Abstract-With the rapid increase in demand for mobile data, mobile network operators are trying to expand wireless network capacity by deploying wireless local area network (LAN) hotspots on which they can offload their mobile traffic. However, these network-centric methods usually do not fulfill the interests of mobile users (MUs). Taking into consideration many issues, MUs should be able to decide whether to offload their traffic to a complementary wireless LAN. Our previous work studied single-flow wireless LAN offloading from a MU's perspective by considering delay-tolerance of traffic, monetary cost and energy consumption. In this paper, we study the multi-flow mobile data offloading problem from a MU's perspective in which a MU has multiple applications to download data simultaneously from remote servers, and different applications' data have different deadlines. We formulate the wireless LAN offloading problem as a finite-horizon discrete-time Markov decision process (MDP) and establish an optimal policy by a dynamic programming based algorithm. Since the time complexity of the dynamic programming based offloading algorithm is still high, we propose a low time complexity heuristic offloading algorithm with performance sacrifice. Extensive simulations are conducted to validate our proposed offloading algorithms.Index Terms-wireless LAN, multiple-flow, mobile data offloading, Markov decision processThe mobile data traffic demand is growing rapidly. According to the investigation of Cisco Systems [1], the mobile data traffic is expected to reach 24.3 exabytes per month by 2019, while it was only 2.5 exabytes per month at the end of 2014. On the other hand, the growth rate of the mobile network capacity is far from satisfying that kind of the demand, which has become a major problem for wireless mobile network operators (MNOs). Even though 5G technology is promising for providing huge wireless network capacity [2], the development process is long and the cost is high. Economic methods such as time-dependent pricing [3] [4] have been proposed to change users' usage pattern, which are not user-friendly. Up to now, the best practice for increasing mobile network capacity is to deploy complementary networks (such as wireless LAN and femtocells), which can be quickly deployed and are cost-efficient. Using such methods, part of the MUs' traffic demand can be offloaded from a MNO's cellular network to the complementary network.The process that a mobile device automatically changes its connection type (such as from cellular network to wireless LAN) is called vertical handover [5]. Mobile data offloading is facilitated by new standards such as Hotspot 2.0 [6] and the 3GPP Access Network Discovery and Selection Function (ANDSF) standard [7], with which information of network (such as price and network load) can be broadcasted to MUs in real-time. Then MUs can make offloading decisions intelligently based on the real-time network information.There are many works related to the wireless LAN offloading problem. However, p...