Distributionally Robust Virtual Network Allocation Under Uncertainty of Renewable Energy Power with Wasserstein Metric

To achieve carbon neutrality in telecommunication networks, this paper focuses on a virtual network (VN) allocation problem for telecommunication networks powered by renewable energy (RE). One of the most critical issues is the fluctuation of RE power caused by uncertain weather conditions. Under the fluctuation of RE power, we must allocate multiple VNs so that RE power is efficiently used while avoiding waste. To deal with the fluctuation problem of RE power, we model RE power as a stochastic variable that follows a certain probability distribution. However, there are still challenges in accurately estimating the true distribution due to the limited size and nonstationarity of RE power data. To this end, we propose a distributionally robust VN allocation model that minimizes the expectational cost of the total excess power for the worst-case probability distribution in the set of all possible distributions that generate actual RE power, i.e., the uncertainty set. The uncertainty set is defined on the basis of the Wasserstein ball, in which the center is an empirical distribution constructed from the accumulated RE data and the radius is a certain Wasserstein metric. Then, the true probability distribution is assumed to be in the uncertainty set. Finally, through numerical experiments, the effectiveness of the proposed method is shown even if the estimation of RE power distribution is uncertain due to the small size of RE power data.