Wireless Network Design: Optimization Models and Solution ...

5 Mathematical Programming Models for Third Generation Wireless Network Design 113
5.3.4 The Power-Revenue Trade-Off
In this section we briefly illustrate how the models described above can be used to
investigate the tradeoff between profit and power consumption. The objective here
is neither minimization of total transmit power in the network nor maximization
of network operator revenue. Instead we find the optimal tradeoff between total
revenue and total transmit power. Network operators could use this type of analysis
to trade a portion of their net revenue for a substantial reduction in transmit power
for their subscribers. Such lowered transmit powers would lead to larger talk and
stand-by times for the mobile devices and could be an effective and new dimension
of product differentiation.
The objective function in this illustration is
max ∑ ∑ rmxmℓ − ∑ aℓyℓ − λ ∑ ∑
m∈M ℓ∈Lm ℓ∈L
m∈M
gmℓ ℓ∈Lm
� �� � � �� � � �� � (5.40)
Subscriber Tower Power
revenue cost cost
where rm is the annual revenue (in $) generated from each subscriber serviced in area
m and λ is a penalty term balancing the dollar costs with power. In this example we
seek a solution that optimizes (5.40) subject to the KKOIP constraints related to
tower location and subscriber assignment, (5.19)-(5.22) and (5.9).
Table 1: The Power-Revenue Trade-Off.
λ Tot. Power Demand Tot. Rev. Tower Cost Towers Profit
2.00E-12 1.70822E+12 100.00% $4,067,900 $729,725 5 $3,338,172
3.00E-12 1.70822E+12 100.00% $4,067,900 $729,725 5 $3,338,170
4.00E-12 1.70822E+12 100.00% $4,067,900 $729,725 5 $3,338,168
5.00E-12 1.70822E+12 100.00% $4,067,900 $729,725 5 $3,338,166
6.00E-12 1.70822E+12 100.00% $4,067,900 $729,725 5 $3,338,165
7.00E-12 1.17521E+12 100.00% $4,067,900 $875,670 6 $3,192,222
8.00E-12 7.45158E+11 100.00% $4,067,900 $1,021,615 7 $3,046,279
9.00E-12 7.45158E+11 100.00% $4,067,900 $1,021,615 7 $3,046,278
1.00E-11 7.45158E+11 100.00% $4,067,900 $1,021,615 7 $3,046,278
1.00E-10 1.60E+11 82.11% $3,339,960 $1,313,505 9 $2,026,439
The results given in Table 1 illustrate this tradeoff quantitatively. It can be seen
that all the demand can be satisfied using different amounts of power and at different
costs. Thus, a network operator may decide to provide service at lower net revenue
since it could reduce power consumption for users in the network. For example, a
reduction in net profit from $3,338,172 to $3,046,278 results in 3.6dB savings in
power. This substantially lower power consumption in the mobiles would lead to
increased battery, talk, and standby times and indirectly result in higher customer
satisfaction and increases in revenue. The reduction in power is due to the fact that
more towers are used in service, thus reducing the distance over which each mobile
needs to transmit.
xmℓ