In this paper, we develop a queueing analysis for opportunistic decode-and-forward (DF) relay networks. It is assumed that the networks undergo Nakagami-m fading and that the external arrival process follows a Poisson distribution. By selecting the best relay according to the opportunistic relaying scheme, the source first transmits its signal to the best relay which then attempts to decode the reception and forwards the output to the destination. It is assumed that each relay operates in full-duplex mode, i.e., it can receive and transmit signals simultaneously. The communication process throughout the network can be modeled as a queueing network which is structured from sub-systems of M/G/1 and G/G/1 queueing stations. We invoke the approximate analysis, so-called method of decomposition, to analyze the performance behavior of the considered relay network. The whole queueing network is broken into separate queues which are then investigated individually. Based on this approach, the end-to-end packet transmission time and throughput of the considered relay network are quantified in comparison with the networks with partial relay selection (PRS).