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In a WLAN context, rate region properties have mainly been studied for Aloha networks. The log-convexity of the Aloha rate region in general mesh network settings has been established by several authors in the context of utility optimisation. All of these results make the standard Aloha assumption of equal idle and busy slot durations, whereas in 802.11 WLANs highly unequal slot durations are the norm e.g. it is not uncommon to have busy slot durations that are 100 times larger than the PHY idle slot duration.
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