security guarantees for virtual machine (VM) cloud applications. In this paper we study a new flow migration problem in VNF-enabled cloud data centers where the traffic rates of VM flows are constantly changing. Our goal is to minimize the total network traffic (therefore optimizing the network resources such as bandwidth and energy) while considering that VNFs have limited processing capability. We formulate the flow migration problem and design two efficient benefit-based greedy algorithms. The simulations show that our algorithms are effective in reducing the network traffic as well as in achieving load balance among VNFs. In particular, our flow migration algorithms can reduce upto 15% network traffic compared to the case without flow migration.