A Geometric Theorem for Network Design

Consider an infinite square grid G. How many discs of given radius r, centered at the vertices of G, are required, in the worst case, to completely cover an arbitrary disc of radius r placed on the plane? We show that this number is an integer in the set {3,4,5,6} whose value depends on the ratio of r to the grid spacing. One application of this result is to design facility location algorithms with constant approximation factors. Another application is to determine if a grid network design, where facilities are placed on a regular grid in a way that each potential customer is within a reasonably small radius around the facility, is cost effective in comparison to a nongrid design. This can be relevant to determine a cost effective design for base station placement in a wireless network

Demand-based Network Planning for WLANs

The explosive recent growth in Wireless Local Area Network (WLAN) deployment has generated considerable interest among network designers. Previous design approaches have mostly focused on coverage based optimization or the application of trial and error strategies. These only ensure that adequate signal strength is maintained in the intended service area. WLAN service environments, however, require a network designed to provide not only radio coverage but also adequate capacity (data rate) across the service area so that it can carry traffic load from a large number of users with certain Quality of Service (QoS) requirements. Thus, current design techniques are insufficient to provide data communication services to WLAN users.In this dissertation, a novel approach to the WLAN design problem is proposed that takes into account user population density in the service area, traffic demand characteristics and the structure of the service area. The resulting demand-based WLAN design results in a network that provides adequate radio signal coverage and the required data rate capacity to serve expected user traffic demand in the service region. The demand-based WLAN design model is formulated as a Constraint Satisfaction Problem (CSP). An efficient heuristic solution technique is developed to solve the CSP network design problem in reasonable computational time. The solution provides the number of access points required and the parameters of each access point, including location, frequency channel, and power level. Extensive numerical studies have been reported for various service scenarios ranging from a single floor with small and large service areas to a multiple floor design to a design that includes outside areas. The results of these studies illustrate that the demand-based WLAN design approach is more appropriate for the design of the WLAN systems than are existing coverage based design approaches. Additionally, extensive sensitivity analysis was conducted to study the effects of user activity level (traffic load), shadow fading, and the use of different path loss models in network design