Optimal power procurement for green cellular wireless networks under uncertainty and chance constraints
Nadhir Ben Rached, Shyam Mohan Subbiah Pillai, Raúl Tempone
TL;DR
This paper tackles the problem of minimizing operating expenditure and carbon footprint for green cellular networks under uncertainty in renewable generation and wireless channels. It introduces a time-continuous Lagrangian relaxation to handle a probabilistic QoS constraint, turning the original constrained stochastic control problem into a dual problem solved via an upwind HJB PDE solver and a combined LMBM-SSM optimization scheme. The methodology is grounded in data-driven SDEs for renewable power and Nakagami fading, with a running-horizon framework to avoid end-of-day artifacts, and validated on a German power-system–driven base station with daily traffic profiles. The results demonstrate computational efficiency and near-optimality, yielding actionable policies that leverage energy storage and renewables while satisfying QoS with high probability, highlighting practical impact for real-world network operators.
Abstract
Given the increasing global emphasis on sustainable energy usage and the rising energy demands of cellular wireless networks, this work seeks an optimal short-term, continuous-time power procurement schedule to minimize operating expenditure and the carbon footprint of cellular wireless networks equipped with energy storage capacity, and hybrid energy systems comprising uncertain renewable energy sources. Despite the stochastic nature of wireless fading channels, the network operator must ensure a certain quality-of-service (QoS) constraint with high probability. This probabilistic constraint prevents using the dynamic programming principle to solve the stochastic optimal control problem. This work introduces a novel time-continuous Lagrangian relaxation approach tailored for real-time, near-optimal energy procurement in cellular networks, overcoming tractability problems associated with the probabilistic QoS constraint. The numerical solution procedure includes an efficient upwind finite-difference solver for the Hamilton--Jacobi--Bellman equation corresponding to the relaxed problem, and an effective combination of the limited memory bundle method (LMBM) for handling nonsmooth optimization and the stochastic subgradient method (SSM) to navigate the stochasticity of the dual problem. Numerical results, based on the German power system and daily cellular traffic data, demonstrate the computational efficiency of the proposed numerical approach, providing a near-optimal policy in a practical timeframe.