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

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.Comment: 24 pages, 4 figure

Calculating the minimum bounds of energy consumption for cloud networks

This paper is aiming at facilitating the energy-efficient operation of an integrated optical network and IT infrastructure. In this context we propose an energy-efficient routing algorithm for provisioning of IT services that originate from specific source sites and which need to be executed by suitable IT resources (e. g. data centers). The routing approach followed is anycast, since the requirement for the IT services is the delivery of results, while the exact location of the execution of the job can be freely chosen. In this scenario, energy efficiency is achieved by identifying the least energy consuming IT and network resources required to support the services, enabling the switching off of any unused network and IT resources. Our results show significant energy savings that can reach up to 55% compared to energy-unaware schemes, depending on the granularity with which a data center is able to switch on/off servers