  Millimeter-wave (mmWave) cellular systems are power-limited and susceptible
to blockages. As a result, mmWave connectivity will be likely to be
intermittent. One promising approach to increasing mmWave connectivity and
range is to use relays. Device-to-device (D2D) communications open the door to
the vast opportunities of D2D and device-to-network relaying for mmWave
cellular systems. In this correspondence, we study how to select a good relay
for a given source-destination pair in a two-hop mmWave cellular system, where
the mmWave links are subject to random Bernoulli blockages. In such a system,
probing more relays could potentially lead to the discovery of a better relay
but at the cost of more overhead. We find that the throughput-optimal relay
probing strategy is a pure threshold policy: the system can stop relay probing
once the achievable spectral efficiency of the currently probed two-hop link
exceeds some threshold. In general, the spectral efficiency threshold can be
obtained by solving a fixed point equation. For the special case with on/off
mmWave links, we derive a closed-form solution for the threshold. Numerical
results demonstrate that the threshold-based relay probing strategy can yield
remarkable throughput gains.
