This paper studies the effect that HOL (Head-of-Line) blocking in the packet injection queue has on the performance of bidirectional k-ary n-cubes, for values of k over a certain threshold (around 20). The HOL blocking causes an unbalanced use of the channels corresponding to the two directions of bidirectional links, which is responsible for a drop in the network throughput and a rise in the network delay. Simulation results show that this anomaly only appears in those rings where most injections are performed (normally, those in the X axis), and that the elimination of the HOL blocking in the injection queue enables the network to sustain peak throughput after saturation.