# Service-Driven Dynamic Beam Hopping with Resource Allocation for LEO Satellites
## 1 Introduction
To achieve more efficient beam resource utilization and better communication services, the determinantal point process algorithm is introduced to solve beam hopping problems in [15], accurately allocating resources according to traffic demands and providing a novel algorithmic-level solution for addressing limited beam resources. The authors propose an efficient beam hopping pattern in [16], optimizing the pattern to enhance resource allocation efficiency and overall system performance. The authors of [17] decompose the bivariate optimization problem of power and bandwidth allocation into two univariate sub-problems, effectively solving the joint optimization challenge. In recent years, reinforcement learning (RL) has emerged as a critical methodology for resource allocation in beam hopping satellite communication systems [11]. In [18], the authors integrate traditional beam hopping optimization with machine learning techniques, using learning algorithms to assist the optimization process. This approach provides a new framework for improving resource utilization efficiency and communication quality, overcoming the limitations of relying solely on traditional algorithms through technological convergence. Building on this, the authors of [19] further advance into the field of deep reinforcement learning, proposing a deep reinforcement learning framework to design beam hopping patterns and applying heuristic algorithms to enhance system capacity. The authors of [20] apply value decomposition network (VDN) learning to the field of multi-agent reinforcement learning (MARL). The authors in [21] introduce a multi-agent reinforcement learning method to optimize beam hopping in multi-beam non-geostationary orbit constellations, marking the application of multi-agent methodologies. In [2], the authors present a multi-agent deep reinforcement learning approach to address dynamic beam pattern and bandwidth allocation in high-throughput beam hopping satellite systems. The authors of [22] employ model-free multi-objective deep reinforcement learning to learn optimal policies through environmental interaction. In [23], the authors combine deep reinforcement learning with genetic algorithms as an auxiliary mechanism to maximize long-term system throughput. The authors propose a parameterized reinforcement learning method in [24], maximizing long-term cumulative rewards by learning a parameterized policy network. The authors in [25] develop a multi-agent deep Q-network algorithm, where agents select optimal strategies based on current network states. Among numerous MARL algorithms, the VDN algorithm has emerged as an effective approach for solving multi-agent cooperative tasks, owing to its unique value decomposition strategy and efficient coordination mechanism. Based on the research of the above studies, we find that with the increase in the number of service beams, the search space of beam hopping patterns grows exponentially, significantly increasing the complexity of heuristic algorithms [2]. In addition, most reinforcement learning algorithms are deployed on satellites centralized after training, making it impossible to make appropriate resource allocation decisions in real time. To address the above issues, this paper proposes applying a value decomposition network algorithm framework based on cooperative multi-agent reinforcement learning (MARL-VDN) in LEO beam hopping satellite communication systems. Each agent makes decisions about the beam hopping pattern and the power allocation of one beam, allowing agents to achieve global objective optimization while making local decisions. The main contributions of this paper are as follows. * To solve the problem of uneven ground traffic distribution in LEO beam hopping satellite communication systems, we establish a downlink transmission link model.