Fairness and system throughput, influenced by wireless interference, are major objectives of resource allocation in wireless networks. Whereas traditionally max-min fairness protocols have been developed for wired networks (where interference is not a factor for network performance), in this paper we investigate the problem of flow routing and fair bandwidth allocation under the constraints of the physical interference model for multihop wireless networks. A max-min fair (MMF) routing algorithm under physical interference constraints is proposed where multiple candidate paths coexist for each user to the base station. The algorithm is formulated as a multicommodity flow problem where the lexicographically largest bandwidth allocation vector is found among all optimal allocation vectors. We compare our approach with two MMF interference routing algorithms in the literature that use the protocol interference model to garner fair bandwidth allocation. We show that our algorithm performs better in terms of blocking probability, bandwidth usage and link load.
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