Boltzmann meets Nash: Energy-efficient routing in optical networks under uncertainty

TL;DR

This paper introduces a distributed Boltzmann routing scheme for optical networks that efficiently minimizes power consumption under uncertainty, converging reliably to optimal states despite network noise and fluctuations.

Contribution

It develops a novel Boltzmann-based distributed learning algorithm with proven convergence properties for energy-efficient routing under uncertainty.

Findings

Converges within O(1/ε^2) time to near-optimal power consumption levels.

Achieves convergence to strict optima even with high noise levels.

Significantly reduces power consumption compared to shortest-path routing in simulations.

Abstract

Motivated by the massive deployment of power-hungry data centers for service provisioning, we examine the problem of routing in optical networks with the aim of minimizing traffic-driven power consumption. To tackle this issue, routing must take into account energy efficiency as well as capacity considerations; moreover, in rapidly-varying network environments, this must be accomplished in a real-time, distributed manner that remains robust in the presence of random disturbances and noise. In view of this, we derive a pricing scheme whose Nash equilibria coincide with the network's socially optimum states, and we propose a distributed learning method based on the Boltzmann distribution of statistical mechanics. Using tools from stochastic calculus, we show that the resulting Boltzmann routing scheme exhibits remarkable convergence properties under uncertainty: specifically, the long-term average of the network's power consumption converges within $\varepsilon$ of its minimum value in time which is at most $\tilde O(1/\varepsilon^2)$, irrespective of the fluctuations' magnitude; additionally, if the network admits a strict, non-mixing optimum state, the algorithm converges to it - again, no matter the noise level. Our analysis is supplemented by extensive numerical simulations which show that Boltzmann routing can lead to a significant decrease in power consumption over basic, shortest-path routing schemes in realistic network conditions.