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Multi-media applications with demanding throughput requirements often raise issues of capacity limitations in wireless networks. High data rate (HDR) wireless personal area networks (WPANs) can operate in a mesh configuration to extend from the legacy single-hop communication to multiple hops. Although the range of WPANs is increased in a mesh configuration, there are capacity constraints because the superframe time is shared by multiple piconet clusters instead of being dedicated for a single piconet cluster just like in the legacy single-hop case. Furthermore, the distributed superframe sharing can cause fairness issues because there is no mechanism to determine the requirement of each mesh piconet coordinator (MPNC) and monitor a fair allocation to each MPNC. Here, the authors propose a centralised resource allocation approach and define three resource allocation policies for meshed HDR WPANs. The proposed approach is augmented by a traffic estimation strategy to predict a suitable fraction of superframe time for each cluster. Simulation results prove the effectiveness of the proposed resource allocation policies and the fairness index is shown to increase upto 42% with the proposed approach in some cases.