Boltzmann meets Nash：不确定条件下光网络中的节能路由
Boltzmann meets Nash: Energy-efficient routing in optical networks under uncertainty
摘要：
出于大规模部署的电力饥饿的数据中心的服务提供，我们研究的问题，在光网络中的路由，以最大限度地减少流量驱动的功耗的目的。为了解决这个问题，路由必须考虑能源效率和容量因素;此外，在快速变化的网络环境中，这必须以实时、分布式的方式完成，并且在存在随机干扰和噪声的情况下保持鲁棒性。鉴于此，我们推导出一个定价方案的纳什均衡与网络的社会最优状态相吻合，我们提出了一种分布式学习方法的基础上的玻尔兹曼分布的统计力学。利用随机微积分的工具，我们证明了所得到的Boltzmann路由方案在不确定性下具有显著的收敛特性：具体地说，无论波动的大小如何，网络功耗的长期平均值都收敛在其最小值的$\varepsilon$内，最多为$\tilde O(1/\varepsilon^2)$;此外，如果网络允许严格的、非混合的最优状态，则算法再次收敛于该状态，而不管噪声水平如何。我们的分析是补充广泛的数值模拟表明，玻尔兹曼路由可以导致显着降低功耗基本，最短路径路由方案在现实的网络条件。
英文摘要：
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.
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