Mobile data offloading plays an important role to alleviate congestion and make better use of available network resources. When a mobile network operator (MNO) wants to offload its cellular traffic to multiple WiFi access points (APs), the problem of how much traffic is allocated to each APs arises. In this paper, a utility function of MNO having the Cobb-Douglas form is constructed. A convex optimization problem to maximize the utility is formulated to decide the optimal volume of offload traffic onto APs.

An exact optimal volume of offload traffic is provided by solving Karush-Kuhn-Tucker (KKT) conditions. Also we show that the optimal utility is convex function of a utility parameter for an efficiency of AP, which reflects the performance of wireless connectivity, the placement and the operating environment of an AP, etc. Numerical investigation verifies the optimality of the proposed offload traffic allocation and gives an insight that how the optimal utility changes depending on the utility parameter.