Following the interest of the global research and industrial community in the concept of Internet of Things, IEEE 802 LAN/MAN standard committee is developing the IEEE 802.11ah amendment that will shift the Wi-Fi technology to the area of Machine-to-Machine communications. One of the most important problems considered by the new amendment is the energy-efficient communication of wireless stations, the number of which can reach thousands per Access Point. Serving such a large number of stations is not a problem itself, because it can be managed by efficient scheduling, but the usage of different advanced control methods requires association. Before the association, the Access Point knows neither the capabilities of the stations, nor their identifiers, therefore it has to rely on the basic random channel access for setting up the link. When number of connecting statios is large, the contention for channel access is inevitable, which can drastically increase the link set-up time. To hasten the link set-up, IEEE 802.11ah proposes the Distributed Authentication Control protocol. This pioneering paper describes a mathematical model of the Distributed Authentication Control that can be used to find the link set-up time and the parameters that minimize it.
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