A Mean Field Game Analysis of Distributed MAC in Ultra-Dense Multichannel Wireless Networks
A Mean Field Game Analysis of Distributed MAC in Ultra-Dense Multichannel Wireless Networks
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DOI：
10.1145/3323679.3326498
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发表时间：
2019-07
期刊：
影响因子：
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通讯作者：
D. Narasimha;S. Shakkottai;Lei Ying
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文献类型：
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作者：
D. Narasimha;S. Shakkottai;Lei Ying
本报告分析了超密集多通道无线网络中分布式介质访问控制（MAC）协议的性能，其中$M=mN$设备共享$N$频段（或信道），设备决定探测然后在可用频段上传输。虽然这样的系统可以被表述为$M$ -玩家贝叶斯博弈，但由于维度的诅咒，计算大规模系统的纳什均衡通常是不可行的。在本报告中，我们利用平均场博弈（MFG）方法并分析了大人口制度下的系统（$N$倾向于$\infty $, $m$是常数）。我们考虑了一个分布式和低复杂性的MAC协议，其中每个设备通过遵循指数时钟探测$d/k$通道，该时钟在有消息要传输时以速率$k$滴答，并优化探测策略以平衡吞吐量和探测成本。我们从MFG的角度进行了全面的分析，包括平均场纳什均衡的存在唯一性和收敛性，以及相对于全局最优解的无政府状态的代价。我们的分析表明，无政府状态的代价最多为一半，但当流量负载或探测成本较低时，无政府状态的代价接近于零。我们的数值结果证实了我们的分析，并表明MFNE是$M$ -player系统的良好近似值。此外，本报告还展示了MFG分析的新颖性，该分析可用于研究超密集无线网络中其他分布式MAC协议。
This report analyzes the performance of distributed Medium Access Control (MAC) protocols in ultra-dense multichannel wireless networks, where $N$ frequency bands (or channels) are shared by $M=mN$ devices, and devices make decisions to probe and then transmit over available frequency bands. While such a system can be formulated as an $M$ -player Bayesian game, it is often infeasible to compute the Nash equilibria of a large-scale system due to the curse of dimensionality. In this report, we exploit the Mean Field Game (MFG) approach and analyze the system in the large population regime ( $N$ tends to $\infty $ and $m$ is a constant). We consider a distributed and low complexity MAC protocol where each device probes $d/k$ channels by following an exponential clock which ticks with rate $k$ when it has a message to transmit, and optimizes the probing strategy to balance throughput and probing cost. We present a comprehensive analysis from the MFG perspective, including the existence and uniqueness of and convergence to the Mean Field Nash Equilibrium and the price of anarchy with respect to the global optimal solution. Our analysis shows that the price of anarchy is at most one half, but is close to zero when the traffic load or the probing cost is low. Our numerical results confirm our analysis and show that the MFNE is a good approximation of the $M$ -player system. Further, this report demonstrates the novelty of MFG analysis, which can be used to study other distributed MAC protocols in ultra-dense wireless networks.