Abstract
We consider the management problem for a cluster of three identical servers treating an external service 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 switch on or off each server, for energy efficiency, while ensuring that the queue of each server asymptotically converges to a desirable level. We formally prove the properties of the proposed law and highlight some interesting peculiarities in terms of non-uniform convergence. While we prove our results for the case of a constant request rate, we show the effectiveness of the proposed strategies by simulations in the more general cases of a time-varying request rate.
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