We address the problem of user association in a dense millimeter wave (mmWave) network, in which each arriving user brings a file containing a random number of packets and each time slot is divided into multiple mini-slots. This problem is an instance of the restless multi-armed bandit problem, and is provably hard to solve. Using a technique introduced by Whittle, we relax the hard per-stage constraint that each arriving user must be associated with exactly one mmWave base station (mBS) to a long-term constraint and then use the Lagrangian multiplier technique to convert the problem into an unconstrained problem. This decouples the process governing the system into separate Markov Decision Processes at different mBSs. We prove that the problem is Whittle indexable, present a scheme for computing the Whittle indices of different mBSs, and propose an association scheme under which, each arriving user is associated with the mBS with the smallest value of the Whittle index. Using extensive simulations, we show that the proposed Whittle index based scheme outperforms several user association schemes proposed in prior work in terms of various performance metrics such as average cost, delay, throughput, and Jain's fairness index.

翻译：本文研究密集毫米波网络中的用户关联问题，其中每个到达用户携带包含随机数量数据包的文件，且每个时隙被划分为多个微时隙。该问题属于多臂赌博机中的非稳定型问题，已被证明难以求解。通过引入惠特尔提出的技术，我们将每个到达用户必须与唯一一个毫米波基站（mBS）关联的每阶段硬约束松弛为长期约束，并利用拉格朗日乘子法将问题转化为无约束问题，从而将系统控制过程解耦为不同mBS处的独立马尔可夫决策过程。本文证明该问题具有惠特尔可指数性，提出计算不同mBS惠特尔指数的方案，并设计了一种关联策略：每个到达用户将与惠特尔指数最小的mBS建立关联。通过大量仿真实验，我们验证了所提出的基于惠特尔指数的方案在平均成本、时延、吞吐量和Jain公平指数等多项性能指标上均优于此前研究中提出的多种用户关联方案。