User association has emerged as a distributed resource allocation problem in the heterogeneous networks (HetNets). Although an approximate solution is obtainable using the approaches like combinatorial optimization and game theorybased schemes, these techniques can be easily trapped in local optima. Furthermore, the lack of exploring the relation between the quality of the solution and the parameters in the HetNet [e.g., the number of users and base stations (BSs)], at what levels, impairs the practicability of deploying these approaches in a real world environment. To address these issues, this paper investigates how to model the problem as a distributed constraint optimization problem (DCOP) from the point of the view of the multiagent system. More specifically, we develop two models named each connection as variable (ECAV) and each BS and user as variable (EBUAV). Hereinafter, we propose a DCOP solver which not only sets up the model in a distributed way but also enables us to efficiently obtain the solution by means of a complete DCOP algorithm based on distributed messagepassing. Naturally, both theoretical analysis and simulation show that different qualitative solutions can be obtained in terms of an introduced parameter η which has a close relation with the parameters in the HetNet. It is also apparent that there is 6% improvement on the throughput by the DCOP solver comparing with other counterparts when η = 3. Particularly, it demonstrates up to 18% increase in the ability to make BSs service more users when the number of users is above 200 while the available resource blocks (RBs) are limited. In addition, it appears that the distribution of RBs allocated to users by BSs is better with the variation of the volume of RBs at the macro BS.

中文翻译：

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将分布式约束优化方法应用于异构网络中的用户关联问题


用户关联已成为异构网络（HetNets）中的分布式资源分配问题。尽管使用组合优化和基于博弈论的方案等方法可以获得近似解，但这些技术很容易陷入局部最优。此外，缺乏对解决方案质量与 HetNet 参数之间关系的探索[例如，用户和基站 (BS) 的数量]，在何种水平上，削弱了在现实世界中部署这些方法的实用性环境。为了解决这些问题，本文从多智能体系统的角度研究如何将问题建模为分布式约束优化问题（DCOP）。更具体地说，我们开发了两个模型，将每个连接命名为变量（ECAV），将每个 BS 和用户命名为变量（EBUAV）。在下文中，我们提出了一种DCOP求解器，它不仅以分布式方式建立模型，而且使我们能够通过基于分布式消息传递的完整DCOP算法有效地获得解。当然，理论分析和仿真都表明，引入与HetNet中的参数关系密切的参数η可以得到不同的定性解。还可以明显看出，当 η = 3 时，DCOP 求解器的吞吐量比其他同类求解器提高了 6%。特别是，当用户数量增加时，它表明使 BS 服务更多用户的能力提高了 18%。超过 200，而可用资源块 (RB) 有限。另外，随着宏基站RB数量的变化，基站分配给用户的RB分布也变得更好。