  Recently, it has been shown that CSMA-type random access algorithms can
achieve the maximum possible throughput in ad hoc wireless networks. However,
these algorithms assume an idealized continuous-time CSMA protocol where
collisions can never occur. In addition, simulation results indicate that the
delay performance of these algorithms can be quite bad. On the other hand,
although some simple heuristics (such as distributed approximations of greedy
maximal scheduling) can yield much better delay performance for a large set of
arrival rates, they may only achieve a fraction of the capacity region in
general. In this paper, we propose a discrete-time version of the CSMA
algorithm. Central to our results is a discrete-time distributed randomized
algorithm which is based on a generalization of the so-called Glauber dynamics
from statistical physics, where multiple links are allowed to update their
states in a single time slot. The algorithm generates collision-free
transmission schedules while explicitly taking collisions into account during
the control phase of the protocol, thus relaxing the perfect CSMA assumption.
More importantly, the algorithm allows us to incorporate mechanisms which lead
to very good delay performance while retaining the throughput-optimality
property. It also resolves the hidden and exposed terminal problems associated
with wireless networks.
