Abstract- Design/planning of WMNs is the key phase before any deployment. Few proposals can be found in the open literature that deal with the design problem; moreover, they do not take into account all the parameters that have an impact on the outcome of the design and they assume the existence of a physical topology where the location and the characteristics of nodes (e.g., number of channels, number of radios) are fixed. In this paper, we define a generalized model for the WMNs design problem that takes into account all the parameters that have a significant impact on the network (interference, multi-channel, transmission power, etc.), the requirements of providers (expected amount of traffic/users), the constraints of the physical environment (potential locations of wireless routers, e.g., poles, and gateways, e.g., data centers), etc. The objective is to minimize the cost of the network and its operations while satisfying the requirements. The proposed model is shown to outperform considerably existing solutions. Keywords- Design, Infrastructure/Backbone WMNs, Gateways placement, General network model. I. INTRODUCTION Wireless mesh networks (WMNs) consist of stationary wireless routers interconnected by wireless links with a small fraction acting as gateways to the Internet via wired (e.g., Ethernet) or wireless (e.g., WIMAX) links. In this paper, mesh clients (e.g., mobile hosts) do not act as routers for mesh networking; we are concerned with Infrastructure/backbone WMNs [7]. The design of WMNs is a challenging issue that did not receive much attention in the literature. We believe that the planning phase of WMNs is one of the most important optimization tasks before any deployment. Most of proposals that deal with WMNs assume the existence of a physical topology where the location and characteristics of the nodes are fixed/predefined. Indeed, most research efforts for WMNs have been focused on developing efficient strategies for routing, channel assignment and scheduling in order to maximize throughput [4], [5], [6]. Only a few proposals can be found in the open literature that deal with the design problem; however, they do not take into account all parameters involved in the design. By fixing the topology and capacity assignments, the design problem is reduced to a routing problem. To date and to the best of our knowledge, no research has dealt with an unfixed topology. The authors in [9] calculate the per-node throughput for a given WMN topology and gateways locations. The authors in [1], [2], and [8] propose techniques to place and minimize the number of gateways while supporting a specific amount of traffic to and from the Internet for fixed topology. It is worth noting that most of existing models are based on the concept of connectivity graph and the conflict graph. The connectivity graph model determines which two nodes have wireless connectivity using some type of measurements while the conflict graph indicates which groups of links mutually interfere and hence cannot be active simultaneously. The connectivity graph model is formulated as an LP and the conflict graph is used to define a set of constraints. The major problem with these models is that (a) the use of the conflict graph is highly complex: for even a moderately-sized network the number of interference constraints can be hundreds of thousands; (b) the objective of the LP is partial (i.e., not global): it does not really optimize WMNs. The deployment and management cost of gateways in WMNs is significant. However, by optimizing the number of gateways [1, 2, 8] we just reduce the total cost and do not minimize it because, for example, (a) a “good” assignment of channels, (b) changing the characteristics of one or more nodes (e.g., adding a radio, using radios with an optimum number of channels [3]), or (c) adding one or more nodes can be far more profitable. In this paper, we propose a unified/generalized model for the design of WMNs. The goal is to determine a topology and configuration of WMNs that satisfy the requirements, in terms of throughput and delay, with a least cost. The proposed solution requires a set of inputs that consists of the traffic demands (throughput and delay), a set of potential locations for nodes (routers and gateways) and cost information. The resulting optimal configuration that satisfies the requirements is described in terms of the total cost, number and locations of routers and gateways, characteristics of the nodes (number of channels and radios per node, power level/range, channel assignment), and routing information. Our contributions can be summarized as follows: (1) The uniqueness of our proposal lies in the fact that rather than treating each of the components (e.g., multi-channel, power control, placement of gateways, cost, etc.) separately, as has been done so far in the literature, we address the above issues using a unified model by exploiting the intimate relationships among them. The proposed model can be used both for a new WMNs solution and for any expansion of the network; (2) The proposed model is formulated as a linear program; its complexity has been considerably reduced by using/defining a relaxation of the interference constraints and an aggregation of the coverage constraints; and (3) Even though we propose, in this paper, an objective function that minimizes the cost of the network while satisfying the requirements, the proposed model can be used with any other objective function, e.g., maximizing the throughput while satisfying the requirements. The paper is organized as follows. Section 2 presents the proposed formulation of the WMNs design problem. Section 3 presents an evaluation of the proposed model. Section 4 concludes the paper and presents future research directions. II. FORMULATION A. Problem description In this section, we present a formulation of the WMNs design problem that takes into account all the parameters that OPTIMAL DESIGN OF BROADBAND WIRELESS MESH NETWORKS A. Beljadid, A. S. Hafid, and M. Gendreau Network Research Lab, University of Montreal {abeljadid, ahafid}@iro.umontreal.ca , michel.gendreau@cirrelt.ca