The authors propose protocols to optimise throughput of a relay in relaying networks where two users communicate only through buffer-aided relay. Both the users randomly access finite size buffer of the relay. The protocols are developed on the basis of buffer state information (BSI) and channel state information (CSI). In their proposed scheme, half-duplex decode-and-forward (DF) concept is used for improving the spectral efficiency of two-way relaying networks. In this work, the authors derive maximum achievable relay throughput with fixed-rate transmission which is in the form of linear-fractional programming. For simplification, they transform the fractional programme into linear programme which is efficiently computed through the standard convex/linear numerical tool. The numerical results are performed with the assisted software such as CVX tool. They theoretically analyse the events to provide necessary performance endorsement. The BSI/CSI outperforms all the cases studied named as conventional relaying, BSI only, and CSI only.