In this paper, a dense Internet of Things (IoT) monitoring system is considered in which a large number of IoT devices contend for channel access so as to transmit timely status updates to the corresponding receivers using a carrier sense multiple access (CSMA) scheme. Under two packet management schemes with and without preemption in service, the closed-form expressions of the average age of information (AoI) and the average peak AoI of each device is characterized. It is shown that the scheme with preemption in service always leads to a smaller average AoI and a smaller average peak AoI, compared to the scheme without preemption in service. Then, a distributed noncooperative medium access control game is formulated in which each device optimizes its waiting rate so as to minimize its average AoI or average peak AoI under an average energy cost constraint on channel sensing and packet transmitting. To overcome the challenges of solving this game for an ultra-dense IoT, a mean-field game (MFG) approach is proposed to study the asymptotic performance of each device for the system in the large population regime. The accuracy of the MFG is analyzed, and the existence, uniqueness, and convergence of the mean-field equilibrium (MFE) are investigated. Simulation results show that the proposed MFG is accurate even for a small number of devices; and the proposed CSMA-type scheme under the MFG analysis outperforms three baseline schemes with fixed and dynamic waiting rates. Moreover, it is observed that the average AoI and the average peak AoI under the MFE do not necessarily decrease with the arrival rate.

翻译：摘要：本文研究了一个密集物联网监测系统，其中大量物联网设备通过载波侦听多路访问机制竞争信道访问，以向相应接收器发送及时的状态更新。在两种数据包管理方案（服务中是否支持抢占）下，推导了每个设备的平均信息年龄（AoI）和平均峰值AoI的闭式表达式。研究表明，与无服务抢占方案相比，支持服务抢占的方案始终能获得更小的平均AoI和平均峰值AoI。随后，建立了一个分布式非合作介质访问控制博弈模型，每个设备在信道感知和数据包传输的平均能量成本约束下，优化其等待速率以最小化平均AoI或平均峰值AoI。为克服超密集物联网中求解该博弈的挑战，提出采用平均场博弈方法研究大规模人口系统中每个设备的渐近性能。本文分析了平均场博弈的准确性，并探讨了平均场均衡的存在性、唯一性及收敛性。仿真结果表明，即便设备数量较少时，所提出的平均场博弈仍具有高精度；基于该分析提出的CSMA方案优于三种采用固定/动态等待速率的基准方案。此外，观察到平均场均衡下的平均AoI和平均峰值AoI并不必然随到达率增加而降低。