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We consider a wireless relay network that consists of a source, half-duplex decode-and-forward buffer-aided relays and a destination. While the majority of previous works on relay selection assume no direct transmission between source and destination in such a setting, we lift this assumption and propose a link selection policy that exploits both the buffering ability and the opportunity for successful reception of a packet directly from the source. The proposed relay selection scheme incorporates the instantaneous strength of the wireless links and adapts the relay selection decision based on the strongest available link. The evolution of the network as a whole is modeled by means of a Markov chain and thus, the outage probability is associated with the steady state of the Markov chain. It is deduced that even if the link between the source and the destination is in principle a very unreliable link, it is always beneficial …