stored in buffer $Q_k$; at the beginning, each relay buffer is empty (i.e., $l_k =0$ for all $k$) We denote by $\mathcal{T}$ all the relays for which their buffer is not empty, i.e., $\mathcal{T} = \{R_k: l_k>0 \}$, $\mathcal{T} \subseteq \mathcal{C}$.

Time is considered to be slotted and at each time-slot the source $S$ and (possibly) one of the relays $R_k$ transmit with power $P_S$ and $P_{R_k}$, respectively. The source node is assumed to be saturated (it has always data to transmit) and the information rate is equal to $r_0$ bits per channel use (BPCU). The retransmission process is based on an Acknowledgment/Negative-Acknowledgment (ACK/NACK) mechanism, in which short-length error-free packets are broadcasted by the receivers (either a relay $R_k$ or the destination $D$) over a separate narrow-band channel in order to inform the network of that packet’s reception status.

All wireless links exhibit fading and Additive White Gaussian Noise (AWGN). The fading is assumed to be stationary, with frequency non-selective Rayleigh block fading. This means that the fading coefficients $h_{ij}$ (for the $i\rightarrow j$ link) remain constant during one slot, but change independently from one slot to another according to a circularly symmetric complex Gaussian distribution with zero mean and 