  Multicast transmissions have been widely analyzed in traditional networks as
a way to improve spectrum efficiency when multiple users are interested in the
same data. However, their application to mmWave communications has been studied
only marginally so far. The goal of this paper is to partially fill this gap by
investigating optimal and suboptimal multicast schemes for mmWave
communications with directional beams. In particular, we propose a Markov setup
to model the retransmission status of the unsuccessfully transmitted packets
and, because of the computational complexity of the optimal solution, we
introduce a suboptimal hierarchical optimization procedure, which is much
easier to derive. Finally, we numerically show that restricting the link to
unicast beams is strongly suboptimal, especially when many packets have to be
transmitted.
