Probabilistic stability of traffic load balancing on wireless complex networks

Load balancing between adjacent base stations (BSs) is important for balancing load distributions and improving service provisioning. While 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 reuse network with no interference, whereby load balancing dynamics does not 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 a generalized network topology, as well as the uncertainty we have in load balancing parameters due to noisy channel or network sensing. We prove that the stability analysis 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 neighbor list of the network. The probabilistic framework provides uncertainty quantification and stability prediction for Digital Twins of wireless infrastructure