Wireless Network Design: Optimization Models and Solution ...

130 Jeff Kennington, Jason Kratz, and Gheorghe Spiride
to mobile orientation and the largest 20% and smallest 20% of the values were
discarded. The average of the remaining 60% was used in an integer programming
model to determine the optimal location for their 3 APs. Using 3 APs is desirable
since each may be assigned a unique frequency and thereby avoid interference.
Site surveys can be useful for developing a coverage-oriented design for low
density areas, but may not produce a good capacity-oriented design for high density
areas. That is, capacity measurements are not part of a site survey but can be
incorporated within software tools. Some clients have found site surveys to be fairly
expensive.
6.2.2 Coverage Models
A simple optimization-based coverage oriented model can be developed by superimposing
two grids onto a site: one for potential AP locations and one for mobile
device (MD) locations. The MD grid is usually finer than the AP grid since in practice
mobile devices could occupy many more positions than APs. The idea is to
select the minimum number of AP grid points so that each MD grid point is covered
(within range) of at least one AP. This can be modeled as a simple binary integer
program. A description of the sets and variables needed for this model may be found
in Table 6.2, and the coverage-oriented model is given as follows:
Minimize ∑ ws
s∈S
Subject to
∑
s∈CMm
ws ≥ 1∀m ∈ M
ws ∈ {0,1} ∀s ∈ S
Table 6.2 Sets and Variables used for the Coverage Model
Name Type Description
S set set of potential APs
M set set of all demand points
CMm subset of S set of APs within range of MD m
ws binary variable ws = 1 if AP s is used; 0 otherwise
This model was used to cover a square site with a dimension of 250 feet as
illustrated in Figure 6.1. Each grid square has a dimension of 50 feet by 50 feet.
The MDs are placed on the 36 grid points and the potential locations for APs are
placed on the 16 internal grid points. For effective communication, the distance