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In this paper, a dense Internet of Things (IoT) monitoring system isconsidered in which a large number of IoT devices contend for channel access soas to transmit timely status updates to the corresponding receivers using acarrier sense multiple access (CSMA) scheme. Under two packet managementschemes with and without preemption in service, the closed-form expressions ofthe average age of information (AoI) and the average peak AoI of each device ischaracterized. It is shown that the scheme with preemption in service alwaysleads to a smaller average AoI and a smaller average peak AoI, compared to thescheme without preemption in service. Then, a distributed noncooperative mediumaccess control game is formulated in which each device optimizes its waitingrate so as to minimize its average AoI or average peak AoI under an averageenergy cost constraint on channel sensing and packet transmitting. To overcomethe 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 devicefor the system in the large population regime. The accuracy of the MFG isanalyzed, and the existence, uniqueness, and convergence of the mean-fieldequilibrium (MFE) are investigated. Simulation results show that the proposedMFG is accurate even for a small number of devices; and the proposed CSMA-typescheme under the MFG analysis outperforms three baseline schemes with fixed anddynamic waiting rates. Moreover, it is observed that the average AoI and theaverage peak AoI under the MFE do not necessarily decrease with the arrivalrate.

Age of Information in Ultra-Dense IoT Systems: Performance and Mean-Field Game Analysis