We model the problem of bandwidth sharing in wireless multi-hop networks as a general utility maximization problem with link bandwidth constraints. Lagrangean relaxation and duality are invoked to derive a gradient-based iterative algorithm to solve the problem. We then investigate the practical aspects of the problem and discuss how such theoretical framework can be used to design practical fair media access control frameworks that can be implemented in real systems based on the IEEE 802.11 distributed coordination function.
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Bensaou et al. (2007) studied this question.
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