Wireless Network Design: Optimization Models and Solution ...

138 Jeff Kennington, Jason Kratz, and Gheorghe Spiride
zs 2m ≤ 1 − ws 1 ∀m ∈ M,s1,s2 ∈ S|s1 �= s2 and γs 1 > γs 2 (6.4)
The next |M| constraints ensure that every MD is assigned to some AP.
∑ zsm = 1
s∈S
∀m ∈ M (6.5)
The next set of constraints force xs 1s 2 f to assume the value 1 if and only if both AP
s1 and s2 are installed and assigned frequency f .
xs 1s 2 f ≤ ys 1 f ∀s1,s2 ∈ S, f ∈ F|s1 < s2 (6.6)
xs 1s 2 f ≤ ys 2 f ∀s1,s2 ∈ S, f ∈ F|s1 < s2 (6.7)
xs 1s 2 f ≥ ys 1 f + ys 2 f − 1 ∀s1,s2 ∈ S, f ∈ F|s1 < s2 (6.8)
Suppose MD m1 is associated with AP s1. The throughput for m1 is related to
the signal-to-noise ratio at m1, as well as the total number of MDs associated with
s1 (see [16]). The signal strength at m1 is given by Ps1 γs1m1 and the noise at m1 is
given by ∑s 2∈S�{s 1} Ps 1 γs 1m 1 + Nm 1 . Let tsm denote the downlink signal strength at m
for the s − m association. Then
tsm = Psγsmzsm ∀s ∈ S,m ∈ M (6.9)
If m is not associated with s then both zsm and tsm will be zero. Let usm denote the
interference at m experienced by the s − m association. Then
usm = ∑ ∑ Ps2
s2∈S�{s}:s