Wireless Network Design: Optimization Models and Solution ...

5 Mathematical Programming Models for Third Generation Wireless Network Design 115
antennas to focus energy in particular directions or sectors of the cell, and signals
from any particular test point are only received in one sector of each cell. Cai [15]
extends the CKKOIP model to include a choice of an omnidirectional antenna (as
in the models described earlier in this chapter) or a directional antenna with either
three 120 ◦ sectors or six 60 ◦ sectors.
The models described above are driven by demand forecasts. In telecommunications
(and many other industries) it is exceedingly difficult to accurately forecast
demand [38]. Optimizing a CDMA network design for a forecast that turns out to
be inaccurate can be very costly. If the forecast overestimates the demand, then the
provider will incur unnecessary costs in building an over-capacitated network. On
the other hand, if the forecast underestimates the demand, then the provider pays
an opportunity cost for missing potential revenue and risks losing market share in a
highly competitive business (at least until they add sufficient capacity to capture all
the demand). Rosenberger and Olinick [48, 52] develop a stochastic programming
model with simple recourse [50] to optimize tower location in CDMA networks under
demand uncertainty. Specifically, the model chooses a set of tower locations that
maximizes the expected profit in the KKOIP model (without the FCC constraints)
given a probability distribution for the demand at each test point.
Robust optimization is another popular strategy for handling uncertainty in mathematical
programming models. The idea behind robust optimization is to create a
design that will be fairly good (robust) no matter which of a given set of scenarios
occurs. There are several different concepts of robustness that appear in the
literature (e.g., [10, 11, 12, 37, 45, 49]) and applications of robust optimization
models for designing fiber-optic telecommunications networks under demand uncertainty
may be found in [14, 30, 35, 38, 54]. Bienstock and D’Andreagiovanni
[13] and D’Andreagiovanni [18] use a robust optimization framework to address
another source of uncertainty in planning wireless networks, the attenuation factors.
Even when these factors are measured empirically, the actual attenuation experienced
when the network is deployed may differ from what was measured due to
weather conditions, new construction, and other factors. This difference can lead to
less coverage and/or lower quality of service than was planned. The model proposed
in [13, 18] produces designs that are “protected” against changes in the attenuation
factors. Eisenblätter et al. [20, 21] describe a very detailed, robust optimizationbased
3G planning system developed for the Models and Simulations for Network
Planning and Control of UMTS (MOMENTUM) project conducted at the Zuse Institute
Berlin. The model developed for MOMENTUM is a robust model that considers
such design elements as sectorization, specific antenna configurations (e.g.,
type, height, and tilt), and transmission power model (power-based vs. SIR-based)
in addition to tower location and subscriber assignment.
The models described in this chapter have been presented as so-called “green
field” problems in which a network is being designed for an area that currently has
no infrastructure in place. In many cases, however, providers seek to leverage their
existing infrastructure when deploying 3G networks. Kalvenes et al. [34] describe
several variations on the theme of using the type of planning models discussed in
this chapter to optimize the expansion of existing infrastructure to increase network