1 Abstract—Wireless Mesh Networks represent an interesting technology due to their reliability, broad coverage and relatively easy and inexpensive scalability. The architecture is mainly a hybrid solution between ad-hoc and infrastructure networking, where each node potentially acts as a relay, forwarding traffic generated by other nodes. Even if solutions are already available, many research topics have yet to be investigated, as no theoretical studies are available to determine the performance of such networking paradigm. In this work, we aim at providing mathematical expressions for connectivity and cumulative capacity of a mesh network on the basis of the network configuration, in order to provide guiding principles in mesh networks’ design and development. An analytical approach is used in determining the connectivity probability, while the “bottleneck collision domain” concept is adopted to estimate capacity. The framework is further validated through comparison with simulation results. Index Terms—Wireless Mesh Networks, Performance Evaluation I. INTRODUCTION Wireless Mesh Network (WMN) [1] represents a hybrid solution between infrastructure and ad-hoc networking paradigms, where data forwarding is enabled by all the nodes in the network. It can be assumed that most of the traffic passing through a mesh network is directed to or coming from the Mesh Routers, located in fixed positions in the coverage area of the WMN, that act as access points and provide Internet connectivity. Nevertheless, ad-hoc communications are also possible. Potentially, all the nodes act as hosts and as routers, forwarding packets generated by other nodes. Mesh networking offers several advantages: (i) it allows the combination of different wireless technologies, such as cellular networks, Wi-Fi, WiMAX, etc.; (ii) WMNs can be incrementally deployed, in order to gradually extend connectivity and capacity, avoiding massive investments. Moreover, WMNs set up and keep the connectivity autonomously: if a node fails, another route to the gateway is Manuscript received September 15, 2006. This work was supported in part by the Italian Ministry for University and Research (MIUR) under grant “Wireless 802.16 Multi-antenna Mesh Networks (WOMEN)”. F. Granelli is Assistant Professor at the Dept. of Information and Communication Technology (DIT), University of Trento, Via Sommarive 14, I-38050, Trento (Phone: +39 0461 882062; fax: +39 0461 882093; e-mail: granelli@dit.unitn.it). E. Miorando is with the Dept. of Information and Communication Technology (DIT), University of Trento, Via Sommarive 14, I-38050, Trento. found through another path, enabling robustness, resilience, preservation and self-healing properties. Currently, several WMN-enabled products are available, even at (relatively) low prices, but no specific and general study of the performance and design principles to fully exploit the features of WMN is published yet [1]. More specifically, main open issues are coverage area (or network connectivity) and data transfer performance and their relationship with the network setup. In the general framework of ad-hoc networks, connectivity has been broadly studied. Percolation is frequently used as a starting point to estimate the probability for a node to be connected to the network. For example, continuum percolation theory is investigated in [15], where Franceschetti and Meester prove the existence of a unique scale-free model that allows short-path point-to-point connections, assuming local knowledge at each node. In [12] broadcast percolation is considered in multi-hop networks modelled by a spatial Poisson process; analysis of relationship between nodes density, transmission range and the diffusion of broadcast percolation is provided. Often, the main goal is to analyze the dependence of the connectivity probability from a specific parameter. Ferrari and Tonguz [11] determine the minimum number of neighbour nodes to ensure an ad-hoc network to be fully connected, while Gupta and Kumar [18] infer the critical power a node should transmit to guarantee a dense network to be completely linked, avoiding interference generation. Similarly, [17] proves the high reliance of power attenuation function’s shape on connectivity and capacity in dense ad-hoc networks, while in [13], authors study connectivity in low- density, large-scale networks, considering both ad-hoc and hybrid case. In this situation, mutual interference is less critical, but bottlenecks are still present. A general conclusion of the above works is that there’s a crucial node density above which connection probability quickly increases. Furthermore, increase in the number of base stations does not provide significant improvement in connectivity, unless the topology is one-dimensional. Kleinrock and Takagi [14] analyze the optimal transmission range to maximize the expected progress of packets in desired directions, comparing slotted-ALOHA and CSMA protocols. They also reveal that both small and large ranges lead to poor connectivity rates due to isolation or interference. Similar conclusions are provided by [19], where lower and upper bounds of transmission range are defined to ensure ad-hoc networks in d-dimensional regions to be connected with high On Connectivity and Capacity of Wireless Mesh Networks Ernesto Miorando and Fabrizio Granelli, Senior Member, IEEE A