  In this paper, we consider a bidirectional relay network with half-duplex
nodes and block fading where the nodes transmit with a fixed transmission rate.
Thereby, user 1 and user 2 exchange information only via a relay node, i.e., a
direct link between both users is not present. Recently in [1], it was shown
that a considerable gain in terms of sum throughput can be obtained in
bidirectional relaying by optimally selecting the transmission modes or,
equivalently, the states of the nodes, i.e., the transmit, the receive, and the
silent states, in each time slot based on the qualities of the involved links.
To enable adaptive transmission mode selection, the relay has to be equipped
with two buffers for storage of the data received from the two users. However,
the protocol proposed in [1] was delay-unconstrained and provides an upper
bound for the performance of practical delay-constrained protocols. In this
paper, we propose a heuristic but efficient delay-constrained protocol which
can approach the performance upper bound reported in [1], even in cases where
only a small average delay is permitted. In particular, the proposed protocol
does not only take into account the instantaneous qualities of the involved
links for adaptive mode selection but also the states of the queues at the
buffers. The average throughput and the average delay of the proposed
delay-constrained protocol are evaluated by analyzing the Markov chain of the
states of the queues.
