Pushing contents to users with device-to-device (D2D) data sharing is considered as a promising solution to overcome backhaul congestion. However, this model is associated with critical issues which are user selfishness in terms of sharing personal resources and security concern when connecting with strange devices. Therefore, in this paper, we propose the notion of random D2D connection where the probabilities that the devices are connected for receiving or sharing data are manipulated by users themselves. Moreover, these probability values can also be treated as variables to be optimized. Based on that, we address the backhaul congestion issue and formulate it as a non-convex optimization problem. Two solving schemes are proposed based on primal decomposition and the alternating direction method of multipliers algorithm, respectively. In addition, these methods are designed in both centralized and distributed manners. Besides that, the congestion probability expression is derived in the special case giving an upper bound for the performance of our presented solution. The numerical results are provided to illustrate the effectiveness of the proposed method.
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