Research Article User Utility Oriented Queuing Model for ...downloads.hindawi.com/journals/jece/2015/246420.pdf · Resource Allocation in Cloud Environment ZheZhangandYingLi Institute

Research ArticleUser Utility Oriented Queuing Model forResource Allocation in Cloud Environment

Zhe Zhang and Ying Li

Institute of Software Nanyang Normal University Nanyang Henan 473061 China

Correspondence should be addressed to Ying Li lying1024163com

Received 20 August 2015 Revised 29 September 2015 Accepted 8 October 2015

Academic Editor James Nightingale

Copyright copy 2015 Z Zhang and Y Li This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Resource allocation is one of the most important research topics in servers In the cloud environment there are massive hardwareresources of different kinds and many kinds of services are usually run on virtual machines of the cloud server In addition cloudenvironment is commercialized and economical factor should also be considered In order to deal with commercialization andvirtualization of cloud environment we proposed a user utility oriented queuing model for task scheduling Firstly we modeledtask scheduling in cloud environment as an MM1 queuing system Secondly we classified the utility into time utility and costutility and built a linear programming model to maximize total utility for both of them Finally we proposed a utility orientedalgorithm to maximize the total utility Massive experiments validate the effectiveness of our proposed model

1 Introduction

Providers of cloud services usually provide different com-puting resources with different performances and differentprices and the requirements of users for performance andcost of resources differ greatly too So how to allocate availableresources for users to maximize the total system utilization isone of the most important objectives for allocating resourcesand scheduling tasks [1] and is also a research focus in cloudcomputing

Traditional resource allocation models mainly focus onthe response or running time saving energy of the wholesystem and fairness of task scheduling and do not take userutility into consideration [2] However the utility of a user incloud environment is the usage value of services or resourcesand it describes how the user is satisfied with the proposedservices or resources while occupying and using them [3 4]In order to maximize the total utility of all users in cloudenvironment it is necessary to analyze andmodel user utilityfirst and then optimize it to get amaximum [5]Themodelingof user utility is very complex as it needs a formal descriptionconsidering many factors such as the processing time thattasks have passed by [6] the ratio of finished tasks [7] the

costs of finished and unfinished tasks [8] and the parallelspeedup [9]

In a cloud server requests of users called tasks comerandomly and a good description of these tasks is thePoisson distribution assumption At the same time underthe commercialization constraint of the cloud environmentthe utility of cloud server becomes much more importantIn this paper we formalized and quantified the problemof task scheduling based on queuing theory divided theutility into time utility and cost utility and proposed a linearprogramming method to maximize the total utility Thecontributions of the paper are as follows

(i) We modeled task scheduling as 1198721198721 queuingmodel and analyzed related features in this queuingmodel

(ii) We classified utility into time utility and cost utilityand built a linear programming method to maximizetotal utility for each of them

(iii) We proposed a utility oriented and cost basedscheduling algorithm to get the maximum utility

(iv) We validated the effectiveness of the proposed modelwith massive experiments

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2015 Article ID 246420 8 pageshttpdxdoiorg1011552015246420

2 Journal of Electrical and Computer Engineering

The rest of the paper is organized as follows In Section 2we review related works about resource allocation and taskscheduling in cloud computing In Section 3 we formalizethe tasks in cloud environment based on the queuing theorydefine a random task model for random tasks describe ourproposed user utility model and design a utility orientedtime-cost scheduling algorithm Experiments and conclusionare given in Sections 4 and 5 respectively

2 Related Works

In cluster systems that provide cloud services there is acommon agreement in researchers that the moments whentasks come into the system conform to the Poisson distri-bution and both the intervals between two coming tasksand the serviced time of tasks are exponentially distributedIn this situation heuristic task scheduling algorithms suchas genetic algorithm and ant colony algorithm have betteradaptability than traditional scheduling algorithms How-ever the deficit of heuristic algorithms is that they havecomplex problem-solving process so they can only be appliedin small cluster systems The monstrous infrastructure ofcloud systems usually hasmany types of tasks a huge amountof tasks andmany kinds of hardware resources whichmakesheuristic algorithms unsuitable

There are a lot of researches about resource allocationor task scheduling in cloud environment especially for theMapReduce programming schema [10] Cheng et al [11] pro-posed an approximate algorithm to estimate the remainingtime (time to end) of tasks in MapReduce environment andthe algorithm scheduled tasks with their remaining timeChen et al [12] proposed a self-adaptive task schedulingalgorithm and this algorithmcomputed the running progress(ratio of time from beginning to total running time) of thecurrent task on a node based on its historical data Theadvantage of [12] is that it can compute remaining timeof tasks dynamically and is more suitable to heterogeneouscloud environment than [11] In addition Moise et al [13]designed a middleware data storage system to improve theperformance and ability of fault tolerance

Traditional task scheduling algorithms mainly focus onefficiency of the whole system However some researchersintroduce economic models into task scheduling and thebasic idea is optimizing resource allocation by adjusting usersrsquorequirements and allocating resources upon price mecha-nism [14] Xu et al [15] proposed a Berger model based taskscheduling algorithm Considering actual commercializationand virtualization of cloud computing the algorithm is basedon the Berger social allocation model and adds additionalcost constraints in optimization objective According toexperiments on the CloudSim platform their algorithm isefficient and fair when running tasks of different users Inaddition with respect to the diversity of resources in cloudenvironment more researchers believe that the diversity willincrease as time goes on with update of hardware resourcesIn order to alleviate this phenomenon and ensure quality ofservices Yeo and Lee [16] found that while the resources wereindependently identically distributed dropping resources

that needed three times the number ofminimal response timecouldmake the whole system use less total response time andthus less energy

The study of random scheduling began in 1966 andRothkopf [17] proposed a greedy optimal algorithm basedon the weights of tasks and expected ratios of finished timeto total time If all tasks had the same weights then thisalgorithm became the shortest expected processing timealgorithm Mohring et al [18] proved the optimal approxi-mation for scheduling tasks with random finished timeTheybegan with the relaxation of linear programming studiedthe problem of integer linear programming for systems withhomogeneous tasks and got an approximate solution withthe lower limit of the linear programming Based on theabove research Megow et al [19] proposed a better optimalsolution with better approximation In addition Scharbrodtet al [20] studied how to schedule independent tasks ran-domly They analyzed the problem of scheduling 119899 taskson 119898 machines randomly and gave the worst performanceof random scheduling under homogeneous environmenttheoretically and their result was the best among relatedworks

All of the above algorithms focus on the response orrunning time of usersrsquo requirements saving energy of thewhole system and fairness of tasks and do not take user utilityinto consideration However utility of users is very importantin cloud service systems In order tomaximize the total utilityof all users in cloud environment we analyze and modeluser utility first and then optimize it to get a maximal solu-tion

In addition Nan et al [21] studied how to optimizeresource allocation for multimedia cloud based on queuingmodel and their aim is tominimize the response time and theresource cost However in this paper we deal with commer-cialization and virtualization of cloud environment and ouraim is maximizing utility Xiao et al [22] presented a systemthat used virtualization technology to allocate data centerresources dynamically Their aim is to minimize the numberof servers in use considering the application demands andutility whereas in this paper we aim to maximize the systemrsquostotal utility under a certain cloud environment

3 Proposed Model

31 Queuing Model of Tasks In this paper we describe ran-domness of tasks with the1198721198721model of queuing theoryand the model is illustrated in Figure 1 The model consistsof one server several schedulers and several computingresourcesWhen user tasks are submitted the server analyzesand schedules them to different schedulers and adds them tolocal task queue of the corresponding scheduler Finally eachscheduler schedules its local tasks to available computingresources In Figure 1 119905(119889) is the waiting time of a task in thequeue and 119905(119890) is the running time

32 Modeling Random Tasks In the following we will ana-lyze the waiting time running time and queue length of theproposed1198721198721model

Journal of Electrical and Computer Engineering 3

User 1

User 2 ServerScheduler 2

Task queue 2

Scheduler 1

Task queue 1

Resource 1

Resource 2

Resource 1

Resource 2

Resource n

Resource nTask queue n

Scheduler nUser n

t(d) t(e)

Figure 1 Scheduling model of user tasks in cloud environment

Definition 1 If the average arrival rate of tasks in a scheduleris 120582 the average service rate of tasks in a scheduler is 120583 andthen the service intensity 120588 is

120588 =120582

120583 (1)

The service intensity describes the busyness of the sched-uler When 120588 approaches zero the waiting time of tasksis short and the scheduler has much idle time when 120588

approaches one the scheduler has less idle time and thustasks would have long waiting time Generally speaking theaverage arrival rate should be equal to or smaller than theaverage service rate otherwise there will be more and morewaiting tasks in the scheduler

Definition 2 If we denote the expected length of tasks in ascheduler as 119871 the expected length of tasks in queuing as119871119902 the expected total time (including both waiting time andrunning time) of a task as119882 and the expectedwaiting time ofa task in queuing as119882119902 then we have the following equationsaccording to queuing theory [17]

119871 =120582

(120583 minus 120582)= 120588 (1 minus 120588)

119871119902 =1205822

120583 (120583 minus 120582)= 1205882(1 minus 120588) = 119871 sdot 120588

119882 =1

(120583 minus 120582)

119882119902 =120582

120583 (120583 minus 120582)= 119882 sdot 120588

(2)

In addition let 119875119899 = 119875119873 = 119899 be the possibility ofnumber of tasks in a scheduler at any moment then we havethe following equation

119875119899 = 120588 (1 minus 120588) (3)

If 119899 = 0 then 1198750 is the possibility that all virtual machines areidle

33 Model of User Utility

331 Time Utility of Tasks As we can see from Figure 1the total time that a user takes from submitting a request togetting the result includes bothwaiting time 119905(119889) and runningtime 119905(119890) Here the computing resources are virtual resourcesmanaged by virtual machines Let 119879 be total time then wehave

119879 = 119905 (119889) + 119905 (119890) (4)

In (4) the running time 119905(119890) is the sum of used time 119905(119891)and remaining time 119905(119906) that is

119905 (119890) = 119905 (119891) + 119905 (119906) (5)

In order to calculate the time requirement of a task thesystem needs to calculate the remaining time 119905(119906) andschedules 119905(119906) for different tasks to different virtualmachines

For analyzing the remaining time we classified tasks intoset 119875 = 119901119894 | 1 le 119894 le 119898 and nodes into set 119881 = 119901119895 | 1 le 119895 le

119899 According to statistical computing we can get the averageexecuting rate of task 119901119894 on node V119895 that is 119877 = 119903119894119895 | 1 le 119894 le

119898 1 le 119895 le 119899 and then the remaining time of 119901119894 on V119895 is

119905 (119906)119894119895 =(119908 minus 119908119906)

119903119894119895

(6)

where 119908 is the number of total tasks and 119908119906 is the numberof finished tasks For computing intensive tasks 119908 is thetotal input data and 119908119906 is the already processed inputdata Schedulers schedule tasks on virtual machine resourcesaccording to their remaining time and assure all tasks arefinished on time

A task can be executed either on one virtual machineor on 119899 virtual machines in parallel while being dividedinto 119898 subtasks We denoted the subtask set as 119863 = 119889119896 |

1 le 119896 le 119898 While these subtasks are executed ondifferent virtualmachines especially different physical nodesthe communication cost increases and we use speedup tomeasure the parallel performance

119904 =1198791

119879119901

(7)

where 1198791 is the time of a task in one node and 119879119901 is the timeof a task in 119901 nodes In order to make sure 119904 le 1198780 all subtasksrun in parallel and total time of the task is

119879 = 119905 (119889) +max 119905 (119890)119896119895 (8)

where 119905(119890)119896119895 is the time of subtask 119889119896 on V119895 and max119905(119890)119896119895is the maximal time of all subtasks

332 Cost Utility of Tasks In this paper we assume that thecost rate of nodes is proportional to CPU and IO speed andtasks of different types consume different energy differentbandwidth and different resource usage So different taskswill have different cost rates


Definition 3 Let 119862 = (119888119894119895 | 1 le 119894 le 119898 1 le 119895 le 119899) be the costmatrix of task 119901119894 on node 119888119895 and then total cost of a task is theproduct of node cost and running time that is

119872 = 119862 times 119879 =

119898

sum

119894=1

119899

sum

119895=1

(119888119894119895 times 119905 (119890)119894119896119895) (9)

where 119888119894119895 is the unit cost of task 119901119894 on node V119895 and 119905(119890)119894119896119895 isthe time of subtask 119889119896 on node V119895

333 Formalization and Optimization of User Utility

Definition 4 Let the time utility function be 119880119905 and let thecost utility function be 119880119888 then the total utility is

119880 = 119886 times 119880119905 + 119887 times 119880119888 (10)

where 119886 + 119887 = 1 0 le 119886 le 1 and 0 le 119887 le 1In (10) both time utility and cost utility are between 0 and

1 and 119886 and 119887 are the weights of time utility and cost utilityrespectively

The aim of utility oriented task scheduling is to maximizethe total utility and the constraints are expected time of tasksexpected cost finished rate speedup and so on In this paperwe classify user tasks into time sensitive and cost sensitive

For time sensitive user tasks change of running time fora task will affect the time utility a lot and its definition is asfollows

Definition 5 The utility model of time sensitive user tasks isdefined by the following equations

119880 = 119886 times 119880119905 + 119887 times 119880119888

119880119905 =119896

(ln (119905 minus 119886) times 119887)

119880119888 = 119886 times 119888 + 119887

(11)

The constrains are

119865 (119863) = 1 (12)

0 le 119880119879 lt 119880119905 le 1 (13)

0 le 119880119862 lt 119880119888 le 1 (14)

119905 (119889) + 119905 (119890) lt 1198790 (15)

119871119902

120582lt 1198791

(16)

max 119905 (119890)119896119895 lt 1198792 (17)

119862 times 119879 lt 1198720 (18)

119904 gt 1198780 (19)

where 119863 is the set of subtasks for all tasks and the aim is tomaximize total utility 119880

For cost sensitive user tasks change of running cost fora task will affect the cost utility a lot and its definition is asfollows

Definition 6 The utility model of cost sensitive user tasks isdefined by the following equations

119880 = 119886 times 119880119905 + 119887 times 119880119888

119880119888 =119896

(ln (119888 minus 119886) times 119887)

119880119905 = 119886 times 119905 + 119887

(20)

The constrains are

119865 (119863) = 1 (21)

0 le 119880119879 lt 119880119905 le 1 (22)

0 le 119880119862 lt 119880119888 le 1 (23)

119905 (119889) + 119905 (119890) lt 1198790 (24)

119871119902

120582lt 1198791

(25)

max 119905 (119890)119896119895 lt 1198792 (26)

119862 times 119879 lt 1198720 (27)

119904 gt 1198780 (28)

In bothDefinitions 5 and 6 their aims aremaximizing thetotal utility 119880 but the differences are the computation of 119880119888and 119880119905 Based on the above definitions we propose a utilityoriented and cost based scheduling algorithm The details ofthe algorithm are as follows

(1) Analyze user type for each user and select computingequations for 119880119888 and 119880119905

(2) Initialize parameters in constraints for1198801198791198801198621198790119879111987921198720 and 1198780

(3) Compute 119871119902 and 119882119902 for each scheduler according to(1) to (3)

(4) With the results of step (3) tag119883 schedulers with leastwaiting time

(5) Input some data into the 119883 schedulers and set thehighest priority for these tasks

(6) Execute the above tasks and record the running timeand cost (see Pseudocode 1)

(7) Predict running time cost and corresponding utilityof all tasks with time and cost of results from step 6and tag the scheduler with the maximal utility

(8) Schedule tasks in the scheduler with maximal utilityand optimize user utility (see Pseudocode 2)

(9) Wait until all tasks finish and record the runningtime cost and corresponding utility


if (user task is time sensitive) select nodes with quickest speed execute the above tasks such that 119904 lt 119878

0

else Select nodes with lowest cost execute the above tasks such that 119904 lt 119878

0

Pseudocode 1

initialize upgrade = 1while (task is time sensitive and upgrade = 1)

let previous user of current be current userunit time cost of current user = unit time cost times (1 + V)unit time cost of previous user = unit time cost times (1 minus 119908)if (both cost of current user and previous user do not decrease) upgrade = 1

else upgrade = 0rescore current user bo be current user

Pseudocode 2

Table 1 Hardware configuration parameters

Number CPU Amount Memory (GB)1 4-core 307GHz 10 42 4-core 27 GHz 10 4

4 Experiments

41 Experimental Setup Wedo experiments on twohardwareconfigurations and the configurations are in Table 1 Bothof the two hardware configurations run on CentOS58 andHadoop-101

There are total 20 computing nodes in our experimentalenvironment and each computing node starts up a virtualcomputing node We start 10 schedulers and each schedulermanages 2 virtual nodes (computing nodes) The applicationthat we use in the experiments is WordCount

According to (1) to (3) we computed the service intensity120588 the expected number of tasks in a scheduler 119871 theexpected length of queuing 119871119902 the expected finishing timeof tasks 119882 and the expected waiting time of queuing 119882119902Figure 2 describes the expected waiting time 119879(119908) on eachscheduler As we can see from the figure the waiting timefrom schedulers 1 3 5 and 7 satisfied (14) and (23) and thuswe can copy and execute some subtasks (data with size 1 KB)on them If the user task is time sensitive thenwe run the taskonnodewith faster speed and if the user is cost sensitive thenwe run the task on node with lower cost

42 Experiments for Time Sensitive User Utility Model Inorder to select the parameters for time utility and cost utilityfunctions we normalize them first and get the following

times10minus3

T(w

)(s

)

101 2 3 4 5 6 7

Scheduler8 9

0

5

10

15

20

25

30

35

Figure 2 Expected waiting time for each scheduler

equations Figure 3 describes the curves of the following twoequations

119880119905 =8

(ln (119905 minus 20) times 5)

119880119888 = minus(1

63) times 119888 +

61

63

(29)

Based on running time and rate total time cost andutility from schedulers 1 3 5 and 7 we set 119886 = 07 and 119887 = 03

in (10) Under constrains from (12) to (19) we compute thetotal utility In Figure 4 119880119905 is the predicted time utility 119880119888 isthe predicted cost utility 1198801015840 is the predicted total utility 119880 is


25

Line of time utilityLine of cost utility

30 35 40

Unit of time or cost

Util

ity

05

06

07

08

09

10

Figure 3 Time and cost utility lines for time sensitive user tasks

Uc

Ut U

U998400

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler

U

Figure 4 Utility distribution of time sensitive user tasks

the actual total utility and119880 is the total utility that we get byrescheduling tasks on the above 1 3 5 and 7 schedulers

In Figure 4 for scheduler 1 119880119905 119880119888 1198801015840 and 119880 are all the

lowest for scheduler 3119880119905 is the highest119880119888 ismuch lower and1198801015840 is the highest too for schedulers 5 and 7 although their119880119888

is higher than scheduler their 1198801015840 is lower than scheduler 3According to the rule ofmaximizing utility we should choosescheduler 3 as the scheduler However in order to furtherimprove the total utility we applied the proposed algorithmin Section 333 By rescheduling the tasks in queuing we getthe actual total utility 119880 for each scheduler In schedulers 5and 7 119880 is much higher than 119880

1015840 of scheduler 3

25


30 35 40


Util

ity

05

06

07

08

09

10

Figure 5 Time and cost utility lines for cost sensitive user tasks

43 Experiments for Cost Sensitive User Utility Model Inorder to select the parameters of time utility and cost utilityfunctions for cost sensitive user tasks we also normalize themand get the following two equations Figure 5 describes thecurves of the following two equations

119880119905 = minus(1

63) times 119905 +

61

63

119880119888 =8


(30)

From Figure 6 we can see that the predicted total utility1198801015840 in scheduler 5 is the highest and if we schedule tasks on

scheduler 5 we would have the highest actual total utility119880So if user tasks have different time and cost requirements wecan choose different computing nodes to execute them andmake the total utilitymaximal In addition after reschedulingthe tasks all tasks have higher actual total utility 119880 thanpredicted utility1198801015840 and actual total utility119880 which validatesthe effectiveness of our proposed algorithm

44 Comparison Experiments In this experiment weselected 10 simulating tasks and compared our algorithmwith both Min-Min and Max-Min algorithms The Min-Min algorithm schedules minimum task to the quickestcomputing node every time and the Max-Min algorithmschedules maximum task to the quickest computing nodeevery time We implemented two algorithms for both timesensitive and cost sensitive user tasks and denoted them asMaxUtility-Time and MaxUtility-Cost The experimentalresult is in Figure 7

In Figure 7 the total utilities of MaxUtility-Time andMaxUtility-Cost algorithms are higher than the other twoalgorithms and are also stable both Min-Min and Max-Minalgorithms have lower total utilities and their values fluctuatevery much Both Min-Min and Max-Min algorithms onlyconsider the running time of tasks and ignore requirements of


Uc

Ut U

U998400

U

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler

Figure 6 Utility distribution of cost sensitive user tasks

MaxUtility-TimeMaxUtility-Cost

Min-MinMax-Min

2 3 4 5 6 7 8 9 101

Scheduler

02

03

04

05

06

07

08

09

10

Tota

l util

ity

Figure 7 Comparison result for different algorithms under simu-lating tasks

both time and cost whichmakes them get lower total utilitiesand fluctuate very much In particular when running tasks8 9 and 10 total utility of the Max-Min algorithm dropsquickly The reason is that it schedules long-running tasks tocomputing nodes with high performance which makes theutility very low

5 Conclusion

In this paper we introduced utility into the cloud envi-ronment quantified the satisfaction of users to services asutility and proposed utility oriented queuing model for taskscheduling We classified utility into time and cost utility

rescheduled tasks according to their remaining time andminimized the total utility by constraints With the proposedmodel we can reschedule remaining tasks dynamically to getthe maximum utility We validated our proposed model bylots of experiments

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A Beloglazov and R Buyya ldquoEnergy efficient resource man-agement in virtualized cloud data centersrdquo in Proceedings of the10th IEEEACM International Symposium on Cluster Cloud andGrid Computing pp 826ndash831 IEEE Melbourne Australia May2010

[2] C S Yeo and R Buyya ldquoService level agreement based alloca-tion of cluster resources handling penalty to enhance utilityrdquoin Proceedings of the IEEE International Conference on ClusterComputing (CLUSTER rsquo05) pp 1ndash10 Burlington Mass USASeptember 2005

[3] J N Silva L Veiga and P Ferreira ldquoHeuristic for resourcesallocation on utility computing infrastructuresrdquo in Proceedingsof the 6th International Workshop on Middleware for GridComputing (MGC rsquo08) pp 93ndash100 ACM Leuven BelgiumDecember 2008

[4] G Song and Y Li ldquoUtility-based resource allocation andscheduling in OFDM-based wireless broadband networksrdquoIEEE Communications Magazine vol 43 no 12 pp 127ndash1342005

[5] T T Huu and J Montagnat ldquoVirtual resources allocation forworkflow-based applications distribution on a cloud infras-tructurerdquo in Proceedings of the 10th IEEEACM InternationalSymposium on Cluster Cloud and Grid Computing (CCGridrsquo10) pp 612ndash617 IEEE Melbourne Australia May 2010

[6] Y Yakov ldquoDynamic resource allocation platform andmethod for time related resourcesrdquo US Patent Application10314198[P] 2002

[7] G Wei A V Vasilakos Y Zheng and N Xiong ldquoA game-theoretic method of fair resource allocation for cloud comput-ing servicesrdquo The Journal of Supercomputing vol 54 no 2 pp252ndash269 2010

[8] D Lopez-Perez X Chu A V Vasilakos and H ClaussenldquoPowerminimization based resource allocation for interferencemitigation in OFDMA femtocell networksrdquo IEEE Journal onSelected Areas in Communications vol 32 no 2 pp 333ndash3442014

[9] XWang and J FMartınez ldquoXChange amarket-based approachto scalable dynamic multi-resource allocation in multicorearchitecturesrdquo in Proceedings of the 21st IEEE InternationalSymposium onHigh Performance Computer Architecture (HPCArsquo15) pp 113ndash125 IEEE Burlingame Calif USA February 2015

[10] L Thomas and R Syama ldquoSurvey on MapReduce schedulingalgorithmsrdquo International Journal of Computer Applications vol95 no 23 pp 9ndash13 2014

[11] D Cheng J Rao Y Guo and X Zhou ldquoImproving MapReduceperformance in heterogeneous environments with adaptive tasktuningrdquo in Proceedings of the 15th International Middleware


Conference (Middleware rsquo14) pp 97ndash108 ACM BordeauxFrance December 2014

[12] Q Chen D Zhang M Guo Q Deng and S Guo ldquoSAMRa self-adaptive mapreduce scheduling algorithm in heteroge-neous environmentrdquo in Proceedings of the 10th IEEE Inter-national Conference on Computer and Information Technology(CIT rsquo10) pp 2736ndash2743 IEEE Bradford UK July 2010

[13] DMoise T-T-L Trieu L Bouge and G Antoniu ldquoOptimizingintermediate data management in MapReduce computationsrdquoin Proceedings of the 1st International Workshop on CloudComputing Platforms (CloudCP rsquo11) pp 37ndash50 ACM SalzburgAustria April 2011

[14] R Buyya D Abramson J Giddy andH Stockinger ldquoEconomicmodels for resource management and scheduling in grid com-putingrdquoConcurrency Computation Practice and Experience vol14 no 13ndash15 pp 1507ndash1542 2002

[15] B Xu C Zhao E Hu and B Hu ldquoJob scheduling algorithmbased on Berger model in cloud environmentrdquo Advances inEngineering Software vol 42 no 7 pp 419ndash425 2011

[16] S Yeo and H-H S Lee ldquoUsing mathematical modeling inprovisioning a heterogeneous cloud computing environmentrdquoComputer vol 44 no 8 Article ID 5740825 pp 55ndash62 2011

[17] M H Rothkopf ldquoScheduling with random service timesrdquoManagement Science vol 12 no 9 pp 707ndash713 1966

[18] R H Mohring A S Schulz and M Uetz ldquoApproximation instochastic scheduling the power of LPmdashbased priority policiesrdquoJournal of the ACM vol 46 no 6 pp 924ndash942 1999

[19] N Megow M Uetz and T Vredeveld ldquoModels and algorithmsfor stochastic online schedulingrdquo Mathematics of OperationsResearch vol 31 no 3 pp 513ndash525 2006

[20] M Scharbrodt T Schickinger and A Steger ldquoA new averagecase analysis for completion time schedulingrdquo Journal of theACM vol 53 no 1 pp 121ndash146 2006

[21] X Nan Y He and L Guan ldquoOptimal resource allocation formultimedia cloud based on queuing modelrdquo in Proceedingsof the 3rd IEEE International Workshop on Multimedia SignalProcessing (MMSP rsquo11) pp 1ndash6 Hangzhou China November2011

[22] Z Xiao W Song and Q Chen ldquoDynamic resource allocationusing virtual machines for cloud computing environmentrdquoIEEE Transactions on Parallel and Distributed Systems vol 24no 6 pp 1107ndash1117 2013

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The rest of the paper is organized as follows In Section 2we review related works about resource allocation and taskscheduling in cloud computing In Section 3 we formalizethe tasks in cloud environment based on the queuing theorydefine a random task model for random tasks describe ourproposed user utility model and design a utility orientedtime-cost scheduling algorithm Experiments and conclusionare given in Sections 4 and 5 respectively

2 Related Works

In cluster systems that provide cloud services there is acommon agreement in researchers that the moments whentasks come into the system conform to the Poisson distri-bution and both the intervals between two coming tasksand the serviced time of tasks are exponentially distributedIn this situation heuristic task scheduling algorithms suchas genetic algorithm and ant colony algorithm have betteradaptability than traditional scheduling algorithms How-ever the deficit of heuristic algorithms is that they havecomplex problem-solving process so they can only be appliedin small cluster systems The monstrous infrastructure ofcloud systems usually hasmany types of tasks a huge amountof tasks andmany kinds of hardware resources whichmakesheuristic algorithms unsuitable

There are a lot of researches about resource allocationor task scheduling in cloud environment especially for theMapReduce programming schema [10] Cheng et al [11] pro-posed an approximate algorithm to estimate the remainingtime (time to end) of tasks in MapReduce environment andthe algorithm scheduled tasks with their remaining timeChen et al [12] proposed a self-adaptive task schedulingalgorithm and this algorithmcomputed the running progress(ratio of time from beginning to total running time) of thecurrent task on a node based on its historical data Theadvantage of [12] is that it can compute remaining timeof tasks dynamically and is more suitable to heterogeneouscloud environment than [11] In addition Moise et al [13]designed a middleware data storage system to improve theperformance and ability of fault tolerance

Traditional task scheduling algorithms mainly focus onefficiency of the whole system However some researchersintroduce economic models into task scheduling and thebasic idea is optimizing resource allocation by adjusting usersrsquorequirements and allocating resources upon price mecha-nism [14] Xu et al [15] proposed a Berger model based taskscheduling algorithm Considering actual commercializationand virtualization of cloud computing the algorithm is basedon the Berger social allocation model and adds additionalcost constraints in optimization objective According toexperiments on the CloudSim platform their algorithm isefficient and fair when running tasks of different users Inaddition with respect to the diversity of resources in cloudenvironment more researchers believe that the diversity willincrease as time goes on with update of hardware resourcesIn order to alleviate this phenomenon and ensure quality ofservices Yeo and Lee [16] found that while the resources wereindependently identically distributed dropping resources

that needed three times the number ofminimal response timecouldmake the whole system use less total response time andthus less energy

The study of random scheduling began in 1966 andRothkopf [17] proposed a greedy optimal algorithm basedon the weights of tasks and expected ratios of finished timeto total time If all tasks had the same weights then thisalgorithm became the shortest expected processing timealgorithm Mohring et al [18] proved the optimal approxi-mation for scheduling tasks with random finished timeTheybegan with the relaxation of linear programming studiedthe problem of integer linear programming for systems withhomogeneous tasks and got an approximate solution withthe lower limit of the linear programming Based on theabove research Megow et al [19] proposed a better optimalsolution with better approximation In addition Scharbrodtet al [20] studied how to schedule independent tasks ran-domly They analyzed the problem of scheduling 119899 taskson 119898 machines randomly and gave the worst performanceof random scheduling under homogeneous environmenttheoretically and their result was the best among relatedworks

All of the above algorithms focus on the response orrunning time of usersrsquo requirements saving energy of thewhole system and fairness of tasks and do not take user utilityinto consideration However utility of users is very importantin cloud service systems In order tomaximize the total utilityof all users in cloud environment we analyze and modeluser utility first and then optimize it to get a maximal solu-tion

In addition Nan et al [21] studied how to optimizeresource allocation for multimedia cloud based on queuingmodel and their aim is tominimize the response time and theresource cost However in this paper we deal with commer-cialization and virtualization of cloud environment and ouraim is maximizing utility Xiao et al [22] presented a systemthat used virtualization technology to allocate data centerresources dynamically Their aim is to minimize the numberof servers in use considering the application demands andutility whereas in this paper we aim to maximize the systemrsquostotal utility under a certain cloud environment

3 Proposed Model

31 Queuing Model of Tasks In this paper we describe ran-domness of tasks with the1198721198721model of queuing theoryand the model is illustrated in Figure 1 The model consistsof one server several schedulers and several computingresourcesWhen user tasks are submitted the server analyzesand schedules them to different schedulers and adds them tolocal task queue of the corresponding scheduler Finally eachscheduler schedules its local tasks to available computingresources In Figure 1 119905(119889) is the waiting time of a task in thequeue and 119905(119890) is the running time

32 Modeling Random Tasks In the following we will ana-lyze the waiting time running time and queue length of theproposed1198721198721model


User 1


Task queue 2

Scheduler 1

Task queue 1

Resource 1

Resource 2

Resource 1

Resource 2

Resource n


Scheduler nUser n

t(d) t(e)



120588 =120582

120583 (1)




119871 =120582

(120583 minus 120582)= 120588 (1 minus 120588)

119871119902 =1205822

120583 (120583 minus 120582)= 1205882(1 minus 120588) = 119871 sdot 120588

119882 =1

(120583 minus 120582)

119882119902 =120582

120583 (120583 minus 120582)= 119882 sdot 120588

(2)


119875119899 = 120588 (1 minus 120588) (3)




119879 = 119905 (119889) + 119905 (119890) (4)


119905 (119890) = 119905 (119891) + 119905 (119906) (5)





119905 (119906)119894119895 =(119908 minus 119908119906)

119903119894119895

(6)




119904 =1198791

119879119901

(7)


119879 = 119905 (119889) +max 119905 (119890)119896119895 (8)





119872 = 119862 times 119879 =

119898

sum

119894=1

119899

sum

119895=1

(119888119894119895 times 119905 (119890)119894119896119895) (9)




119880 = 119886 times 119880119905 + 119887 times 119880119888 (10)






119880 = 119886 times 119880119905 + 119887 times 119880119888

119880119905 =119896

(ln (119905 minus 119886) times 119887)

119880119888 = 119886 times 119888 + 119887

(11)

The constrains are

119865 (119863) = 1 (12)

0 le 119880119879 lt 119880119905 le 1 (13)

0 le 119880119862 lt 119880119888 le 1 (14)

119905 (119889) + 119905 (119890) lt 1198790 (15)

119871119902

120582lt 1198791

(16)

max 119905 (119890)119896119895 lt 1198792 (17)

119862 times 119879 lt 1198720 (18)

119904 gt 1198780 (19)




119880 = 119886 times 119880119905 + 119887 times 119880119888

119880119888 =119896

(ln (119888 minus 119886) times 119887)

119880119905 = 119886 times 119905 + 119887

(20)

The constrains are

119865 (119863) = 1 (21)

0 le 119880119879 lt 119880119905 le 1 (22)

0 le 119880119862 lt 119880119888 le 1 (23)

119905 (119889) + 119905 (119890) lt 1198790 (24)

119871119902

120582lt 1198791

(25)

max 119905 (119890)119896119895 lt 1198792 (26)

119862 times 119879 lt 1198720 (27)

119904 gt 1198780 (28)













0


0

Pseudocode 1




Pseudocode 2



4 Experiments





times10minus3

T(w

)(s

)

101 2 3 4 5 6 7

Scheduler8 9

0

5

10

15

20

25

30

35



119880119905 =8


119880119888 = minus(1

63) times 119888 +

61

63

(29)




25


30 35 40


Util

ity

05

06

07

08

09

10


Uc

Ut U

U998400

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler

U







25


30 35 40


Util

ity

05

06

07

08

09

10



119880119905 = minus(1

63) times 119905 +

61

63

119880119888 =8


(30)






Uc

Ut U

U998400

U

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler



Min-MinMax-Min

2 3 4 5 6 7 8 9 101

Scheduler

02

03

04

05

06

07

08

09

10

Tota

l util

ity



5 Conclusion





References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










User 1


Task queue 2

Scheduler 1

Task queue 1

Resource 1

Resource 2

Resource 1

Resource 2

Resource n


Scheduler nUser n

t(d) t(e)



120588 =120582

120583 (1)




119871 =120582

(120583 minus 120582)= 120588 (1 minus 120588)

119871119902 =1205822

120583 (120583 minus 120582)= 1205882(1 minus 120588) = 119871 sdot 120588

119882 =1

(120583 minus 120582)

119882119902 =120582

120583 (120583 minus 120582)= 119882 sdot 120588

(2)


119875119899 = 120588 (1 minus 120588) (3)




119879 = 119905 (119889) + 119905 (119890) (4)


119905 (119890) = 119905 (119891) + 119905 (119906) (5)





119905 (119906)119894119895 =(119908 minus 119908119906)

119903119894119895

(6)




119904 =1198791

119879119901

(7)


119879 = 119905 (119889) +max 119905 (119890)119896119895 (8)





119872 = 119862 times 119879 =

119898

sum

119894=1

119899

sum

119895=1

(119888119894119895 times 119905 (119890)119894119896119895) (9)




119880 = 119886 times 119880119905 + 119887 times 119880119888 (10)






119880 = 119886 times 119880119905 + 119887 times 119880119888

119880119905 =119896

(ln (119905 minus 119886) times 119887)

119880119888 = 119886 times 119888 + 119887

(11)

The constrains are

119865 (119863) = 1 (12)

0 le 119880119879 lt 119880119905 le 1 (13)

0 le 119880119862 lt 119880119888 le 1 (14)

119905 (119889) + 119905 (119890) lt 1198790 (15)

119871119902

120582lt 1198791

(16)

max 119905 (119890)119896119895 lt 1198792 (17)

119862 times 119879 lt 1198720 (18)

119904 gt 1198780 (19)




119880 = 119886 times 119880119905 + 119887 times 119880119888

119880119888 =119896

(ln (119888 minus 119886) times 119887)

119880119905 = 119886 times 119905 + 119887

(20)

The constrains are

119865 (119863) = 1 (21)

0 le 119880119879 lt 119880119905 le 1 (22)

0 le 119880119862 lt 119880119888 le 1 (23)

119905 (119889) + 119905 (119890) lt 1198790 (24)

119871119902

120582lt 1198791

(25)

max 119905 (119890)119896119895 lt 1198792 (26)

119862 times 119879 lt 1198720 (27)

119904 gt 1198780 (28)













0


0

Pseudocode 1




Pseudocode 2



4 Experiments





times10minus3

T(w

)(s

)

101 2 3 4 5 6 7

Scheduler8 9

0

5

10

15

20

25

30

35



119880119905 =8


119880119888 = minus(1

63) times 119888 +

61

63

(29)




25


30 35 40


Util

ity

05

06

07

08

09

10


Uc

Ut U

U998400

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler

U







25


30 35 40


Util

ity

05

06

07

08

09

10



119880119905 = minus(1

63) times 119905 +

61

63

119880119888 =8


(30)






Uc

Ut U

U998400

U

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler



Min-MinMax-Min

2 3 4 5 6 7 8 9 101

Scheduler

02

03

04

05

06

07

08

09

10

Tota

l util

ity



5 Conclusion





References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119872 = 119862 times 119879 =

119898

sum

119894=1

119899

sum

119895=1

(119888119894119895 times 119905 (119890)119894119896119895) (9)




119880 = 119886 times 119880119905 + 119887 times 119880119888 (10)






119880 = 119886 times 119880119905 + 119887 times 119880119888

119880119905 =119896

(ln (119905 minus 119886) times 119887)

119880119888 = 119886 times 119888 + 119887

(11)

The constrains are

119865 (119863) = 1 (12)

0 le 119880119879 lt 119880119905 le 1 (13)

0 le 119880119862 lt 119880119888 le 1 (14)

119905 (119889) + 119905 (119890) lt 1198790 (15)

119871119902

120582lt 1198791

(16)

max 119905 (119890)119896119895 lt 1198792 (17)

119862 times 119879 lt 1198720 (18)

119904 gt 1198780 (19)




119880 = 119886 times 119880119905 + 119887 times 119880119888

119880119888 =119896

(ln (119888 minus 119886) times 119887)

119880119905 = 119886 times 119905 + 119887

(20)

The constrains are

119865 (119863) = 1 (21)

0 le 119880119879 lt 119880119905 le 1 (22)

0 le 119880119862 lt 119880119888 le 1 (23)

119905 (119889) + 119905 (119890) lt 1198790 (24)

119871119902

120582lt 1198791

(25)

max 119905 (119890)119896119895 lt 1198792 (26)

119862 times 119879 lt 1198720 (27)

119904 gt 1198780 (28)













0


0

Pseudocode 1




Pseudocode 2



4 Experiments





times10minus3

T(w

)(s

)

101 2 3 4 5 6 7

Scheduler8 9

0

5

10

15

20

25

30

35



119880119905 =8


119880119888 = minus(1

63) times 119888 +

61

63

(29)




25


30 35 40


Util

ity

05

06

07

08

09

10


Uc

Ut U

U998400

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler

U







25


30 35 40


Util

ity

05

06

07

08

09

10



119880119905 = minus(1

63) times 119905 +

61

63

119880119888 =8


(30)






Uc

Ut U

U998400

U

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler



Min-MinMax-Min

2 3 4 5 6 7 8 9 101

Scheduler

02

03

04

05

06

07

08

09

10

Tota

l util

ity



5 Conclusion





References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0


0

Pseudocode 1




Pseudocode 2



4 Experiments





times10minus3

T(w

)(s

)

101 2 3 4 5 6 7

Scheduler8 9

0

5

10

15

20

25

30

35



119880119905 =8


119880119888 = minus(1

63) times 119888 +

61

63

(29)




25


30 35 40


Util

ity

05

06

07

08

09

10


Uc

Ut U

U998400

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler

U







25


30 35 40


Util

ity

05

06

07

08

09

10



119880119905 = minus(1

63) times 119905 +

61

63

119880119888 =8


(30)






Uc

Ut U

U998400

U

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler



Min-MinMax-Min

2 3 4 5 6 7 8 9 101

Scheduler

02

03

04

05

06

07

08

09

10

Tota

l util

ity



5 Conclusion





References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










25


30 35 40


Util

ity

05

06

07

08

09

10


Uc

Ut U

U998400

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler

U







25


30 35 40


Util

ity

05

06

07

08

09

10



119880119905 = minus(1

63) times 119905 +

61

63

119880119888 =8


(30)






Uc

Ut U

U998400

U

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler



Min-MinMax-Min

2 3 4 5 6 7 8 9 101

Scheduler

02

03

04

05

06

07

08

09

10

Tota

l util

ity



5 Conclusion





References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Uc

Ut U

U998400

U

02

03

04

05

06

07

08

09

10

Util

ity

3 5 71

Scheduler



Min-MinMax-Min

2 3 4 5 6 7 8 9 101

Scheduler

02

03

04

05

06

07

08

09

10

Tota

l util

ity



5 Conclusion





References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article User Utility Oriented Queuing Model for ...downloads.hindawi.com/journals/jece/2015/246420.pdf · Resource Allocation in Cloud Environment ZheZhangandYingLi Institute