  We consider a network model where the nodes are grouped into a number of
clusters and propose a distributed dynamic frequency allocation algorithm that
achieves performance close to that of a centralized optimal algorithm. Each
cluster chooses its transmission frequency band based on its knowledge of the
interference that it experiences. The convergence of the proposed distributed
algorithm to a sub-optimal frequency allocation pattern is proved. For some
specific cases of spatial distributions of the clusters in the network,
asymptotic bounds on the performance of the algorithm are derived and
comparisons to the performance of optimal centralized solutions are made. These
analytic results and additional simulation studies verify performance close to
that of an optimum centralized frequency allocation algorithm. It is
demonstrated that the algorithm achieves about 90% of the Shannon capacities
corresponding to the optimum/near-optimum centralized frequency band
assignments. Furthermore, we consider the scenario where each cluster can be in
active or inactive mode according to a two-state Markov model. We derive
conditions to guarantee finite steady state variance for the output of the
algorithm using stochastic analysis. Further simulation studies confirm the
results of stochastic modeling and the performance of the algorithm in the
time-varying setup.
