Hybrid control of a three-agent network cluster

We consider the management problem for a cluster of three identical servers treating an external request. We assume that each server has a constant computational speed and we build a deterministic hybrid dynamical model of the overall system. Then, inspired by consensus theory, we propose a centralized control law distributing the computational load among the servers and deciding when to turn on or off each server, for energy efficiency, while ensuring that the queues of each server asymptotically converge to a desirable level. We prove the properties of the proposed law and highlight some interesting peculiarities in terms of non-uniform convergence.