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Resource and Interference Management
Published in Wen Sun, Qubeijian Wang, Nan Zhao, Haibin Zhang, Chao Shen, Ultra-Dense Heterogeneous Networks, 2023
Wen Sun, Haibin Zhang, Nan Zhao, Chao Shen, Lawrence Wai-Choong Wong
A novel approach for joint power control and UE scheduling is proposed in UNDs [54]. The energy efficiency is formulated as a dynamic stochastic game between small BSs due to severe coupling in interference. As shown in Fig. 2.4, as the number of interfering small BSs grows, the interference observed at a generic UE becomes independent of individual states and transmission policies of small BSs and only depends on the time t and the limiting distribution ρ(t). In such a scenario, dynamic stochastic game can be solved by mean field game. Mean field game is the study of strategic decision making in very large populations of small interacting agents [55]. In continuous time, a mean field game is typically composed of a Hamilton-Jacobi-Bellman (HJB) equation and a Fokker-Planck-Kolmogorov (FPK) equation. Under fairly general assumptions, a mean field game is the limit as N→∞ of an N-player Nash equilibrium [56]. UE scheduling is formulated as a stochastic optimization problem and solved by using the drift plus penalty approach in the framework of Lyapunov optimization.
Low Power Dynamic Scheduling for Computing Systems
Published in F. Richard Yu, Xi Zhang, Victor C. M. Leung, Green Communications and Networking, 2016
To stabilize the queues while minimizing time average power, we use Lyapunov optimization theory, which gives rise to the drift-plus-penalty ratio algorithm[25]. First define L[k] as the sum of the squares of all queues on frame k (divided by 2 for convenience later):
Storage trade-offs and optimal load scheduling for cooperative consumers in a microgrid with different load types
Published in IISE Transactions, 2018
Ashutosh Nayak, Seokcheon Lee, John W. Sutherland
The deterministic model suffers from uncertainty and scalability issues. Due to the uncertainty involved with renewables, a dynamic model based on Lyapunov optimization is proposed in this article. In this model, no assumptions are made on the future values of energy from renewables or future prices. We do not consider any probability density distribution for the generation from renewables. Since all the decisions are made based on current information, we solve a deterministic problem in each time step t. We consider that the energy harvest at time t is known, and we make dynamic scheduling decisions based on real-time information. The model is based on the method proposed in Lakshminarayana et al. (2014). However, they do not consider movable loads. It has also been discussed in Chen et al. (2017), but they do not consider production line loads or moveable loads. To comply with space limitations, we refer interested readers to the work of Huang and Neely (2011) for detailed discussion on Lyapunov optimization models. We built our Lyapunov optimization model as discussed in Nayak and Lee (2017), where industrial loads were not considered. Since a bigger problem is broken down into smaller deterministic sub-problems to be solved in every time slot t, the model is scalable. In this article, we solve 24 × 4 = 96 sub-problems, as we consider a time resolution of 15 minutes. Lyapunov optimization makes a decision at every time slot on minimizing the weighted sum of the drift function and the penalty function. A Lyapunov optimization-based algorithm is simple to implement and has desirable convergence properties.