Wireless Network Design: Optimization Models and Solution ...

6 Optimization Based WLAN Modeling and Design 137
device requesting service will typically connect to the nearest AP. The MD and the
AP enter into a negotiation to determine the highest transmission rate that can be
safely used. This transmission rate is a function of the received signal power and the
interference caused by other active MDs and other APs operating on the same frequency.
Given a WLAN design that covers all floors of a building and a set of MDs
with known locations requesting service, the network capacity can be calculated as
the sum of the transmission rates of all MDs. We use Shannon’s capacity calculation
to estimate the capacity of a given design with a given set of users.
For this model, the user must provide a set of potential locations for the APs and
select a set of static locations for all MDs to be serviced. Therefore, the attenuation
factor between each AP and each MD can be computed and are given constants for
this model. The model description shown in Table 6.4 requires four sets, two types
of constants, and six types of variables.
Table 6.4 Sets, Constants, and Variables used for the Capacity Model
Name Type Description
S set set of potential APs
M set set of all demand points
P set set of potential power levels
F set set of potential non-overlapping frequencies
γsm constant attenuation between AP s and MD m
Nm constant noise associated with MD m
ws binary variable ws = 1 if AP s is used; 0 otherwise
ys f binary variable ys f = 1 if AP s is assigned frequency f ; 0 otherwise
zsm binary variable zsm = 1 if MD m is affiliated with AP s; 0 otherwise
xs 1s 2 f binary variable xs 1s 2 f = 1 if both AP s1 and s2 are assigned frequency f
NS integer variable the number of APs to be installed in the design
Ps variable power setting for AP s
The first constraint ensures that exactly NS APs are selected for installation. This
constraint is simply
∑ ws = NS (6.1)
s∈S
The next |S| constraints ensure that each AP that is installed is assigned one of the
possible frequencies. These constraints are as follows:
∑ ys f = ws
f ∈F
∀s ∈ S (6.2)
The third set of constraints forbids assignment of an MD to an AP that is not installed.
zsm ≤ ws ∀s ∈ S,m ∈ M (6.3)
The following set of constraints ensures that each mobile is assigned to the installed
AP having the strongest signal.