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In this paper, we consider a wireless powered cooperative non-orthogonal multiple access (NOMA) relay network, in which one source is supposed to send independent messages to two users with the assistance of one energy-constrained relay that harvests energy from the source. Firstly, we study the minimum power consumption at the source node to fulfill the least required transmission rates by two users in both time switching relaying (TSR) strategy and power splitting relaying (PSR) one. Secondly, when the relay is provisioned with data buffer and energy storage, the long-term average power consumption minimization problem is formulated to take into account of the data and energy queue causality, peak transmit power constraint, and transmission mode selection. By using Lyapunov optimization framework, a novel buffer-aided transmission scheme (BATS) is proposed to asymptotically approach the …