  In a federated setting, agents coordinate with a central agent or a server to
solve an optimization problem in which agents do not share their information
with each other. Wirth and his co-authors, in a recent paper, describe how the
basic additive-increase multiplicative-decrease (AIMD) algorithm can be
modified in a straightforward manner to solve a class of optimization problems
for federated settings for a single shared resource with no inter-agent
communication. The AIMD algorithm is one of the most successful distributed
resource allocation algorithms currently deployed in practice. It is best known
as the backbone of the Internet and is also widely explored in other
application areas. We extend the single-resource algorithm to multiple
heterogeneous shared resources that emerge in smart cities, sharing economy,
and many other applications. Our main results show the convergence of the
average allocations to the optimal values. We model the system as a
non-homogeneous Markov chain with place-dependent probabilities. Furthermore,
simulation results are presented to demonstrate the efficacy of the algorithms
and to highlight the main features of our analysis.
