Cost-efﬁcient Capacitation of Cloud Data Centers for QoS-aware

Multimedia Service Provision

Ronny Hans

1

, Ulrich Lampe

1

, Michael Pauly

2

and Ralf Steinmetz

1

1

Multimedia Communications Lab (KOM), TU Darmstadt, Rundeturmstr. 10, 64283 Darmstadt, Germany

2

T-Systems International GmbH, Pascalstr. 51, 52076 Aachen, Germany

Keywords:

Cloud Computing, Data Center, Capacitation, Quality of Service, Multimedia, Service.

Abstract:

Cloud infrastructure is increasingly used for the provision of sophisticated multimedia services, such as cloud

gaming or Desktop as a Service, with stringent Quality of Service demands. Serving these service demands

results in the need to cost-efﬁciently select and capacitate data centers. In the work at hand, we introduce the

corresponding Cloud Data Center Capacitation Problem and propose two optimization approaches. Through

a quantitative evaluation, we demonstrate that an exact solution approach is only practically applicable to

small problem instances, whereas a heuristic based on Linear Program relaxation achieves signiﬁcant reduc-

tions in computation time of about 80% while retaining a favorable solution quality, with cost increases of

approximately 5% or less.

1 INTRODUCTION

Since the term was ﬁrst coined in the mid-2000s,

cloud computing has received increasing attention by

both IT practitioners and researchers. In this con-

text, a focus has often been on Infrastructure as a

Service, given that it is the most ﬂexible among the

three cloud computing service models (Briscoe and

Marinos, 2009) and that its successful application has

been widely documented in the literature, e. g., (Arm-

brust et al., 2009). However, with the increasing ma-

turity of cloud computing, the focus is shifting toward

the cloud-based delivery of sophisticated multimedia

services. Such software-oriented services include, for

example, cloud gaming / Games as a Service (Chang,

2010) or Dekstop as a Service (Erdogmus, 2009).

Due to their nature, such multimedia services pose

high demands concerning Quality of Service (QoS)

attributes. Unfortunately, past empirical research has

shown that the current cloud infrastructure is partially

insufﬁcient to meet those demands, most notably due

to the latency that arises from the massive centraliza-

tion of cloud data centers in few geographical loca-

tions (Choy et al., 2012).

Accordingly, in the work at hand, we examine

how cloud data centers can be appropriately selected

and capacitated in order to serve QoS-aware multime-

dia services. In our previous work (Hans et al., 2013),

we have addressed the selection of cloud data centers

for single service types and time-invariant service de-

mands. The work at hand expands our past research

through the consideration of multiple service types, as

well as ﬂuctuating service demands, and also regards

the resulting distinction between variable costs for op-

eration and reservation of cloud infrastructure. In this

context, we propose an exact solution approach, based

on an Integer Program (IP) formulation, as well as a

heuristic approach based on Linear Program (LP) re-

laxation.

The remainder of this paper is structured as fol-

lows: In Section 2, we brieﬂy explain the speciﬁc

problem that is addressed in this paper. In Sec-

tion 3, we introduce formal notations, based on which

we specify two optimization approaches. These ap-

proaches are quantitatively evaluated in Section 4. An

overview of related work is given in Section 5. Sec-

tion 6 concludes the paper with a brief summary and

outlook on future work.

2 PROBLEM STATEMENT

In this work, we assume the role of a service provider,

who aims to deliver multimedia services to a dis-

tributed set of users. Speciﬁcally, we consider a set

of so-called user clusters, each of which represents

a predeﬁned number of users in a certain geographi-

158

Hans R., Lampe U., Pauly M. and Steinmetz R..

Cost-efﬁcient Capacitation of Cloud Data Centers for QoS-aware Multimedia Service Provision.

DOI: 10.5220/0004947101580163

In Proceedings of the 4th International Conference on Cloud Computing and Services Science (CLOSER-2014), pages 158-163

ISBN: 978-989-758-019-2

Copyright

c

2014 SCITEPRESS (Science and Technology Publications, Lda.)

cal location, e. g., a state or county. Each user cluster

exhibits speciﬁc demands for a given set of service

types, with the demand ﬂuctuating over a predeﬁned

number of time slots. If these demands cannot be

met, certain penalties accrue. Furthermore, each ser-

vice type is associated with certain QoS requirements,

e. g., concerning permissible latency.

In order to deliver his/her services, the provider

has the choice among a given set of data centers. The

selection of a data center incurs certain ﬁxed costs,

e. g., for construction or long-term lease. In addition,

the operation of a server within each data center re-

sults in certain variable costs. Furthermore, the reser-

vation of a number of servers over the planning period

may incur certain variable reservation costs. Due to

the geographical distribution, each data center makes

different QoS guarantees with respect to each user

cluster.

The aim of the provider is to choose among the

data centers and further take a capacitation decision,

i. e., decide on the number of reserved servers, such

that the overall cost of the solution is minimized. In

the following, we refer to this problem – which is a

generalization of a research issue we previously ex-

amined (Hans et al., 2013) – as Cloud Data Center

Capacitation Problem (CDCCP).

3 OPTIMIZATION APPROACHES

In the following, we ﬁrst introduce a set of nota-

tions to formally represent the CDCCP (cf. Sec-

tion 3.1). Subsequently, we introduce two optimzi-

ation approaches, namely an exact approach based on

Integer Programming (cf. Section 3.2) and a heuristic

approach based on LP relaxation (cf. Section 3.3).

3.1 Formal Notations

In order to represent the CDCCP in the form of a

mathematical model, a few formal notations are re-

quired. To begin with, we formally deﬁne the basic

entities within the CDCCP using the following sym-

bols:

• D = {1, 2, ..., D

#

}: Set of (potential or existing)

data centers

• U = {1, 2, ..., U

#

}: Set of user clusters

• S = {1, 2, ..., S

#

}: Set of available services

• Q = {1, 2, ..., Q

#

}: Set of considered QoS at-

tributes

• T = {1, 2, ..., T

#

}: Set of discrete time slots within

the planning period

Based on the previously introduced basic entities, the

parameters that are associated with the individual en-

tities can be deﬁned as follows:

• SD

u,s,t

: Service demand of user u for service s at

time t

• K

min

d

∈ R: Minimal capacity of data center d

• K

max

d

∈ R: Maximal capacity of data center d

• CF

d

∈ R: Fixed cost of selecting data center d

• CVO

d

∈ R: Variable cost for operating one server

unit for one time unit in data center d

• CVR

d

∈ R: Variable cost for reserving one server

unit in data center d

• CP

u,s

∈ R: Penalty cost per service unit not pro-

vided to user u w.r.t. service s

• QG

d,u,q

∈ R: QoS guarantee of data center d w.r.t.

user u for QoS attribute q

• QR

u,s,q

∈ R: QoS requirement of user u w.r.t. ser-

vice s for QoS attribute q

Lastly, in order to model the CDCCP as optimization

problem, we use the following decision variables:

• x

d

: Selection of a data center d

• y

d,u,s,t

: Capacity provided by data center d to user

cluster u concerning service s at time t

• y

0

u,s,t

: Penalty-bound capacity not provided to user

cluster u concerning service s at time t

• z

d

: Capacity reserved in data center d

3.2 Exact Optimization Approach

CDCCP-EXA.KOM

Based on the notations from the previous section, the

CDCCP can be modeled as an optimization prob-

lem in an intuitive manner. The result is provided in

Model 1 and will be explained in detail in the fol-

lowing. To begin with, Equation 1 deﬁnes the objec-

tive function, aiming at a minimization of total costs,

depending on the values of the decision variables.

Equation 2 ensures that all service demands will be

satisﬁed or that corresponding penalties will accrue.

Equation 3 links the decision variables y and z, ensur-

ing that only the reserved capacity in each data center

may be used in each time slot. Equations 4 and 5

make sure that the capacity constraints for each data

center are held. Equation 6 ensures that the QoS re-

quirements of each user cluster are matched by the

corresponding data center guarantees, depending on

the value of the auxiliary variable p from Equation 7.

Lastly, Equation 8 deﬁnes the decision variables as

binary and natural.

Cost-efficientCapacitationofCloudDataCentersforQoS-awareMultimediaServiceProvision

159

As can easily be seen, Model 1 constitutes an IP.

Such problems can be solved using off-the-shelf al-

gorithms, most notably the branch-and-bound algo-

rithm (Domschke and Drexl, 2004). However, despite

its efﬁciency in many application scenarios, branch-

and-bound is based on the principle of enumeration

(Hillier and Lieberman, 2005). Hence, in the worst

case, the time complexity of computing a solution to

a given problem instance grows exponentially with

the number of decision variables, i. e., the number

of entities in the model. Accordingly, the practical

applicability of CDCCP-EXA.KOM is likely limited

to smaller problem instances and situations where the

computation time requirements play an inferior role.

3.3 Heuristic Optimization Approach

CDCCP-REL.KOM

The brief qualitative analysis from the previous sec-

tion indicates a potentially high computational com-

plexity for the exact approach CDCCP-EXA.KOM.

Based on this notion, we introduce a heuristic ap-

proach that is based on the common concept of LP

relaxation (Domschke and Drexl, 2004). Speciﬁcally,

the binary and integer decision variables in the initial

model (cf. Equation 8) are substituted by correspond-

ing natural variables (cf. Equation 9).

The resulting LP formulation of the initial prob-

lem can be solved using another set of off-the-shelf

algorithms, such as interior point methods. In contrast

to branch-and-bound, such algorithms are character-

ized by polynomial, rather than exponential worst

case time complexity (Hillier and Lieberman, 2005).

This renders them potentially applicable to larger

problem instances, even under relatively rigid time

constraints. From the LP-based solution, a ﬁnal so-

lution can simply be deduced by rounding all natural

values of the decision variables to the next-highest in-

teger.

4 EVALUATION

4.1 Setup

In order to assess the applicability of our proposed

optimization approaches, we prototypically imple-

mented them in Java 7. As solver framework, we

used IBM ILOG CPLEX 12.5

1

, which was accessed

through the JavaILP middleware

2

.

1

http://www.ibm.com/software/integration/optimization

/cplex-optimizer/

2

http://javailp.sourceforge.net/

Model 1. Cloud Data Center Capacitation Problem.

Min. C(x, y, z) =

∑

d∈D

x

d

×CF

d

(1)

+

∑

d∈D,u∈U,s∈S,t∈T

y

d,u,s,t

×CVO

d

+

∑

d∈D,u∈U,s∈S,t∈T

y

0

u,s,t

× ×CP

u,s

+

∑

d∈D

z

d

×CV R

d

y

0

u,s,t

+

∑

d∈D

y

d,u,s,t

≥ SD

u,s,t

(2)

∀u ∈ U, ∀s ∈ S, ∀t ∈ T

∑

u∈U,s∈S

y

d,u,s,t

≤ z

d

∀d ∈ D, ∀t ∈ T (3)

z

d

≤ x

d

× K

max

d

∀d ∈ D (4)

z

d

≥ x

d

× K

min

d

∀d ∈ D (5)

y

d,u,s,t

≤ p

d,u,s

× K

max

d

(6)

∀d ∈ D, ∀u ∈ U, ∀s ∈ S, ∀t ∈ T

p

d,u,s

=

(

1 if QG

d,u,q

≤ QR

u,s,q

∀q ∈ Q

0 else

(7)

x

d

∈ {0, 1} ∀d ∈ D (8)

y

d,u,s,t

∈ N ∀d ∈ D, ∀u ∈ U, ∀s ∈ S, ∀t ∈ T

y

0

u,s,t

∈ N ∀u ∈ U, ∀s ∈ S, ∀t ∈ T

z

d

∈ N ∀d ∈ D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

d

∈ R, 0 ≤ x

d

≤ 1 ∀d ∈ D

y

d,u,s,t

∈ R, y

d,u,s,t

≥ 0 ∀d ∈ D, ∀u ∈ U, ∀s ∈ S, ∀t ∈ T

y

0

u,s,t

∈ R, y

u,s,t

≥ 0 ∀∀u ∈ U, ∀s ∈ S, ∀t ∈ T

z

d

∈ R, z

d

≥ 0 ∀d ∈ D

(9)

In accordance with Silver (Silver, 2004), our eval-

uation focuses on two dependent variables, namely

computation time and solution quality (i. e., total cost

associated with the computed solution). As indepen-

dent variables, we considered the number of data cen-

CLOSER2014-4thInternationalConferenceonCloudComputingandServicesScience

160

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

Cost-efficientCapacitationofCloudDataCentersforQoS-awareMultimediaServiceProvision

161

0.1

1

10

100

1000

D

#

= 5

(50)

D

#

= 10

(50)

D

#

= 15

(50)

D

#

= 20

(49)

D

#

= 25

(50)

U

#

= 25

(50)

U

#

= 50

(49)

U

#

= 75

(49)

U

#

= 100

(50)

U

#

= 125

(50)

S

#

= 1

(50)

S

#

= 2

(50)

S

#

= 3

(49)

S

#

= 4

(50)

S

#

= 5

(49)

T

#

= 3

(50)

T

#

= 6

(49)

T

#

= 9

(50)

T

#

= 12

(50)

T

#

= 15

(50)

Mean Computation Time [s]

Test Case (Sample Size)

CDCCP-REL.KOM CDCCP-EXA.KOM

Figure 1: Observed mean computation times (with 95% conﬁdence intervals) by test case. Please note the logarithmic scaling

of the ordinate. If not speciﬁed differently, we use D

#

= 15, U

#

= 75, S

#

= 3, and T

#

= 9 for the independent variables.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

D

#

= 5

(50)

D

#

= 10

(50)

D

#

= 15

(50)

D

#

= 20

(49)

D

#

= 25

(50)

U

#

= 25

(50)

U

#

= 50

(49)

U

#

= 75

(49)

U

#

= 100

(50)

U

#

= 125

(50)

S

#

= 1

(50)

S

#

= 2

(50)

S

#

= 3

(49)

S

#

= 4

(50)

S

#

= 5

(49)

T

#

= 3

(50)

T

#

= 6

(49)

T

#

= 9

(50)

T

#

= 12

(50)

T

#

= 15

(50)

Ratio of Computation Time

Test Case (Sample Size)

CDCCP-REL.KOM / CDCCP-EXA.KOM

Figure 2: Ratio of computation times (based on macro-average; with 95% conﬁdence intervals) between the two optimization

approaches by test case. Conﬁguration identical to Figure 1.

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

D

#

= 5

(50)

D

#

= 10

(50)

D

#

= 15

(50)

D

#

= 20

(49)

D

#

= 25

(50)

U

#

= 25

(50)

U

#

= 50

(49)

U

#

= 75

(49)

U

#

= 100

(50)

U

#

= 125

(50)

S

#

= 1

(50)

S

#

= 2

(50)

S

#

= 3

(49)

S

#

= 4

(50)

S

#

= 5

(49)

T

#

= 3

(50)

T

#

= 6

(49)

T

#

= 9

(50)

T

#

= 12

(50)

T

#

= 15

(50)

Ratio of Cost

Test Case (Sample Size)

CDCCP-REL.KOM / CDCCP-EXA.KOM

Figure 3: Ratio of costs (based on macro-average; with 95% conﬁdence intervals) between the two optimization approaches

by test case. Conﬁguration identical to Figure 1.

consider time-variant service demands.

(Choy et al., 2012) study the current cloud infras-

tructure with respect to cloud gaming. The authors

demonstrate that the current Amazon EC2 data cen-

ters could only serve 70% of the US population with

adequate latency. Based on this ﬁnding, they propose

the use of so-called edge servers to extend the current

existing infrastructure, and validate their proposal us-

ing simulation approaches. In contrast to us, Choy et

al. do not propose an exact approach for data center

capacitation, and do not consider time-variant service

demand.

(Larumbe and Sans

`

o, 2012) present an optimiza-

tion approach that addresses three distinct, yet inter-

CLOSER2014-4thInternationalConferenceonCloudComputingandServicesScience

162

linked problems: the geographical location of data

centers, the location of software components that are

hosted in network nodes and routing. Because the au-

thors see a close connection between these problems,

they integrated them in one mathematical framework

using an optimal approach. Similar to the two afore-

mentioned papers, this work only considers static ser-

vice demand. Also, it exclusively provides an exact,

but not a heuristic solution approach.

In summary, to the best of our knowledge, our

work is the ﬁrst to address the cost-efﬁcient capaci-

tation and placement of cloud data centers for QoS-

aware services under consideration of time-variant

service demand. In this context, this paper not

only provides the exact solution approach CDCCP-

EXA.KOM but also an initial heuristic solution,

CDCCP-REL.KOM, which features substantially re-

duced computation times.

6 SUMMARY AND OUTLOOK

Cloud-based delivery of multimedia services, such as

cloud gaming or Desktop as a Service, offers great

economic potential. However, the adequate design

of the underlying cloud infrastructure is a challeng-

ing task that has been only insufﬁciently addressed

in research so far. In this work, we introduced the

according Cloud Data Center Capacitation Problem

(CDCCP). We proposed an exact solution approach,

named CDCCP-EXA.KOM, based on Integer Pro-

gramming. We further proposed a basic heuristic,

called CDCCP-REL.KOM, which is based on the

principle of Linear Program relaxation. Based on

a quantitative evaluation, we showed that CDCCP-

EXA.KOM is only practically applicable to smaller

problem instances due to its exponential computa-

tional complexity. In contrast, CDCCP-REL.KOM

features polynomial time complexity, thus signiﬁ-

cantly reducing the required computational effort for

solving individual problem instances by 80% or more.

At the same time, the heuristic maintains a favor-

able solution quality, with cost increases generally

amounting to less than 5% compared to an exact so-

lution.

Our future work primarily aims at the develop-

ment of further heuristic approaches, which provide

an even more favorable tradeoff between computa-

tional complexity and solution quality. Furthermore,

we will extend the proposed approaches to account for

stochastic, rather than just deterministic parameters,

e. g., uncertain service demands or QoS properties.

ACKNOWLEDGEMENTS

This work has partly been sponsored by the E-Finance

Lab e.V., Frankfurt a.M., Germany and by the Ger-

man Research Foundation (DFG) in the CRC 1053 –

MAKI.

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