Wireless Network Design: Optimization Models and Solution ...

110 Eli Olinick
gmℓ
∑ ∑
m∈M
gm j∈Lm j
xm j ≤ s + (1 − yℓ)βℓ ∀ℓ ∈ L. (5.22)
KKOIP also includes a set of constraints that model a minimum-service requirement
that the United States Federal Communications Commission (FCC) imposes
on cellular service providers as part of its licensing regulations. After receiving a license
from the FCC, the service provider has a five-year time window during which
it must install enough network capacity so that it could provide service to at least
a certain fraction ρ of the population in the market or else forfeit its license. The
value of ρ depends on the frequency band of the license [23, 34]. The constraints
enforcing the FCC requirement are
qm ≤ ∑ yℓ
ℓ∈Lm
∀m ∈ M, (5.23)
qm ≥ yℓ ∀m ∈ M,ℓ ∈ Lm, (5.24)
∑ dmqm ≥ ρ ∑ dm, (5.25)
m∈M
m∈M
qm ∈ {0,1} ∀m ∈ M, (5.26)
where qm is one if, and only if, test point m can be serviced by at least one of the
selected towers. Constraint set (5.23) ensures that a test point is only considered
capable of receiving service if there is at least one selected tower within its reach as
determined by Pmax. Conversely, constraint set (5.24) forces the indicator variable
qm equal to one if there is at least one selected tower in range of test point m. Constraint
(5.25) ensures that the proportion of the demand at the test points that could
be assigned to the selected towers is at least ρ, and (5.26) defines the qm variables
as binary. Hence, KKOIP maximizes (5.18) subject to (5.19)-(5.26) and (5.9).
5.3.3 Infrastructure
As described earlier, a comprehensive CDMA planning model should consider other
elements of the network infrastructure (e.g., MTSOs) in addition to the tower locations.
A cost minimization model that includes tower-to-MTSO wiring cost and
handoff cost for a given traffic volume at the base stations was developed by Merchant
and Sengupta [43] and refined by Li et al. [40]. Cai et al. [16, 17] build on this
work and on the KKOIP model to develop an integrated profit maximization model
considering the selection of tower, MTSO and PSTN gateway locations, tower-to-
MTSO connections, subscriber assignment, and the backbone network as depicted
in Figures 5.1 and 5.2. In addition to the input parameters described previously, the
model in [17] includes a set of candidate MTSO locations denoted by K. The set
K0 denotes the union of K and the PSTN gateway (i.e., location zero). The binary
variable zk is equal to one if, and only if, the design uses an MTSO at location k,
and binary variable sℓk indicates whether or not tower ℓ is connected to the MTSO