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This paper considers the problem of optimizing the downlink capacity of broadband fixed wireless access systems in two representative scenarios: a non-line-of-sight terrestrial system, and a system operating from a high altitude platform. In each case a packet-based system is considered, with the delay through the system of constant-length packets taken as the metric to evaluate the effectiveness of the resource allocation schemes considered. The joint optimization of adaptive modulation, channel selection scheme and queueing strategies is a complex multidimensional problem and a simulation approach is taken to evaluate the trade-offs. It is shown that good performance can be obtained from a simple resource allocation scheme over a wide range of different operating conditions, that consideration of queueing strategy is important to minimizing packet delay through the systems, and that the capacity of a broadband system using a high-altitude platform can be over three times as great as a terrestrial system of the same bandwidth.