  Load balancing between adjacent base stations (BSs) is important for
balancing load distributions and improving service provisioning. Whilst load
balancing between any given pair of BSs is beneficial, cascade load sharing can
cause network level instability that is hard to predict. The relationship
between each BS's load balancing dynamics and the network topology is not
understood. In this seminal work on stability analysis, we consider a frequency
re-use network with no interference, whereby load balancing dynamics doesn't
perturb the individual cells' capacity. Our novelty is to show an exact
analytical and also a probabilistic relationship for stability, relating
generalized local load balancing dynamics with generalized network topology, as
well as the uncertainty we have in load balancing parameters. We prove that the
stability analysis given is valid for any generalized load balancing dynamics
and topological cell deployment and we believe this general relationship can
inform the joint design of both the load balancing dynamics and the neighbour
list of the network.
