Cellular networks are facing explosive growth of mobile data traffic due to the proliferation of smart devices and traffic-intensive applications. As a cost-effective solution, delayed Wi-Fi offloading was introduced to shift the delay-tolerant traffic from cellular to Wi-Fi networks by trading additional delays. Our paper studies a multi-flow rate control problem where each flow has different traffic load and a deadline. To maximize user satisfaction defined as offloading efficiency minus disutility caused by deadline violation, we propose a dynamic programming-based rate control algorithm. Moreover, to reduce the computation and memory, we propose a simple threshold-based rate control algorithm. (C) 2016 The Korean Institute of Communications Information Sciences. Publishing Services by Elsevier B. V. This is an open access article under the CC BY-NC-ND license.