![](bg4.png)
ters (D
#
), user clusters (U
#
), service types (S
#
), and
time slots (T
#
), since they have a direct impact on the
number of decision variables, and hence, the size of
the solution space. We used a fractional factorial de-
sign, varying the value of each independent variable
separately while treating the remaining variables as
controlled, i. e., assuming a fixed value.
In accordance with our previous work (Hans et al.,
2013), we employed data from the 2010 United States
census
3
as the basis for problem generation. In or-
der to model data centers and user clusters, we ran-
domly drew US counties from the census data, and
set the service demands and different cost parameters
based on the according county population and median
income. As the only QoS requirement, we consid-
ered latency and set it to represent different multi-
media service types, ranging from cloud gaming to
Desktop as a Service. The QoS guarantees were fi-
nally computed based on the geographical distance
between data centers and user clusters.
For each test case, i. e., distinct combination of
values for the independent variables, we randomly
created 50 problem instances. Problems that could
not be successfully solved by the heuristic approach
CDCSP-REL.KOM were removed from the sample;
such invalid solutions may result from certain capac-
ity constraints not being met due our simplistic next-
highest integer rounding approach (cf. Section 3.3).
Based on the samples, we subsequently computed the
observed mean absolute computation times, as well
as the macro-averaged ratios of computation time and
total cost between CDCCP-REL.KOM and CDCCP-
EXA.KOM, along with the respective 95% confi-
dence intervals based on a t-distribution (Kirk, 2007).
The evaluation was conducted on a desktop computer,
equipped with an Intel Core 2 Quad Q9450 processor
and 4 GB of memory, operating under Microsoft Win-
dows 7.
4.2 Results and Discussion
The results of our evaluation are presented in Fig-
ures 1 through 3. As can be seen in Figure 1, the
observed mean absolute computation times strikingly
confirm the different computational complexity of
CDCCP-EXA.KOM and CDCCP-REL.KOM. Even
for the smallest considered test cases, the computa-
tion time for CDCCP-EXA.KOM ranges in the order
of magnitude of 1 s, quickly growing to 10 s or even
100 s with an increasing size of the problem instances.
In contrast, the mean computation times for CDCCP-
REL.KOM remain in the order of magnitude of 10 s,
3
http://www.census.gov/geo/maps-data/data/gazetteer
.html
even for the largest problem classes. These find-
ings are also confirmed by the macro-averaged ratios
of computation times, as given in Figure 2. Except
for the smallest problem classes, CDCCP-REL.KOM
consistently reduces the computation time by about
80% or more to CDCCP-EXA.KOM. The reduction
is statistically significant across all test cases at the
assumed confidence level of 95% (i. e., α = 0.05).
On the downside, Figure 3 indicates that the appli-
cation of LP relaxation in CDCCP-REL.KOM comes
at a certain amount of additional cost, i. e., degra-
dation in solution quality. Compared to CDCCP-
EXA.KOM, the increase ranges between approxi-
mately 0.4% and 4.3%; however, it does not exceed
1.5% for all considered test cases except one. Thus,
while the slight increase is statistically significant for
practically all test cases at the 95% confidence level,
it can be considered quite marginal and most likely
acceptable in practical applications. In addition, as
can be seen from the given sample sizes, CDCCP-
REL.KOM is able to provide valid solutions to essen-
tially all considered problem instances, except in six
test cases, where one instance respectively could not
be solved.
In conclusion, we find that the exact optimiza-
tion approach CDCCP-EXA.KOM is associated with
high computational complexity and hence, its practi-
cal application is limited to small problem instances.
However, the approach can also serve as a benchmark
for the assessment of alternative solution approaches,
such as CDCCP-REL.KOM. The latter has presented
a much more favorable performance in our experi-
ments with respect to computational demands. Never-
theless, the development of custom-tailored optimiza-
tion approaches for the CDCCP that do not rely on LP
formulations may provide further improvements con-
cerning the trade-off between computational require-
ments and solution quality.
5 RELATED WORK
In recent years, there has been vivid research in the
area of cloud computing. In the following, we briefly
discuss selected works that are most closely related to
our research.
(Goiri et al., 2011) present an approach for effi-
cient data center placement based on several factors,
e. g., available network backbones and proximity of
population centers. To find a solution for the place-
ment problem, the authors use a combination of ex-
act and approximate approaches. Thereby, Goiri et al.
focus on design time, i. e., construction planning for
new data centers. In contrast to our work, they do not
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