  We investigate the role of a relay in multiple access channels (MACs) with
bursty user traffic, where intermittent data traffic restricts the users to
bursty transmissions. As our main result, we characterize the degrees of
freedom (DoF) region of a $K$-user bursty multi-input multi-output (MIMO)
Gaussian MAC with a relay, where Bernoulli random states are introduced to
govern bursty user transmissions. To that end, we extend the noisy network
coding scheme to achieve the cut-set bound. Our main contribution is in
exploring the role of a relay from various perspectives. First, we show that a
relay can provide a DoF gain in bursty channels, unlike in conventional
non-bursty channels. Interestingly, we find that the relaying gain can scale
with additional antennas at the relay to some extent. Moreover, observing that
a relay can help achieve collision-free performances, we establish the
necessary and sufficient condition for attaining collision-free DoF. Lastly, we
consider scenarios in which some physical perturbation shared around the users
may generate data traffic simultaneously, causing transmission patterns across
them to be correlated. We demonstrate that for most cases in such scenarios,
the relaying gain is greater when the users' transmission patterns are more
correlated, hence when more severe collisions take place. Our results have
practical implications in various scenarios of wireless networks such as
device-to-device systems and random media access control protocols.
