CSP Formulation for Scheduling Independent Jobs in Cloud Computing

M’hamed Mataoui

, Faouzi Sebbak

, Kada Beghdad Bey

and Farid Benhammadi

IS & DB Laboratory, Ecole Militaire Polytechnique, Algiers, Algeria

AI Laboratory, Ecole Militaire Polytechnique, Algiers, Algeria

Keywords:

Scheduling Algorithms, Cloud Computing, Job Scheduling, Resource Allocation, CSP Formulation.

Abstract:

This paper investigates the use of Constraint Satisfaction Problem formulation to schedule independent jobs in

heterogeneous cloud environment. Our formulation provides abasis for computing an optimal Makespan using

job and machine reordering heuristics based on Min-min algorithm result. The combination of these heuristics

with the weighted constraints allows improving the efﬁciency of the tree search algorithm to schedule jobs with

considerable space search reduction. The proposed CSP model is validated through simulation experiments

against clusters of 10 virtual machines. The results demonstrate that our model is able to efﬁciently allocate

resources for jobs with signiﬁcant performance gains between 18% - 40% compared to the Min-Min heuristic

results to optimize the Makespan.

1 INTRODUCTION

Nowadays heterogeneous cloud computing is expand-

ing its services to data-intensive computing on cloud

platforms because each job (application) of users runs

on a separate virtual machine. In these platforms,

the jobs are independent and different from one an-

other and it needs an optimal maximal completion

time (Makespan). Hence the Scheduling process in

cloud computing systems is useful for several dif-

ferent user needs. Static or dynamic heuristics are

proposed for cloud to ﬁnd an optimal solution to the

scheduling. Static heuristics deﬁne a schedule at com-

piled time based on the knowledge of the processors

availability and tasks to be executed. Dynamic heuris-

tics, on the other hand, are applied when the tasks ar-

rival time is not beforehand known and therefore the

system needs to schedule tasks as they arrive (Bar-

bosa and Moreira, 2009). The scheduling strategy

deﬁnes the instants when the scheduling algorithm

is called to produce a schedule based on forecasting

resources performances and independent tasks to be

executed. The aim of task scheduler in cloud com-

puting environment is to determine a proper assign-

ment of resources to the tasks of jobs to complete

all the jobs received from clients. Large numbers

of jobs scheduling heuristics are available for maxi-

mizing proﬁt via resources allocation in cloud com-

puting systems (Kuribayashi, 2011; Abirami and Ra-

manathan, 2012; Gouda et al., 2013; Irugurala and

Chatrapati, 2013).

The challenge that needs to be addressed is how

efﬁciently schedule jobs in cloud computing based on

the job completion time’s optimization to increase re-

source utilization. In this paper, we consider the prob-

lem of resource allocation in heterogeneous cloud

environment. The proposed solution in this work

is based on the computing power parameter for re-

sources allocation in cloud environment. Clients

in our case are jobs decomposed into various tasks

where each task should be assigned to one of the

resources, which is best suited for its execution to

maximize the proﬁt. The proposed approach uses

constraint satisfaction problem formulation to sched-

ule independent jobs in heterogeneous cloud environ-

ment. Our formulation provides a basis for comput-

ing an optimal Makespan using job and machine re-

ordering heuristics based on Min-min algorithm re-

sult. The combination of these heuristics with the

weighted constraints allows improving the efﬁciency

of the tree search algorithm to schedule jobs with

considerable space search reduction. The proposed

CSP model is validated through simulation experi-

ments. Our evaluation shows that the proposed ap-

proach can improve efﬁciency and effectiveness of

heterogeneous cloud computing systems with signif-

icant performance gains between 18% - 40% com-

pared to the Min-Min heuristic results to optimize the

Makespan.

This paper is organized as follows. Related works

105

Mataoui M., Sebbak F., Beghdad Bey K. and Benhammadi F..

CSP Formulation for Scheduling Independent Jobs in Cloud Computing.

DOI: 10.5220/0005438801050112

In Proceedings of the 5th International Conference on Cloud Computing and Services Science (CLOSER-2015), pages 105-112

ISBN: 978-989-758-104-5

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

about resources allocation strategies in cloud comput-

ing environment are introduced in Section 2. Section

3 presents the makespan optimization problem deﬁni-

tion. Section 4 describes the proposed solution in re-

source allocation in heterogeneous cloud computing

environments, assuming both task arrive simultane-

ously and machine available time updated. The simu-

lation results are presented in Section 5 and Section 6

concludes this paper.

2 RELATED WORK

There has been a large amount of work focusing

on static scheduling approaches on cloud computing

platforms and are currently prevalent in clouds. These

approaches use static heuristics which are suitable for

known prior time execution of jobs. Yuan et al. (Yuan

et al., 2011) propose an intelligent scheduler which

can handle heterogeneous resources. , and be able

to allocate resources according to user needs. The

proposed intelligent scheduler shows an improved

scheduling algorithm for making efﬁcient resources

allocation in cloud. Zhang et al. (Xie et al., 2012) uses

the a dynamic constraint programming to solve the

problem of virtual cloud resource allocation model.

This approach takes into account both users’ QoS re-

quirements and the cost of virtual cloud resources.

The simulation results show that the proposed ap-

proach can efﬁciently allocate and manage the virtual

resources of the cloud platform, and are in agreements

with those of (Zhang et al., 2013). Goudarzi and Pe-

dram (Goudarzi and Pedram, 2011), address the Ser-

vice Level Agreements (SLA)-based resource alloca-

tion problem for cloud and a distributed solution for

this problem is proposed. The response time of the

request based on the different allocation of resources

for different servers and the cluster is modeled and

used in the proﬁt optimization problem.

In (Santos et al., 2002), the authors propose a

mathematical formulation for the resource allocation

problem in clusters. The authors describe a method

to ﬁnd the best resource assignment in a cluster in

the case that the application has certain resource re-

quirements. Experimental results proved that the pro-

posed method was able to realize best load balanc-

ing and reasonable resources utilization. In (Li et al.,

2010), an adaptive resource allocation algorithm for

the cloud system with preemptable tasks is consid-

ered. The proposed algorithms adjust the resource al-

location adaptively based on the updated of the actual

task executions. A. Kundu et al (Kundu et al., 2010)

proposed the memory utilization method in cloud

computing environment based on transparency. The

proposed mechanism enables users to access mem-

ories depending on the predeﬁned criteria. The re-

source allocation is made based on the selection crite-

ria which will improve the efﬁciency of the cloud en-

vironment. The memory manager is responsible for

allocating memory resources to the clients. The au-

thors introduced a cloud service based memory uti-

lization which is an effective mechanism for allocat-

ing memories in cloud computing environment. A

scheduling algorithm named as Linear Scheduling for

Tasks and Resources (LSTR) is designed in (Abi-

rami and Ramanathan, 2012). This algorithm per-

forms tasks and resources scheduling respectively.

The combination of Nimbus and Cumulus services

are imported to a server node to establish the IaaS

cloud environment. The virtualization technique used

with the scheduling algorithm will yield higher re-

source utilization, and improvethe performance of the

cloud resources.

Chen et al. (Chen and Tseng, 2012) intro-

duced an Improved Load Balanced algorithm on the

groundof Min-Min algorithm to reduce the Makespan

and increase resource utilization. Another optimal

joint multiple resource allocation method based on

the above resource allocation model is presented in

(Kuribayashi, 2011). The Author develops a resource

allocation model for cloud computing environments,

assuming both processing ability and bandwidth are

allocated simultaneously to each service request and

rented out on an hourly basis. Gouda et al. (Gouda

et al., 2013) proposed a new approach that allocates

resource with minimum wastage and provides max-

imum proﬁt. This approach used priority algorithm

which decides the allocation sequence for different

jobs requested among the different users after consid-

ering the priority based on some optimum threshold

decided by the cloud owner. An innovative admis-

sion control and scheduling algorithms for efﬁcient

resource allocation to maximize proﬁt by minimizing

cost and improving customer level is introduced in

(Irugurala and Chatrapati, 2013). The authors showed

that the algorithms work well in a number of scenar-

ios and give the maximum proﬁt among all proposed

algorithms by varying all types of QoS parameters.

Silva et al. (Silva et al., 2008) presented a heuris-

tic for optimizing the number of machines that should

be allocated for processing an analytical task so that

maximum speedup can be achieved within a limited

budget. The trafﬁc of web applications is dynamic

and random; hence predicting the optimal number

of machines for the completion of the client appli-

cations in real time and within budget is not a triv-

ial task. Gomathi and Karthikeyan (Krishnasamy and

Gomathi, 2013) proposed Hybrid Particle Swarm Op-

CLOSER2015-5thInternationalConferenceonCloudComputingandServicesScience

106

timization (HPSO) based scheduling heuristic to bal-

ance the load across the entire system while trying to

minimize the makespan as well as to utilize the re-

sources in an efﬁcient way in cloud environment. In

addition, the results are in agreement with those of

(Guo et al., 2012).

In (Katyal and Mishra, 2014), authors have dis-

cussed a selective algorithm for resources alloca-

tion in cloud environment to end-users on-demand

basis. The proposed algorithm is based on min-

min and max-min conventional task scheduling algo-

rithms. The selective algorithm uses certain heuristics

to select between the two algorithms so that overall

makespan of tasks on the machines is minimized. In

(Han et al., 2013), the authors presented a QoS guided

task scheduling model based on Sufferage-Min-Min

heuristic algorithm. An efﬁciency improvement has

been obtained by dividing the tasks and resources into

two groups of high QoS level.

3 RESOURCES ALLOCATION

STRATEGY

To meet the increasing computational requirements

of scientist needs, cloud computing environments are

promising platforms which ensure the resources al-

location with high quality of service. Therefore the

essential challenge of cloud computing scheduler is

to provide an optimal scheduling of the jobs based on

Makespan optimization to allocate jobs on suitable re-

sources.

The scheduling problem of ﬁnding the optimal

Makespan is a known NP-complete problem. The

scheduling problem that we consider can be stated as

follows. Let J = { j

, j

, ··· , j

} denote the set of jobs

which are independent and let M = {m

, m

, ··· , m

}

be the set of machines in the cloud computing envi-

ronment. We assume that each machine can estimate

how much time is required to perform each job. In

(Minarolli and Freisleben, 2011), Expected Time to

Compute (ETC) is an m× n matrix, used to estimate

the expected execution time of the job J

on the ma-

chine m

. In ETC matrix, n is the number of jobs

and m is the number of machines. One column of

the ETC matrix contains the estimated execution time

for a given job on each machine. Similarly one row

of the ETC matrix contains the estimated execution

time of a given machine for each job. Hence, for a

given job J

and a given machine m

, ETC

is the es-

timated execution time of job J

on machine m

. For

this problem, we assume take the hypothesis that the

computing capacity of each resource and the running

time of each job are known.

The Makespan is equal to maximum completion

time of all jobs and can be estimated using the fol-

lowing equation (Eq.1):

makespan = max

i∈{1,···,m}

{

∑

j∈J

ETC

} (1)

where J

is the set of the jobs mapped on the machine

4 OUR STATIC SCHEDULING AS

CSP FORMULATION

In this study we start with a presentation to the prac-

tical part of our Constraint Satisfaction problem mod-

elling for independenttasks scheduling to improvethe

Min-Min algorithm result. Thereafter we show that

this problem can be described using this formalism

using the Min-Min developed job and machine order-

ing heuristics. These heuristics aim to minimize the

total completion time (Makespan).

4.1 SCSP Problem Formulation

The Constraint Satisfaction Problem model is widely

used to represent and solve various AI related prob-

lems such as Scheduling or Optimization. A SCSP

(Scheduling CSP) is deﬁned by a set of jobs, a set

of allowed estimated execution time of machines

(the domain) is associated to each job and a Global

Completion Time constraint (GCT). Solving a SCSP

means ﬁnding an assignment for each job on one ma-

chine that satisﬁes a GCT constraint.

Based on the Min-min scheduling results, we

present a formal model for minimizing the completion

time obtained by this algorithm. Using this model, we

formulate the static scheduling problem for indepen-

dent job scheduling in heterogeneous environment as

a constraint satisfaction problem (CSP). Our formula-

tion provides a basis for computing an optimal com-

pletion time based on several CSP search strategies to

reﬁne the Makespan obtained by Min-min algorithm.

The SCSP consists of:

• N jobs J

, J

, ··· , J

, and M machines

, M

, ··· , M

• D = {D

, ··· , D

} is a set of n domains where

each D

= {ETCn

, ETCn

, ··· , ETCn

} is asso-

ciated with J

• GCT

∑

ETC

< (1− α) ×C

max

for all m ∈

{1, ··· ,M}. GCT is the global completion time

constraint on the machine m. The parameter α ∈

[0, 1[ represents the improvement of the C

max

ob-

tained by the Min-Min algorithm. The search

CSPFormulationforSchedulingIndependentJobsinCloudComputing

107

Table 1: An ETC matrix example.

Jobs Completion Time

Machines j

129 109 42 218 113 168 779

89 73 33 178 83 106 562

164 141 45 305 148 221 1024

Table 2: Execution results of Min-Min algorithm.

Jobs Total

Machines j

0 0 0 218 113 0 331

0 73 33 0 0 106 212

164 0 0 0 0 0 164

space can be reduced by applying this parameter

as mentioned in experimental section. If α = 0 we

use the C

max

of the Min-Min algorithm to avoid

the systematic search assignation which explores

systematically the whole search space. So using

this GCT constraint, we minimize the maximum

completion time for all machines. Note that the

max

value is modiﬁed in the search process ac-

cording to the obtained maximal completion time.

As example, consider a simple SCSP of 3 ma-

chines m

, m

and m

and 6 jobs J

, J

, ···, J

A scenario of ETC (durations) is given in Table 1.

First, Min-Min algorithm determines that the mini-

mum completion time for J

will be achieved on m

and makes this assignment. After the ﬁrst assign-

ment, Min-Min algorithm continues to schedule the

jobs J

, J

and J

as well on m

, m

machines respectively. Consequently, this algo-

rithm ﬁnds that the maximum completion time is 331

seconds on m

as reported on Table 2. The schedul-

ing, like the following can be expressed as SCSP:

• (06) Jobs J

, J

and J

as variables

• (06) Domains D

= {89, 129, 164}, D

{73, 109, 141}, ···, and D

= {106, 168, 221}.

• GCT < (1 − α) × 331

Most algorithms for solving CSP

search system-

atically through the possible assignments of values to

variables. These algorithms seek any solution or all

solutions of a CSP. Or they try to prove that no solu-

tion exists. In the present work, we have adapted the

Forward Checking (FC) algorithm to ﬁnd all SCSP

solutions because the original algorithm aimed simply

at ﬁnding a feasible solution. So we use FC algorithm

with an incremental and modiﬁed maximal comple-

tion time process. However, the order in which jobs

are considered for allocation on machines (instantia-

tion) has a dramatic effect on the time taken to solve

our SCSP, relatively to the order in which each job’s

ETC

are considered. There are general principles

which are commonly used in selecting the jobs and

their ETC values on the machines ordering. The job

and machine ordering may be either a static or dy-

namic ordering according to the current state of the

search. In our approach, we use both job and ma-

chine ordering heuristics. The job ordering uses the

inverse job order obtained by the Min-Min algorithm.

The machine ordering heuristic is based on the global

completion time of each machine under hypothesis

that all jobs are affected to the same machine.

The SCSP formalism allows deﬁning the space of

a combinatorial search as a tree. To cut branches in

the search tree based on our adapted FC algorithm,

we add job and machine ordering heuristics with the

incremental maximal completion time as follow:

• The job ordering heuristic uses the order J

≪

≪ J

which is the inverse order

obtained by Min-Min algorithm. (see Fig.1)

• The value (machine) ordering heuristic uses the

completion time reported in Table 1. So we ob-

tained m

≪ m

for J

. (see Fig.1)

• Modiﬁcation of the maximal completion time

max

in the GCT constraint in the search tree pro-

cess.

Applying our search algorithm, more work per

node but, presumably, the extra effort will be com-

pensated by the reduction on the number of visited

nodes. Fig. 2 shows an example of search space re-

duction obtained by our FC algorithm. As can be seen

the use of the C

max

modiﬁcation in the search pro-

cess offers more reduction of the visited nodes to skip

the instantiations with no possibleC

max

improvement.

For instance, the new obtained C

max

= 260 allows to

cut practically the whole branches in the rest of the

search tree. So for this example, our algorithm visited

only 117 nodes instead of 1093. For example, our

algorithm FC has detected that the partial assignment

with GCT

= 305 is inconsistent with the global con-

straint (GCT

> C

max

= 260), and the algorithm will

CLOSER2015-5thInternationalConferenceonCloudComputingandServicesScience

108

Figure 1: Search tree for the instance: 6 jobs and 3 machines (data from Table 1).

Figure 2: The search tree generated by our algorithm (with α = 0).

Figure 3: The search of tree generated by our algorithm (α = 0.2).

therefore backtrack immediately.

In order to make our search algorithm more efﬁ-

cient, another preprocessing treatment can be added

that initially introduces the α parameter value for the

global completion time constraint. Hence, if we ﬁx

α = 0.2, the space of a combinatorial search tree will

be reduced to only 66 visited nodes (Fig. 3).

5 SIMULATION RESULTS

Simulation evaluations of our formalism have been

CSPFormulationforSchedulingIndependentJobsinCloudComputing

109

Table 3: The resulting Makespans compared to Min-Min algorithms for 20 jobs ( α = 0).

max

Machines Time Total nodes Explored nodes Min-Min Proposed Makespan

Algorithm approach Improvement

2 2.00 2097151 33794 1074 973 9%

3 18.22 5.23E+09 434382 744 692 7%

4 58.73 1.47E+12 1718228 684 562 18%

5 80.73 1.19E+14 2747020 571 480 16%

performed. The SCSP resolution uses the inverse of

the obtained total order from the Min-Min algorithm

to optimize the maximum completion time. The de-

tails of the simulation setting are presented in the

following. In the literature, many heuristic-based

techniques have been proposed for independent job

scheduling in heterogeneous environment. The Min-

Min heuristic algorithm is the most efﬁcient and used

one.

The proposed scheduling algorithm has been ap-

plied on simulated data, with 3 different types of ETC

matrices up to 3 heterogeneous machines, and up to

20 randomly generated heterogeneous jobs used in

(Ibarra and Kim, 1977). These different types of ETC

matrices are generated based on the following proper-

ties (Inomata et al., 2011):

• Job Heterogeneity – represents the amount of

variance among the jobs execution times for a

given machine. The job heterogeneity is deﬁned

as: J(l): Job low and J(h): Job high.

• Machine Heterogeneity – represents the varia-

tion among the execution times for a given job

across all machines. The machine heterogeneity

is deﬁned as: M(l): Host low and M(h): Host

high.

• Consistency – an ETC matrix is said to be con-

sistent (c) whenever a machine m executes all

jobs faster than another machine and the incon-

sistency (i) if the machine m may be faster than

another machine for some jobs and slower for

others. Partially-consistent (s) matrices are in-

consistent matrices that include a consistent sub-

matrix of a predeﬁned size and are a combination

of consistent and inconsistent matrices (Minarolli

and Freisleben, 2011). Instances are labeled as

J(x)M(y)C(z) as follows: x indicates the job het-

erogeneity, y represents the machine heterogene-

ity and z shows the type of consistency.

Table 3 shows the results of the maximum com-

pletion times compared to the Min-Min algorithm for

scheduling 20 jobs (J(l)M(l)c(c)) based on theC

max

this algorithm (α = 0). The results are based on the

computation of job completion times across explored

nodes. As can be seen the search space can be reduced

by applying our heuristics where the total explored

nodes are widely lower compared to the total nodes of

the search space. Moreover, we obtain minimal com-

pletion times with the improvements 9%, 7%, 18%

and 16% for 2, 3, 4 and 5 machines respectively.

Table 4 reports the speed-ups for the same in-

stance with different values of α parameter. The ef-

ﬁciency observed is very good where the computa-

tion time’s decrease for all instances compared to the

above results from 1 to 5 machines. Also, it is ob-

served that for 6, 7, 8, 9 and 10 machine instances,

the execution times are considerably reduced. For ex-

ample, for the last instance (20 jobs on 10 machines)

the execution time 2748 seconds and is reduced to

3.79 seconds with α = 40.45. It is interesting to note

that the execution time is reduced by 99.85% for 10

machines and we note that the resulting Makespan of

Min-Min heuristic is constant starting from 571 be-

cause the Min-Min algorithm does not maximize the

use of resources. Overall, our results demonstrate that

where there is a consistency for low jobs, and having

large number of machines, we obtains an efﬁciency

superior to 95% with α >= 30%.

Finally, Table 5 presents the results of the com-

pletion times compared to Min-Min heuristic using

maximal values of the parameter α. It is interesting to

note that our heuristic outperforms the Min-Min al-

gorithm in all cases (job heterogeneity, machine het-

erogeneity and consistency) by obtaining the minimal

Makespan. Clearly, with the use of an adequate α

value, our algorithm performs well in all cases and

reduces the tree space search and the execution time

to schedule these instances from many hours to a few

minutes. A remark has to be made on the computation

time irregularity observed for the inconsistent cases

for high jobs and low machines. So a major drawback

of α values determined by our simulations is that the

execution times for the same scheduling problem can

be very different from an execution to another for dif-

ferent types of ETC matrix up to 10 heterogeneous

machines, and up to 20 randomly generated heteroge-

neous jobs of the same instance category. An impor-

tant point to notice is that our approach cannot consid-

ered as very effective for large scheduling problems.

To be efﬁcient we remedied the poor performance of

CLOSER2015-5thInternationalConferenceonCloudComputingandServicesScience

110

Table 4: The computation time reduction using different values of α parameter for 20 jobs.

max

Machines Time Total nodes Explored nodes α(%) Min-Min Proposed

(second) Algorithm approach

2 01.53 2097151 24990 10 1074 973

3 11.50 5.23E+09 266832 8 744 692

4 39.75 1.47E+12 1167804 18 684 562

5 49.73 1.19E+14 1683660 15 571 480

6 51.92 4.39E+15 1945518 23.5 571 434

7 89.72 9.31E+16 3690876 30.29 571 398

8 27.67 1.32E+18 1215384 33.97 571 377

9 10.09 1.37E+19 469152 38.01 571 353

10 03.79 1.11E+20 185420 40.45 571 340

Table 5: Makespan results for all heterogeneity and consistency cases.

max

Instance Time (s) α(%) Min-Min Algorithm Proposed approach

J(l)M(l)C(c) 03.79 40 571 340

J(l)M(h)C(c) 35.1 32 17271 11627

J(h)M(l)C(c) 1029.4 13 10640 8167

J(h)M(h)C(c) 36.3 37 685303 427236

J(l)M(l)C(i) 1290.4 10 442 397

J(l)M(h)C(i) 62.7 35 22947 14734

J(h)M(l)C(i) 1304.2 38 11495 7109

J(h)M(h)C(i) 1265.9 38 1068180 654517

J(l)M(l)C(s) 7.3 18 341 278

J(l)M(h)C(s) 6.37 16 20025 14734

J(h)M(l)C(s) 3.86 22 10286 6992

J(h)M(h)C(s) 8.82 22 969294 654517

our FC search algorithm by avoiding the recursivetree

traversal based on a parallel computation for global

completion time constraint. This parallelization uses

decomposition methods which distribute the search

tree at a particular depth level (Habbas et al., 2005).

6 CONCLUSION

In this work, a static scheduling problem in cloud en-

vironment based on a combination of a CSP formu-

lation and Min-Min job ordering heuristic. To im-

prove the Min-Min algorithm result a reﬁnement pro-

cess uses the incremental maximal completion time

as weighted global constraint.

We used various ETC matrixes to investigate ef-

ﬁciency of our approach based on different degrees

of job and machine heterogeneities and consistencies.

The results indicated that our CSP solver provides to

reach an optimal completion time in very short time

for small instances compared to Min-Min algorithm.

However, our approach cannot considered as very ef-

fective for large instances.

For future work, there are still some aspects for

further investigation in our CSP job scheduling al-

gorithm especially for parallel CSP solver using de-

composition strategy of the search tree in cloud en-

vironment and prediction model for the job comple-

tion time distribution that is applicable to making de-

cisions in scheduling.

REFERENCES

Abirami, S. and Ramanathan, S. (2012). Linear scheduling

strategy for resource allocation in cloud environment.

International Journal on Cloud Computing: Services

and Architecture (IJCCSA), 2(1):9–17.

Barbosa, J. and Moreira, B. (2009). Dynamic job schedul-

ing on heterogeneous clusters. In Eighth International

Symposium on Parallel and Distributed Computing,

2009. ISPDC’09., pages 3–10. IEEE.

Chen, C.-Y. and Tseng, H.-Y. (2012). An exploration of

the optimization of excutive scheduling in the cloud

computing. In Advanced Information Networking and

CSPFormulationforSchedulingIndependentJobsinCloudComputing

111

Applications Workshops (WAINA), 2012 26th Interna-

tional Conference on, pages 1316–1319. IEEE.

Gouda, K., Radhika, T., and Akshatha, M. (2013). Prior-

ity based resource allocation model for cloud com-

puting. International Journal of Science, Engineering

and Technology Research (IJSETR), ISSN, 2(1):2278–

7798.

Goudarzi, H. and Pedram, M. (2011). Maximizing proﬁt

in cloud computing system via resource allocation.

In 31st International Conference on Distributed Com-

puting Systems Workshops (ICDCSW), 2011, pages 1–

6. IEEE.

Guo, L., Zhao, S., Shen, S., and Jiang, C. (2012). Task

scheduling optimization in cloud computing based on

heuristic algorithm. Journal of Networks, 7(3):547–

553.

Habbas, Z., Krajecki, M., and Singer, D. (2005). Decompo-

sition techniques for parallel resolution of constraint

satisfaction problems in shared memory: a compar-

ative study. International Journal of Computational

Science and Engineering, 1(2):192–206.

Han, H., Deyui, Q., Zheng, W., and Bin, F. (2013). A

qos guided task scheduling model in cloud comput-

ing environment. In Fourth International Conference

on Emerging Intelligent Data and Web Technologies

(EIDWT), 2013, pages 72–76. IEEE.

Ibarra, O. H. and Kim, C. E. (1977). Heuristic algorithms

for scheduling independent tasks on nonidentical pro-

cessors. Journal of the ACM (JACM), 24(2):280–289.

Inomata, A., Morikawa, T., Ikebe, M., Okamoto, Y.,

Noguchi, S., Fujikawa, K., Sunahara, H., and Rah-

man, M. (2011). Proposal and evaluation of a dy-

namic resource allocation method based on the load

of vms on iaas. In 4th IFIP International Conference

on New Technologies, Mobility and Security (NTMS),

2011, pages 1–6. IEEE.

Irugurala, S. and Chatrapati, K. S. (2013). Various schedul-

ing algorithms for resource allocation in cloud com-

puting. The International Journal Of Engineering And

Science (IJES), 2(5):16–24.

Katyal, M. and Mishra, A. (2014). Application of selec-

tive algorithm for effective resource provisioning in

cloud computing environment. International Jour-

nal on Cloud Computing: Services and Architecture

(IJCCSA),, 4(1):1–10.

Krishnasamy, K. and Gomathi, B. (2013). Task scheduling

algorithm based on hybrid particle swarm optimiza-

tion in cloud computing environment. Journal of The-

oretical & Applied Information Technology, 55(1):33–

38.

Kundu, A., Banerjee, C., Guha, S. K., Mitra, A.,

Chakraborty, S., Pal, C., and Roy, R. (2010). Mem-

ory utilization in cloud computing using transparency.

In 5th International Conference on Computer Sci-

ences and Convergence Information Technology (IC-

CIT), 2010, pages 22–27. IEEE.

Kuribayashi, S.-i. (2011). Optimal joint multiple resource

allocation method for cloud computing environments.

International Journal of Research & Reviews in Com-

puter Science, 2(1).

Li, J., Qiu, M., Niu, J.-W., Chen, Y., and Ming, Z. (2010).

Adaptive resource allocation for preemptable jobs in

cloud systems. In 10th International Conference on

Intelligent Systems Design and Applications (ISDA),

2010, pages 31–36. IEEE.

Minarolli, D. and Freisleben, B. (2011). Utility-based re-

source allocation for virtual machines in cloud com-

puting. In IEEE Symposium on Computers and Com-

munications (ISCC), 2011, pages 410–417. IEEE.

Santos, C., Zhu, X., and Crowder, H. (2002). A mathemat-

ical optimization approach for resource allocation in

large scale data centers. Technical Report HPL-2002-

64, HP Labs, March 2002.

Silva, J. N., Veiga, L., and Ferreira, P. (2008). Heuristic for

resources allocation on utility computing infrastruc-

tures. In Proceedings of the 6th international work-

shop on Middleware for grid computing , MGC ’08,

pages 1–6. ACM.

Xie, W.-j., Tang, Z., Yang, L., and LI, R.-f. (2012). Re-

search on the virtual machine placement algorithm in

cloud computing based on stochastic programming.

Computer Engineering & Science, 5(5):95–100.

Yuan, J.-B., Lee, Y.-C., Wu, W., Young, H.-C., and Liang,

K.-H. (2011). Building an intelligent provisioning en-

gine for iaas cloud computing services. In 13th Asia-

Paciﬁc Network Operations and Management Sympo-

sium (APNOMS), 2011, pages 1–6. IEEE.

Zhang, L., Zhuang, Y., and Zhu, W. (2013). Constraint

programming based virtual cloud resources allocation

model. International Journal of Hybrid Information

Technology, 6(6):333–344.

CLOSER2015-5thInternationalConferenceonCloudComputingandServicesScience

112