Software Defined Networking (SDN) provides flexible and convenient means to support fine-grained management by the logically centralized control. Thus SDN can not only result in better network capacity utilization but can offer better customer satisfaction. In this paper, we analyze and consolidate the utility theory of network bandwidth allocation to offer better customers' satisfaction in SDNs especially when SDNs are incrementally introduced into an existing network. The utilities are modeled as sigmoid curves, since they are well-known functions and often used to describe the perception of Quality of Service (QoS). We propose an optimization bandwidth allocation strategy to maximize the network utility and thus increase the customer satisfaction. The results show that the network utility based on customer satisfaction improvements are possible with proper bandwidth allocation even only a part of SDN forwarding devices in a network topology. Compared with other bandwidth allocation strategies based on fairness, our strategy is more efficient in fulfilling the basic demand of customers.