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In this paper, the demands made by a set of spatially Poisson point distributed primary users on available channels in their proximity is considered and their effect on channel availability for secondary users under various channel requesting distributions is assessed. It is shown that for some "greedy" systems, providing more subcarriers will not increase the spectrum availability for a secondary network. The sustainable traffic of the system subject to a fixed spectrum outage probability is also investigated. It is shown that for a fixed spectrum outage probability, as long as the system is "greedy", providing more subcarriers does not help to support more primary users to successfully avoid spectrum outage.