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Optical-Wireless (FiWi) access network is a newly emerged access network architecture which integrates passive optical networks (PONs) with wireless mesh networks (WMNs) to provide the ubiquitous, low cost, high bandwidth last mile Internet access. Though the PON subnetwork of FiWi network can provide high bandwidth, the interference in the wireless subnetwork still limits the throughput of FiWi network if all traffic goes online to the Internet. However, when peer-to-peer communication from one wireless client to another wireless client is introduced, the proposed integration of PONs and WMNs can significantly improve the network throughput. In traditional WMNs, peer-to-peer communication from one wireless client to another wireless client is carried in the wireless network, which is subject to interferences in wireless communications. In FiWi network, peer-to-peer communication can be carried through the wireless-optical-wireless mode in which the traffic is sent from the source wireless client to its nearest ONU, which is then sent to the ONU close to the destination wireless client through the PON subnetwork and then delivered to the destination wireless client. Such wireless-optical-wireless communication mode introduced by FiWi networks can sustain the interference in wireless subnetwork, thus improving the network throughput. This paper aims to study the network throughput gain in FiWi network subject to peer-to-peer communications and parameters which can affect the network throughput gain. We first have a fair modeling of FiWi networks and traditional WMNs. We then present an LP based routing algorithm for FiWi networks. Extensive simulations have been carried to study the network throughput gain in FiWi networks subject to peer-to-peer communications compared with traditional WMNs. The work provides insightful observations for fully utilizing advantages brought by the integration of PONs and WMNs in FiWi networks.