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Random access protocols, such as Aloha, are commonly modeled in wireless ad-hoc networks by using the protocol model. However, it is well-known that the protocol model is not accurate and particularly it cannot account for aggregate interference from multiple interference sources. In this paper, the authors use the more accurate physical model, which is based on the Signal-to-Interference-plus-Noise-Ratio (SINR), to study optimization-based design in wireless random access systems, where the optimization variables are the transmission probabilities of the users. They focus on throughput maximization, fair resource allocation, and network utility maximization, and show that they entail non-convex optimization problems if the physical model is adopted.
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