Solution methods for planning problems in wireless mesh networks

Wireless Mesh Networks (WMNs) consist of a finite number of radio nodes. A subset of these nodes, called gateways, has wired connection to the Internet and the non-gateway nodes transmit their traffic to a gateway node through the wireless media in a multi-hop fashion. Wireless communication signals that propagate simultaneously within the same frequency band may interfere with one another at a receiving node and may therefore prevent successful transmission of data. In order to circumvent this problem, nodes on the network can be configured to receive and send signals in different time slots and through different frequency bands. Therefore, a transmission slot can be defined as a pair of a certain frequency band and a specific time slot. In addition, by adjusting the power level of a radio node, its transmission range can be modified. Given a wireless mesh network with fixed node locations, demand rate at each node, and maximum power level for each node, we study the problem of carrying the traffic of each node to the Internet through the network. Our goal is to allocate capacities in proportion to the demand of each node in such a way that the minimum ratio is maximized. We propose a mixed integer linear programming (MILP) formulation to select a given number of gateway locations among the nodes in the network, to determine the routing of the traffic of each node through the gateway nodes, to assign transmission slots to each node in order to ensure no interference among wireless signals, and to determine the transmission power levels. In our study, we adopt the physical interference model, instead of the protocol interference, since this is more realistic. Since MILP formulation becomes computationally inefficient for larger instances; we developed several different approaches. Then, we proposed a combinatorial optimization model which successfully solves most of the instances. We tested our models and methods in several data sets, and results are presented.