The mobile users experience the growing demand for wirelessly accessing the networks for various services. Therefore, the theoretical analysis of wireless network capacity is an essential issue in the mobile network. In an ad hoc network, for instance, the throughput available to nodes is unexpectedly limited by the relaying load created by other distant nodes, as most of data packets have to be forwarded by intermediate nodes before reaching the destination. Let us consider an ad hoc network in which  nodes are randomly placed in the network, using a common single wireless channel. The theoretical analysis of Gupta and Kumar shows that the end-to-end throughput per node approaches to zero as the number of nodes goes to infinity. After Gupta and Kumar’s initial work, a number of theoretical analyses have been conducted for investigating the network capacity of wireless multi-hop networks. M. Grossglauser studied how the node mobility can increase the network capacity.  Wang et al. further studied the throughput capacity of random ad hoc networks in which the traffic is transmitted by means of unicast routing, multicast routing, broadcasting, or different forms of anycasting. Liu et al., Kozat et al., and Zemlianov et al. consider the network capacity in the Multi-hop Cellular Networks. Kyasanur and Vaidya addressed the network capacity in a multiple channel wireless network.

In this talk, we will first review the theoretical results of various multi-hop networks. We then present our work that mathematically analyzes the maximum Internet capacity for wireless mesh networks. We established the analytical mesh network model in which wireless mesh routers are interconnected by multiple links. At the same time, the infrastructure such as Internet Gateway provides the Internet connectivity and thus the mobile users in the network access the Internet by multi-hop route of mesh routers. In addition, the mobile users are able to communicate with each other by the ad hoc backbone of mesh routers without any infrastructure. We specifically show the upper bounds of the Internet capacity and its ad hoc capacity as well.