research article a robust service selection method based...

Research ArticleA Robust Service Selection Method Based on Uncertain QoS

Yanping Chen1 Lu Jiang2 Jianke Zhang3 and Xiaoxiao Dong1

1School of Computer Science Xirsquoan University of Posts and Telecommunications Xirsquoan 710121 China2ZTE Corporation Xirsquoan 710114 China3School of Science Xirsquoan University of Posts and Telecommunications Xirsquoan 710121 China

Correspondence should be addressed to Yanping Chen chenypxupteducn

Received 14 October 2015 Revised 11 January 2016 Accepted 27 January 2016

Academic Editor Alireza Amirteimoori

Copyright copy 2016 Yanping Chen et al 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

Nowadays the number ofWeb services on the Internet is quickly increasingMeanwhile different service providers offer numerousservices with the similar functions Quality of Service (QoS) has become an important factor used to select the most appropriateservice for usersThemost prominent QoS-based service selection models only take the certain attributes into account which is anideal assumption In the real world there are a large number of uncertain factors In particular at the runtime QoS may becomevery poor or unacceptable In order to solve the problem a global service selection model based on uncertain QoS was proposedincluding the corresponding normalization and aggregation functions and then a robust optimizationmodel adopted to transformthe model Experiment results show that the proposed method can effectively select services with high robustness and optimality

1 Introduction

With the wide use of the Web service in various fields moreand more services have been developed rapidly But singleservice can only implement single function service compo-sition becomes the primary measure to provide user with ahigh-quality and personalized complex service And theWebservice selection is the foundation and precondition of ser-vice composition With the number of Web services increas-ing gradually a key issue arises immediately there are manyservices providing same functions but differing in theQualityof Service (QoS) Therefore in the process of service compo-sition we need to select service not only depending on thefunctions but also according to the userrsquos QoS requirement

Web service selection based on QoS is a combinatorialoptimization problem Traditional QoS-based Web serviceselection algorithms mainly use linear programming [1] andGreedy Algorithm [2] Currently more popular service selec-tion algorithms are mainly using smart algorithms such asGenetic Algorithms [3] Particle Swarm Optimization [4]and Ant Colony Optimization Algorithm [5] These algo-rithms are often designed for certain QoS attributes andassumed that after the service provider has provided servicesthe services would run as the described state without change

But in fact this ideal situation does not exist Web service isprovided as a distributed loosely couplingAPI on theWeb soQoS is uncertain factor for example the response timewouldfluctuate with the change of the network It will fluctuate theQoS of the composed services which are solved by the deter-ministic algorithms at the running time and cannot satisfy theQoS requirements of users or is unusable Therefore whendealing with the service selection problem the uncertainfactors must be considered

Uncertainty is themost important factor that the require-ments of users cannot be satisfied We consider that theuncertainty of the service composition is mainly caused bythe following reasons

(1) QoS information is incomplete The Web servicedescription emphasizes more on functional infor-mation so the description of QoS attributes is notaccurate enough

(2) There is no unified QoS metric of Web servicesand only one way can gain service QoS value fromservice providers Due to the fuzziness of the natu-ral language there may be divergence between theservice providers and the users even about the sameattributes For example there is one attribute called

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 9480769 10 pageshttpdxdoiorg10115520169480769

2 Mathematical Problems in Engineering

throughput one definition is the number of requestsfor a service successfully executed and the other is theaverage rate of successful message size delivery over acommunication channel per second

(3) Internet environment cannot be repeated When ser-vices are used on the Internet some attributes of QoSof the Web services are influenced by the runningstate of the Internet such as security and responsetimeThe real situation of service cannot be describedby the QoS obtained from once request

Because of the existing uncertainties the compositeservice could hardly be accomplished in the dynamic exe-cution process These uncertainties also affect the individualrequirements of users When the QoS deviation occurs wemust replan and compose services otherwise it would causea lot of problems But the replanning will lead to the waste ofcomputing resources so this paper studies how to ensure thatservice composition is feasible with the uncertain conditionsthus avoiding the replanning of composited service For theuncertainty of the QoS properties this paper combined theuncertain optimization theory described the uncertainty byusing the ldquointervalrdquo modeled a service composition modelbased on workflow (order circulation choice and parallel)proposed the service selection model under the conditionswith uncertain QoS put forward the corresponding normal-ization and aggregation function and ensured that when thechange occurred in the part of QoS attributes the obtainedsolution can adapt to the most cases and close to the optimal

The rest of the sections are organized as follows Section 2describes related works Section 3 details the robust opti-mization method used in service selection model based onthe uncertain QoS Section 4 presents the experiment andanalysis result Finally Section 5 draws some conclusions

2 Related Works

In Zeng et alrsquos paper [1] QoS was introduced intoWeb serviceat the first time the QoS of Web service was used to dis-tinguish the Web services with similar functions From thenon service selection based on QoS plays a more and moreimportant role in the Web service composition area QoS-based service selection methods are mainly divided into twodirections semantic QoS [6] andQoS value According to thedifferent QoS requirements the Web service selection strat-egy can be divided into two kinds namely the local optimalstrategy and the global optimal strategy Local optimal strat-egy selects component services for a single service functionrespectively compares the candidate atomic service set sortsQoS values for each candidate atomic service and then selectsthe best oneThemain algorithm is theGreedyAlgorithm [2]Global optimal strategy aims to make the global QoS of thecomposite services to satisfy the given constraints or achievethe desired goals the main methods are Genetic Algorithm[3] PSO [4] and Ant Colony Algorithm [5]

In recent years the researchers have also addressed somestudies for service selection based on uncertain QoS Zeng etal [1] proposedQoS-based service selection at the same timethey proposed that uncertain response time was introduced

into the service selection model They assumed the responsetime of service subjected to normal distribution and intro-duced the variance of the normal distribution into theconstraints Alferez and Pelechano [7] leveraged models atruntime to guide the dynamic evolution of context-awareWeb service compositions to deal with unexpected events inthe open world In order to manage uncertainty a model thatabstracts the Web service composition self-evolves to pre-serve requirements Benouaret et al [8] represented eachQoSattribute of a Web service using a possibility distribution andintroduced two skyline extensions on uncertain QoS calledpos-dominant skyline and nec-dominant skyline Wu et al[9] proposed an ldquoon-demandrdquo strategy for QoS-aware servicecomposition to replace the traditional ldquobest-effortrdquo strategyMostafa and Zhang [10] presented two approaches basedon the Multiobjective Reinforcement Learning (MORL) toaddress multiobjective service composition in uncertain anddynamic environments Wagner et al [11] developed a newQoS model that helps to predict the resulting QoS of aworkflow by considering service failures during the initialselection phase For each service a set of possible backup ser-vices and the corresponding QoS are computed beforehand

In recent years it has been recognized that dealing withuncertain data is amajor challenge in optimization As can beseen from the above literaturesWeb serviceQoSmodels withuncertainty dispose uncertain data in two ways one wouldassume that the data is subject to one kind of distributionsto compute the uncertainty of QoS and the other solves theproblem by using intelligent algorithms But the problem ofthe formermethod is that the assumptionmay be not reason-able In the real world we could not get the exact distributionof the data And for the latter method different intelligentalgorithms have different problem like premature conver-gence for Genetic Algorithm And for all intelligent algo-rithms they always solve different solutions in different timeseven if they use the same data We need an approach to selectservice considering all possible situations but it does nottake whether the uncertain data is subject to any distributionsinto account

The researches of the traditional optimization problemsare mostly about deterministic problems When solvinguncertain optimization problems researchers mainly focuson the following ways stochastic programming fuzzy pro-gramming interval programming and robust optimizationWhen solving the uncertain problems the stochastic pro-gramming and fuzzy programming need precise distributionof the parameters and the precise distribution is difficult toobtain in the real world When solving these two kinds ofprogramming problems the commonly used method is theMonte Carlo method but this method shows slow conver-gence and low efficiency Facing more complex constraintsthey are only to use approximate method Interval program-ming and robust optimization are all converting the uncertainoptimization to determine problem for solving The differ-ence is that the robust optimization considers the worst casethe result may be conservative And the interval program-ming eventually provides decision-makers with a range ofoptimal value they will have a better space to select [12]When converting the interval programming upper and lower

Mathematical Problems in Engineering 3

bounds of uncertainty goals and constraints will become anested optimization model so the problem is always a multi-objective optimization problem and difficult to solve

In the 1973s Soyster [13] proposed an approach toaddress data uncertainty named robust optimization Robustoptimization means finding a solution which can deal withall possible realizations of the uncertain data The firstrobust optimization method proposed by Soyster considersthe maximum uncertainty That means only considering theworst case the uncertain programming is converted into thecorresponding deterministic model to obtain robust optimalsolution The model only considers the worst case and leadsto the very conservative solutions Conservatism in robustoptimization means that the solution ensures a high robust-ness level but is ldquofar awayrdquo from optimality In other words arobust solution is not optimal for all realizations of the uncer-tain data but performs well even for the worst case Laterresearches focus on how to keep the optimality and robust-ness at the same time At the end of the last century Ben-Tal and Nemirovski [14] gave an approach that convertedthe linear programming to the robust counterpart problemwith the ellipsoid uncertain set but the converted problemis a Second-Order Cone Programming (SOCP) and difficultto calculate In 2003 Bertsimas and Sim [15 16] proposed anew robust approach which obtained the solution consider-ing optimality and robustness and analyzed the probabilitybounds of constraint violations Existing researches based onthe two approaches used the robust optimization in the fieldof supply chain planning network flow and logistics pro-gramming

In this paper we propose using robust optimizationmethod to select service The difference between the existingstudy and this method is that this method considers all possi-ble situations during the service as invoking And it is solvedby mathematical methods which means that if the data isconstant the results are constant

3 Service Selection Method Based onRobust Optimization

31 QoS of the Candidate Services Since Zeng et al [1] com-binedWeb service with QoS together there have been a largenumber ofQoS attribute definitions which describe nonfunc-tional properties of Web services In many literatures QoSattributes are using the determinate data to make it clearbut some QoS attributes should be described as uncertaininterval data such as response time This paper uses thefollowing three kinds of commonQoS attributes as a basis forservice selectionDefining that response time and throughputare described by the interval data and the reliability is realdata We consider that the value of QoS is not subject to anydistribution

Definition 1 (response time) Response time measures theexpected delay in seconds from a request sent to the resultswhich are received [1] It is computed using the expression asfollows

119876rt = 119879tran + 119879proc (1)

where 119879tran is the transmission time of request and responsein the network 119879proc is the time of processing the request

In the past literatures the response time is often usingthe minimum value or average value of the response timein a period of time as a certain value to calculate But thenature of the response time should be uncertain Due to thedifferent network status the same service will show differentresponse times Using traditional QoS models always masksthe uncertainty of response time ignoring the unstablefactors Without considering the uncertainty of responsetime the selected service would take a bad response time Forexample the minimum and average response time of serviceA respectively are 01 s and 02 s and of service B are 015 s and022 s However the intervals of response time of services Aand B respectively are [01 10] and [015 05] From the twointervals it can be seen that the response time of service B ismore stable and robust Using the traditional service selectionmethod service A is better than service B When we use thetwo services the response time of service A may be 09 s andthat of service B may be 03 The purpose of this paper is tochoose amore robust serviceWe use interval [119876rt 119876rt+Δ119876rt]to indicate the uncertainty of response time

Definition 2 (throughput) For the throughput one definitionis the number of requests for a service successfully executedand the other is the average rate of successful message sizedelivery over a communication channel per second In thispaper we define it as in the second definition It is also uncer-tain So we describe the throughput like response time with[119876tp 119876tp + Δ119876tp]

Definition 3 (reliability) Reliability of service is the proba-bility of a request that is correctly responded to within themaximum number of total requests It is computed using theexpression as follows

119876re =119873re119899 (2)

where 119873re means the number of successful requests in 119899invocations and 119899 is the total number of service executions Inthis paper the reliability is derived from the service attributedataset and is a certain value

32 Service Composition Based on Workflow Most of singleWeb service is usually providing only a single way to imple-ment a single function but the composite services can takeadvantage of many small particle size distributions of theatomic services on the network and combine them to be ableto implement complex functions loosely coupled compositeservices

As shown in Figure 1 business logic of each kind ofcomplex application is fixed which has been divided intoservice classes by domain experts and then the service classis advertised After that service providers could publish theirWeb service into registry and point out which certain serviceclass it belongs toWhenusersrsquo requirement is coming (mean-ing that user selects a certain business logic) then the properservices should be selected according to usersrsquo QoS In orderto solve the problem a global service selection model based


Table 1 Aggregate formulas of QoS

Response time Throughput Reliability

Sequence [119899

sum119894=1

119876rti119899

sum119894=1

(119876rt119894 + Δ119876rt119894)] [min119894

119876tp119894min119894

(119876tp119894 + Δ119876tp119894)]119899

prod119894=1

119876re119894

Selection [119899

sum119894=1

119888119894119876rt119894119899

sum119894=1

119888119894(119876rt119894 + Δ119876rt119894)] [min

119894

119888119894119876tp119894min

119894

119888119894(119876tp119894 + Δ119876tp119894)]

119899

sum119894=1

119888119894119876re119894

Loops [119896119876rt 119896 (119876rt + Δ119876rt)] [119876tp 119876tp + Δ119876tp] 119876119896

re

Parallel [max119894

119876rt119894max119894

(119876rt119894 + Δ119876rt119894)] [min119894

119876tp119894min119894

(119876tp119894 + Δ119876tp119894)]119899

prod119894=1

119876re119894

Function Function Function

Web services

Composed service

SC1 SC2 SC3

Figure 1 QoS-based Web services composition problem

on uncertainQoSwas proposed including the correspondingnormalization and aggregation functions and then a robustoptimization model is adopted to transform the model

Techniques of composite services are various Mainlymethods include modeling based on workflow modelingbased on Petri nets and semantic modeling This paperfocuses on how to select the atomic service to accomplish thefunction regardless of the composite modeling techniqueshow to choose the specific combination service workflowmodel is also the key problem

Workflowmodel has four basic atomic structures namelysequence selection loop and parallel The flow of compositeservices can be combined or nested by the basic structures Ifwe can find a corresponding calculation method of each QoSfor each basic structure we can give the global QoS of com-posite services In the traditional QoS-driven service selec-tion algorithms when aggregating the QoS of the servicesthe algorithms only consider the determined QoS so that theaggregate formula is simple But there is uncertainty in theQoS and we described it by interval numbers so the tradi-tional function cannot be used for calculating global QoS Inorder to solve this problemwe combined the interval numberalgorithm with the characteristics of response time andthroughput and proposed the aggregation formulas of threeQoS properties corresponding to each basic structure inTable 1

33 Normalization Different QoS attributes always have dif-ferent dimensions Some value of QoS attributes is the biggerthe better such as throughput and reliability and this kind ofattributes is called benefit type attribute some is the smaller

the better such as response time called cost type attribute Inthis case integrating global QoS of composite service couldresult in additional cost In order to easily calculate andcompare data in the decision matrix needs to be normalizedinto the same dimension The service selection algorithmbased on real number generally used 0-1 normalizationmethod the attributesrsquo values are converted to interval [0 1]by linear calculations However in this paper response timeand throughput are interval data and cannot use the methodof real number to normalize The researches about normal-izationmethods of interval data are not toomany andmainlyfocused on twoways One is to convert the interval data into areal numberThe other is to use some kinds of normalizationfunctions to directly convert the interval number the result isstill interval number While the former method will lose theuncertain information which is what this paper focused onwe use the latter method

Common methods convert interval numbers into stan-dardized interval number including the method based oninterval number operation method vector-based normaliza-tion method method based on a linear scale transformationand method based on the range transformation [17] Thesethree former methods combine the normalization methodof real number with interval number operation methodHowever the data obtained by these methods always is out of[0 1] and these methods are based on nonlinear transforma-tionThere has been a huge impact on the decision results Sowe use themethod based on the range transformation to nor-malize response time and throughput Because the value ofthe reliability is taken in the range of [0 1] it does not need tobe normalized

There are 119899 services realizing one function Assuming thatthe QoS attribute of each service takes values in the interval[119876119894 119876119894+ Δ119876119894] the QoS after normalization is written as [1198761015840

119894

1198761015840

119894+ Δ1198761015840

119894] In order to easily calculate we need to normalize

the attributes data to be cost type data The normalizationformula is established as follows

Cost type

1198761015840

119894=

119876119894minusmin

119894119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

1198761015840

119894+ Δ1198761015840

119894=

(119876119894+ Δ119876119894) minusmin

119894119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

(3)


Benefit type

1198761015840

119894=

max119894(119876119894+ Δ119876119894) minus 119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

1198761015840

119894+ Δ1198761015840

119894=max119894(119876119894+ Δ119876119894) minus (119876

119894+ Δ119876119894)

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

(4)

34 Service Selection Model Based on Uncertain QoS Atpresent many scholars transform the service selection prob-lem as mathematical problems from different ways anddesigned the corresponding selection model The trans-formed mathematical problems include linear or integerprogramming problem multiple choice knapsack problemmultiple attribute decision-making problems single objectivecombinatorial optimization problems with QoS constraintsandmultiobjective combinatorial optimization problemwithQoS constrained But these problems always do not considerthe uncertainty of QoS so we propose a service selectionmodel considering the uncertainty

According to the global service selection strategy wepropose a service selection model based on uncertain QoSAssuming that there are119901 tasks in the workflow each task has119902 candidate atomic services so that the number of all possiblecomposite services is 119902119901 We propose a method based onrobust optimization (RO) which can select one service withhigh robustness level from 119902119901 composite services In order toimplement our approach firstly we need to formulate a linearprogramming model

There are three inputs in linear programming problemvariables objective function and constraint conditions inwhich the objective function and constraints must be linearLinear programming is to maximize or minimize the value ofobjective function by adjusting the value of the variablesTheoutput of linear programming is maximum (or minimum)value of objective function We assume that the variable is119909119894119895 which means whether the service 119904

119894119895is selected to execute

plan or not If the service 119904119894119895is selected then the value of the

variable 119909119894119895is 1 otherwise it is 0The objective function of the

model is the following formula

min119876rt sdot 1205961 + 119876tp sdot 1205962 + 119876re sdot 1205963 (5)

where we transformed three QoS attributes into cost typeattributes and119876rt119876tp and119876re are globalQoS120596

119894is theweight

of the QoS and sum119899119894=1120596119894= 1 120596

119894isin [0 1]

We used 119876rt(119909119894119895) to express the response time of service119904119894119895for task 119905

119894 so we have the following constraint

119876rt =119899

sum

119894=1

119898119894

sum

119895=1

119876rt (119909119894119895) sdot 119909119894119895 (6)

Assume that there are 119899workflow tasks and there is a set of119898119894services that can be provided to the user for each task but

there is only one service selected in each set so 119909119894119895(119909119894119895= 0 1)

indicates whether the service is selected 119909119894119895has the following

constraints119898119894

sum

119895=1

119909119894119895= 1 (7)

For example there are 100 candidate Web services thatcan execute the task 119905

119894 however only one of them will be

selected to the task so it issum100119895=1119909119894119895= 1

We used 119876tp(119909119894119895) to express the throughput of service119904119894119895 From Table 1 we can see that the aggregate formula of

throughput is looking for the minimum throughput in theprocess as the global throughput But before the calculationof QoS value we need to normalize it the throughput will beconverted from the benefit type to the cost type so the globalthroughput is the maximum value The constraint to thethroughput is as follows

119876tp = max119876tp (119909119894119895) sdot 119909119894119895 (8)

119876re(119909119894119895)means the reliability of service 119904119894119895 Like through-

put the reliability also needs to be converted so the globalreliability is as follows

119876re = 1 minus119899

prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895 (9)

However the constraint of attribute can be introducedinto the linear programming problem which is not limited tothe defined one in this section If the aggregate function couldbe given it also can be added to the model

We can propose the following model

min

1205961

119899

sum

119894=1

119898119894

sum

119895=1

119876rt (119909119894119895) sdot 119909119894119895 + 1205962 sdotmax119876tp (119909119894119895) sdot 119909119894119895 + 1205963(1 minus119899

prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895)

st3

sum

119894=1

120596119894= 1

119899

sum

119894=1

119909119894= 1

119909119894119895isin 0 1

(10)


where there exists uncertainty in twoQoS attributes responsetime and throughput For each entry 119876rt(119909119894119895) is independentand bounded random variable and takes values inlfloor119876rt(119909119894119895) 119876rt(119909119894119895) + Δ119876rt(119909119894119895)rfloor Δ119876rt(119909119894119895)means the deviationof the coefficient119876rt(119909119894119895) It is the same as throughput in thatfor each entry 119876tp(119909119894119895) is independent and bounded randomvariable and takes values in lfloor119876tp(119909119894119895) 119876tp(119909119894119895) + Δ119876tp(119909119894119895)rfloorand Δ119876tp(119909119894119895) means the deviation of the coefficient119876tp(119909119894119895)

Obviously model (10) cannot be solved with the tradi-tional optimization method or intelligent algorithm In orderto be able to consider the uncertainty of QoS in the solutionwe used the robust optimization model proposed by Bertsi-mas to deal with the uncertainty Due to the uncertainty thatonly appears in the objective function we introduce a param-eter Γ which takes value in the interval [0 119896] where 119896 is thenumber of selected services in the model For one flow therewill be only one composite service selected so the range of Γshould be [0 1] So we propose the following service selectionmodel

min

1205961

119899

sum

119894=1

119898119894

sum

119895=1


prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895) + max119878|119878sube119860|119878|leΓ

1205961sum

(119894119895)isin119878

Δ119876rt (119909119894119895) sdot 119909119894119895 + 1205962maxΔ119876tp (119909119894119895) sdot 119909119894119895

st119899

sum

119894=1

120596119894= 1 120596

119894isin [0 1]

119898119894

sum

119895=1

119909119894119895= 1

119909119894119895isin 0 1

(11)

Γ in objective function (11) is to adjust the robustness ofthe solution against the level of conservatism of the solutionΓ = 0 the model will completely ignore all uncertain factorsso that the solution is the same as the solution obtainedby solving with minimum values 119876rt(119909119894119895) and 119876tp(119909119894119895) thissolution is called the optimal solution Γ = 1 the model willconsider all uncertainties but the solution is too conservativethis solution is called robust solution If the value of Γ is moreclose to 1 we say the corresponding solution has a higherlevel of robustness So robust solution has the highest level ofrobustness In general a higher value of Γ increases the levelof robustness at the expense of higher nominal cost

4 Experiment Analyses

In order to verify the effectiveness of the proposed methodwe developedWeb service testing and selection managementsystem in the early study In the literature the researchersusually solved deterministic model The value of QoS theyused is from one test result or some random numbers pro-duced in a certain range This paper is to study and calculateuncertain data once test result or random numbers cannotdescribe uncertainty of the service used in the real world Weuse the response time and throughput datasets from Zhenget alrsquos paper In the literature [18] about 19 million piecesof data were provided by 339 users calling the 5825 atomicservices In this dataset we found that when users invokedthe service the request may succeed or not and the values ofresponse time and throughput are always varied

In this experiment the workflow is a simple sequenceflow with four tasks each task would invoke in order Eachtask has 10 candidate services so the number of all possiblecomposite services is 104 Set three QoS attributes that havethe same weight and calculate the uncertainty QoS interval of

composite service through the front of the aggregation func-tion Table 2 is the QoS value of 40 candidate services

In Table 2 the data comes from Zheng et alrsquos dataset Wefind out the maximum and minimum value as the upper andlower bounds of the response time and throughput intervalsIn the dataset minus1 means the request is failed so we calculatethe reliability by failure number and total number

Since Γ gt 1 the obtained composite service is the sameas when Γ = 1 so in the experiment Γ takes value inthe interval [0 1] If Γ is an integer it can only take 0 or 1in both cases obtained composite services are respectivelythe optimal solution and the robust solution mentioned inSection 32 To validate the method Γ will be taking decimalto analysis

When solving (11) we have two ways The first way issolving the robust counterpart of (11) and the second is usingone algorithm The solving algorithm is as follows

(1) For 119897 = 1 119899 + 1 solve the 119899 + 1 nominal problems

119866119897

= Γ sdot 119889119897+min119909isin119883

(1198881015840

sdot 119909 +

119897

sum

119895=1

(119889119895minus 119889119897) sdot 119909119895) (12)

and let 119897lowast be an optimal solution of the correspondingproblem

(2) Let 119897lowast = argmin119897=1119899+1

119866119897

(3) 119885lowast = 119866119897lowast

xlowast = x119897lowast

Although there are a lot of methods and tools for solvinginteger programming it would spend toomuch time and thealgorithm can quickly find a solution in few seconds So thisexperiment uses the above algorithm to solve it

The experiment is divided into two parts The first partis to adjust the value of Γ and observe parameter effect on


Table 2 The QoS value of 40 candidate services

Number 119876rt 119876tp 119876re

Task 11 [0432 16523] [002 4629] 97942 [0078 429] [0932 51282] 98233 [0084 13835] [0433 71428] 98534 [0061 3317] [0602 32786] 98535 [0071 3103] [0644 28169] 98536 [0015 6582] [0455 2000] 99717 [0154 9626] [0207 12987] 99718 [022 9552] [11201 486363] 99719 [0115 3726] [0536 17391] 985310 [0169 13237] [0226 17751] 9823

Task 211 [0301 16648] [012 6644] 979412 [0444 15867] [0126 4504] 946913 [1541 16807] [3093 33744] 988214 [0455 9651] [1347 28571] 979415 [0191 19652] [0101 10471] 746316 [0116 15877] [006 17241] 982317 [0466 1127] [0798 19313] 982318 [0502 11187] [0804 17928] 979419 [0284 1087] [0275 10563] 1000020 [0164 2149] [1395 18292] 10000

Task 321 [0164 3594] [0834 18292] 1000022 [0325 9772] [0306 923] 1000023 [0162 3512] [0854 18518] 1000024 [0162 3816] [0786 18518] 1000025 [0345 7115] [0421 8695] 1000026 [017 2066] [1452 17647] 1000027 [0169 2173] [138 17751] 1000028 [017 2349] [1277 17647] 1000029 [0379 14363] [0208 7915] 1000030 [0194 432] [0694 15463] 10000

Task 431 [0195 14418] [0208 15384] 1000032 [0217 13192] [0227 13824] 988233 [02 3272] [0916 150] 988234 [0202 361] [0831 14851] 988235 [0383 19796] [0146 7832] 994136 [0216 5397] [0555 13888] 997137 [0276 11531] [0433 18115] 985338 [0496 16851] [0534 18145] 1000039 [0422 15991] [2814 106635] 1000040 [0343 915] [0546 14577] 10000

the results by solving the robust optimization method Thesecond part is to analyze the different results solved byusing robust optimization (RO) linear programming (LP)and Linear Programming with Uncertain Response Time [1](LPURT)

1 2 3 4

Max value 0536 0541 1002 1162Min value 0325 0332 0073 0037

002040608

11214

Max valueMin value

Figure 2 The global QoS range of four composite services

In order to compare the results of the different methodsthis paper will show the global QoS of services which areselected by methods If the global QoS of the selected com-posite service is lower we believe that the optimality of theservice is better If the deviation of service QoS is smaller andthe upper QoS is smaller we believe the robustness of the ser-vice is better In all results of the experiment the QoS valuesof all component services are standardized before except thatthe totalQoS inTable 4 is the result of the standardization andthe aggregation

41 Effect of Adjusting the Value of Γ In the experiment thevalue of Γ only can be taken in the interval [0 1] so chooseΓ isin 1 08 06 04 02 0 to solve the proposed model Thespecific results are shown in Table 3

It can be seen from Table 3 that when Γ dropped to 04the atomic services of composite service began to changeIn Table 4 we give out the QoS attributes of four compositeservices

The global QoS has been normalized and aggregatedWhen we are calculating the global QoS first we adjust reli-ability to cost type attribute (the smaller the better) and thensum the three QoS attributes with weight (weight of threeQoS attributes is equal ie 120596

1= 1205962= 1205963= 13)

We named the four combination services from CS1to

CS4 It can be seen from Figure 2 that Γ takes value from 1

to 0 and the deviations of global QoS are increasing If theservices are invoked in the real world we contrast CS

4and

CS1 the formermay realize a smaller QoS value but the latter

is more stable and more robustThe experiment proved that we can take a tradeoff

between optimality and robustness by adjusting the value of Γwith user demand

42 Contrast RO LP and LPURT First respectively weuse three methods for selecting services in the mentionedworkflow obtaining three services called composite servicesA B and C as shown in Table 5 Among them when usingLP the response time is the minimum response time of eachatomic service and throughput is the maximum throughput(the best case) As noted above all of these methods consider


Table 3 Solutions of different values of Γ

Values of Γ 1 08 06 04 02 0Result of service selection [5 20 26 33] [5 20 26 33] [5 20 26 33] [4 20 26 33] [8 14 26 39] [8 13 24 39]

Table 4 The QoS attributes of four composite services

Number Γ Composite service Response time Throughput Reliability Global QoS1 1 [5 20 26 33] [0605 1059] [1452 28169] 9730 [0325 0536]2 04 [4 20 26 33] [0595 10804] [1452 32786] 9730 [0332 0541]3 02 [8 14 26 39] [1267 3726] [11201 48636] 9760 [0073 1002]4 0 [8 13 24 39] [2345 46166] [11201 48636] 9850 [0037 1162]

Table 5 The results of three methods

Solving method Robust optimization Linear programming Linear programming withuncertain response time

Composite service A B CAtomic services [5 20 26 33] [6 16 23 31] [4 20 24 33]Response time [0605 1059] [0488 40389] [0587 12554]Throughput [0644 15] [006 15384] [0602 15]Reliability 9732 9791 9732

Table 6 The global QoS of three selected composite services

Methods Compositeservice (CS)

Atomicservices User ID 1 2 3 4 5 6 7 8 9 10

RO A [5 20 26 33] Response time 151 1517 0956 092 0989 1361 1582 1001 1469 1004Throughput 4878 6369 9049 813 8583 6172 4538 8474 6355 7272

LP B [6 16 23 31] Response time 4011 2727 1268 1109 1677 2386 2053 1649 2355 1074Throughput 1066 1809 5181 4672 2702 1915 2929 2832 2057 5665

URTLP C [4 20 24 33] Response time 1536 1525 0959 094 0993 4504 1527 1009 1467 1013Throughput 4962 6153 909 8032 8474 0614 4538 851 6355 7194

determined values When using LPURT the response timeis assumed to be subject to a normal distribution in [1]while throughput still is the maximum throughput withoutuncertainty

As it is shown in Table 5 there are two different atomicservices between composite services A and C They havethe same reliability but the deviations of response time andthroughput of composite service A are smaller In the bestcase composite service B is seen a little better than A and Chowever the deviation is bigger than the other ones

Then we select randomly QoS of 40 candidate atomicservices invoked by 10 users from dataset and compute globalQoS of composite services Table 6 and Figure 2 show theglobal QoS of three selected composite services

We firstly compare composite services A and B From thedata in Figure 3 and Table 6 we can see that response timeand throughput of composite service A are obviously betterthan B Then compare composite services A and C From thedata the QoS of composite service A is better than service Cin most cases From Figure 3 we can see the QoS of the sixthuser and response time and throughput of composite serviceChave an obviously deteriorated case After checking theQoS

Table 7 The QoS fluctuation of combination services

Deviation ofresponse time

Deviation ofthroughput

Composite service A 0662 4511Composite service B 2937 4599Composite service C 3564 8476

of each atomic service we found that one atomic service ofcomposite service C has a bad case at this user The reasonfor this is that LPURT assumed the response time of atomicservice subject to normal distribution and introduced themean and variance to the constraintsWhile in the realworldwe cannot confirm what the probability distribution of theresponse time of services is subject to when we request someservices their quality may be more likely to deteriorate as wehave mentioned Here we could calculate the QoS deviationsof the three composite services by 10 users invoked as shownin Table 7 From Table 7 we can see that the response timeand throughput deviations of composite service A are mini-mal Influenced by the result of the sixth user the deviation


0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10

CS ACS BCS C

(a) Response time

CS ACS BCS C

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10

(b) Throughput

Figure 3 The global QoS of three selected composite services

of QoS of composite service C is maximum That meansrobustness level of service A is higher than B and C

Therefore the composite service selected by our approachhas optimality and robustness And we can control thetradeoff between optimality and robustness by adjusting theattributeThe proposedmethodwithout consideringwhetherthe uncertain QoS is subject to some distributions is moresuitable for the real network environment

5 Conclusions

This paper studies the robust optimization used in the Webservice selection based on uncertain QoS On the basis ofcertain QoS-based Web service selection method first weconsidered the uncertainty of QoS second established uncer-tainQoS-based service selectionmodel and then used robustoptimization methods to convert and solve the proposedmodel In the end the experiment verifies that the proposedmodel and method can deal with uncertain data withoutobvious distribution And we compared the composite ser-vices obtained by our approach and other two methods theresult showed that the service selected by our approach hadhigher robustness and optimality levels

Uncertain QoS-based Web service composition has thefollowing advantages firstly for the software developer pay-ing attention to this can improve usersrsquo acceptance enhanceproduct competitiveness and corporate reputation Secondlyfor users paying attention to this can improve usersrsquo produc-tivity reduce training and support costs improve satisfactionand comfort for usersrsquo work and increase constructioninvestment system efficiency and utilization Thirdly serviceselection study under uncertainty will increase the accuracyof the services provided and give full potential of each serviceand the effect of cooperating with other services Finally

the composite services with uncertainty focus on providingcontinuity of services to ensure that when QoS changes in acertain range the composite service is robust and minimizesthe impact of service errors or failure

Over the past few years cloud computing has been moreandmore attractive as a new computing paradigmdue to highflexibility for provisioning on-demand computing resourcesthat are used as services through the Internet [19 20] It isvery necessary that cloud users be vigilant while selecting theservice providers present in the cloud [21 22] The proposedapproach in this paper is valid in cloud service selection

Conflict of Interests

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

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (Grant no 61100166) and Xirsquoan Scienceand Technology Program (Grant no CXY1437(8))

References

[1] L Z Zeng B Boualem D Marlon J Kalagnanam and Q ZSheng ldquoQuality driven Web services compositionrdquo in Proceed-ings of the 12th International Conference on World Wide Web(WWW rsquo03) pp 411ndash421 Budapest Hungary May 2003

[2] Q Yu M Rege A Bouguettaya B Medjahed and M OuzzanildquoA two-phase framework for quality-aware Web service selec-tionrdquo Service Oriented Computing and Applications vol 4 no2 pp 63ndash79 2010


[3] C-W Zhang S Su and J-L Chen ldquoGenetic algorithm on webservices selection supporting QoSrdquo Chinese Journal of Com-puter vol 29 no 7 pp 1029ndash1037 2006 (Chinese)

[4] T Wen G-J Sheng Q Guo and Y-Q Li ldquoWeb servicecomposition based on modified particle swarm optimizationrdquoChinese Journal of Computers vol 36 no 5 pp 1031ndash1046 2013(Chinese)

[5] Y-M Xia B Cheng J-L Chen X-WMeng and D Liu ldquoOpti-mizing services composition based on improved ant colonyalgorithmrdquoChinese Journal of Computers vol 35 no 2 pp 270ndash281 2012 (Chinese)

[6] S-G Deng L-T Huang B Wu J-W Yin and G-X Li ldquoQoSoptimal automatic composition of semantic Web servicesrdquoChinese Journal of Computers vol 36 no 5 pp 1015ndash1030 2013(Chinese)

[7] G H Alferez and V Pelechano ldquoFacing uncertainty in Webservice compositionsrdquo in Proceedings of the IEEE 20th Interna-tional Conference onWeb Services (ICWS rsquo13) pp 219ndash226 SantaClara Calif USA July 2013

[8] K Benouaret D Benslimane and A Hadjali ldquoSelecting skylineweb services from uncertain QoSrdquo in Proceedings of the IEEE9th International Conference on Services Computing (SCC rsquo12)pp 523ndash530 IEEE Honolulu Hawaii USA June 2012

[9] Q Wu Q Zhu X Jian and F Ishikawa ldquoBroker-based SLA-aware composite service provisioningrdquo Journal of Systems ampSoftware vol 96 no 4 pp 194ndash201 2014

[10] AMostafa andMZhang ldquoMulti-objective service compositionin uncertain environmentsrdquo IEEE Transactions on ServicesComputing 2015

[11] F Wagner F Ishikawa and S Honiden ldquoRobust servicecompositions with functional and location diversityrdquo IEEETransactions on Services Computing 2014

[12] J K Zhang Optimality and duality for generalized convexuncertain programming [PhD thesis] Xidian University XirsquoanChina 2012 (Chinese)

[13] A L Soyster ldquoConvexprogramming with set-inclusive con-straints and applications to inexact linear programmingrdquoOper-ations Research vol 21 no 5 pp 1154ndash1157 1973

[14] A Ben-Tal and A Nemirovski ldquoRobust solutions of uncertainlinear programsrdquo Operations Research Letters vol 25 no 1 pp1ndash13 1999

[15] D Bertsimas and M Sim ldquoRobust discrete optimization andnetwork flowsrdquoMathematical Programming vol 98 no 1-3 SerB pp 49ndash71 2003

[16] D Bertsimas and M Sim ldquoThe price of robustnessrdquoOperationsResearch vol 52 no 1 pp 35ndash53 2004

[17] M L Hu C X Fan and K Q Shi ldquoCharacter analysis ofstandardization methods of decision matrix with intervalsrdquoComputer Science vol 40 no 10 pp 203ndash207 2013 (Chinese)

[18] Z B Zheng Y L Zhang and M R Lyu ldquoDistributed QoSevaluation for real-world Web servicesrdquo in Proceedings of theIEEE 8th International Conference on Web Services (ICWS rsquo10)pp 83ndash90 IEEE Miami Fla USA July 2010

[19] Y Zhong W Li W Guo L Gong and G Lodewijks ldquoAmethod of modeling and service encapsulation on cloud logis-tics resourcesrdquo in Proceedings of the 19th IEEE InternationalConference on Computer Supported Cooperative Work in Design(CSCWD rsquo15) pp 383ndash388 IEEE Calabria Italy May 2015

[20] W Li Y Zhong X Wang and Y Cao ldquoResource virtualizationand service selection in cloud logisticsrdquo Journal of Network andComputer Applications vol 36 no 6 pp 1696ndash1704 2013

[21] P Bedi H Kaur and B Gupta ldquoTrustworthy service providerselection in cloud computing environmentrdquo in Proceedings ofthe International Conference on Communication Systems andNetwork Technologies (CSNT rsquo12) pp 714ndash719 Rajkot IndiaMay 2012

[22] R Karim C Ding A Miri and X Liu ldquoEnd-to-end QoSmapping and aggregation for selecting cloud servicesrdquo in Pro-ceedings of the International Conference on Collaboration Tech-nologies and Systems (CTS rsquo14) pp 515ndash522 IEEE MinneapolisMinn USA May 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


throughput one definition is the number of requestsfor a service successfully executed and the other is theaverage rate of successful message size delivery over acommunication channel per second

(3) Internet environment cannot be repeated When ser-vices are used on the Internet some attributes of QoSof the Web services are influenced by the runningstate of the Internet such as security and responsetimeThe real situation of service cannot be describedby the QoS obtained from once request

Because of the existing uncertainties the compositeservice could hardly be accomplished in the dynamic exe-cution process These uncertainties also affect the individualrequirements of users When the QoS deviation occurs wemust replan and compose services otherwise it would causea lot of problems But the replanning will lead to the waste ofcomputing resources so this paper studies how to ensure thatservice composition is feasible with the uncertain conditionsthus avoiding the replanning of composited service For theuncertainty of the QoS properties this paper combined theuncertain optimization theory described the uncertainty byusing the ldquointervalrdquo modeled a service composition modelbased on workflow (order circulation choice and parallel)proposed the service selection model under the conditionswith uncertain QoS put forward the corresponding normal-ization and aggregation function and ensured that when thechange occurred in the part of QoS attributes the obtainedsolution can adapt to the most cases and close to the optimal

The rest of the sections are organized as follows Section 2describes related works Section 3 details the robust opti-mization method used in service selection model based onthe uncertain QoS Section 4 presents the experiment andanalysis result Finally Section 5 draws some conclusions

2 Related Works

In Zeng et alrsquos paper [1] QoS was introduced intoWeb serviceat the first time the QoS of Web service was used to dis-tinguish the Web services with similar functions From thenon service selection based on QoS plays a more and moreimportant role in the Web service composition area QoS-based service selection methods are mainly divided into twodirections semantic QoS [6] andQoS value According to thedifferent QoS requirements the Web service selection strat-egy can be divided into two kinds namely the local optimalstrategy and the global optimal strategy Local optimal strat-egy selects component services for a single service functionrespectively compares the candidate atomic service set sortsQoS values for each candidate atomic service and then selectsthe best oneThemain algorithm is theGreedyAlgorithm [2]Global optimal strategy aims to make the global QoS of thecomposite services to satisfy the given constraints or achievethe desired goals the main methods are Genetic Algorithm[3] PSO [4] and Ant Colony Algorithm [5]

In recent years the researchers have also addressed somestudies for service selection based on uncertain QoS Zeng etal [1] proposedQoS-based service selection at the same timethey proposed that uncertain response time was introduced

into the service selection model They assumed the responsetime of service subjected to normal distribution and intro-duced the variance of the normal distribution into theconstraints Alferez and Pelechano [7] leveraged models atruntime to guide the dynamic evolution of context-awareWeb service compositions to deal with unexpected events inthe open world In order to manage uncertainty a model thatabstracts the Web service composition self-evolves to pre-serve requirements Benouaret et al [8] represented eachQoSattribute of a Web service using a possibility distribution andintroduced two skyline extensions on uncertain QoS calledpos-dominant skyline and nec-dominant skyline Wu et al[9] proposed an ldquoon-demandrdquo strategy for QoS-aware servicecomposition to replace the traditional ldquobest-effortrdquo strategyMostafa and Zhang [10] presented two approaches basedon the Multiobjective Reinforcement Learning (MORL) toaddress multiobjective service composition in uncertain anddynamic environments Wagner et al [11] developed a newQoS model that helps to predict the resulting QoS of aworkflow by considering service failures during the initialselection phase For each service a set of possible backup ser-vices and the corresponding QoS are computed beforehand

In recent years it has been recognized that dealing withuncertain data is amajor challenge in optimization As can beseen from the above literaturesWeb serviceQoSmodels withuncertainty dispose uncertain data in two ways one wouldassume that the data is subject to one kind of distributionsto compute the uncertainty of QoS and the other solves theproblem by using intelligent algorithms But the problem ofthe formermethod is that the assumptionmay be not reason-able In the real world we could not get the exact distributionof the data And for the latter method different intelligentalgorithms have different problem like premature conver-gence for Genetic Algorithm And for all intelligent algo-rithms they always solve different solutions in different timeseven if they use the same data We need an approach to selectservice considering all possible situations but it does nottake whether the uncertain data is subject to any distributionsinto account

The researches of the traditional optimization problemsare mostly about deterministic problems When solvinguncertain optimization problems researchers mainly focuson the following ways stochastic programming fuzzy pro-gramming interval programming and robust optimizationWhen solving the uncertain problems the stochastic pro-gramming and fuzzy programming need precise distributionof the parameters and the precise distribution is difficult toobtain in the real world When solving these two kinds ofprogramming problems the commonly used method is theMonte Carlo method but this method shows slow conver-gence and low efficiency Facing more complex constraintsthey are only to use approximate method Interval program-ming and robust optimization are all converting the uncertainoptimization to determine problem for solving The differ-ence is that the robust optimization considers the worst casethe result may be conservative And the interval program-ming eventually provides decision-makers with a range ofoptimal value they will have a better space to select [12]When converting the interval programming upper and lower








119876rt = 119879tran + 119879proc (1)





119876re =119873re119899 (2)







Sequence [119899

sum119894=1

119876rti119899

sum119894=1

(119876rt119894 + Δ119876rt119894)] [min119894

119876tp119894min119894

(119876tp119894 + Δ119876tp119894)]119899

prod119894=1

119876re119894

Selection [119899

sum119894=1

119888119894119876rt119894119899

sum119894=1

119888119894(119876rt119894 + Δ119876rt119894)] [min

119894

119888119894119876tp119894min

119894

119888119894(119876tp119894 + Δ119876tp119894)]

119899

sum119894=1

119888119894119876re119894


re

Parallel [max119894

119876rt119894max119894

(119876rt119894 + Δ119876rt119894)] [min119894

119876tp119894min119894

(119876tp119894 + Δ119876tp119894)]119899

prod119894=1

119876re119894


Web services

Composed service

SC1 SC2 SC3









119894

1198761015840

119894+ Δ1198761015840



Cost type

1198761015840

119894=


119894119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

1198761015840

119894+ Δ1198761015840

119894=

(119876119894+ Δ119876119894) minusmin

119894119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

(3)


Benefit type

1198761015840

119894=

max119894(119876119894+ Δ119876119894) minus 119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

1198761015840

119894+ Δ1198761015840

119894=max119894(119876119894+ Δ119876119894) minus (119876

119894+ Δ119876119894)

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

(4)










119894is theweight

of the QoS and sum119899119894=1120596119894= 1 120596

119894isin [0 1]



119876rt =119899

sum

119894=1

119898119894

sum

119895=1

119876rt (119909119894119895) sdot 119909119894119895 (6)





sum

119895=1

119909119894119895= 1 (7)






119876tp = max119876tp (119909119894119895) sdot 119909119894119895 (8)



119876re = 1 minus119899

prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895 (9)



min

1205961

119899

sum

119894=1

119898119894

sum

119895=1


prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895)

st3

sum

119894=1

120596119894= 1

119899

sum

119894=1

119909119894= 1

119909119894119895isin 0 1

(10)




min

1205961

119899

sum

119894=1

119898119894

sum

119895=1


prod

119894=1

119898119894

prod

119895=1


1205961sum

(119894119895)isin119878


st119899

sum

119894=1

120596119894= 1 120596

119894isin [0 1]

119898119894

sum

119895=1

119909119894119895= 1

119909119894119895isin 0 1

(11)










119866119897

= Γ sdot 119889119897+min119909isin119883

(1198881015840

sdot 119909 +

119897

sum

119895=1

(119889119895minus 119889119897) sdot 119909119895) (12)



119866119897

(3) 119885lowast = 119866119897lowast






Number 119876rt 119876tp 119876re

Task 11 [0432 16523] [002 4629] 97942 [0078 429] [0932 51282] 98233 [0084 13835] [0433 71428] 98534 [0061 3317] [0602 32786] 98535 [0071 3103] [0644 28169] 98536 [0015 6582] [0455 2000] 99717 [0154 9626] [0207 12987] 99718 [022 9552] [11201 486363] 99719 [0115 3726] [0536 17391] 985310 [0169 13237] [0226 17751] 9823

Task 211 [0301 16648] [012 6644] 979412 [0444 15867] [0126 4504] 946913 [1541 16807] [3093 33744] 988214 [0455 9651] [1347 28571] 979415 [0191 19652] [0101 10471] 746316 [0116 15877] [006 17241] 982317 [0466 1127] [0798 19313] 982318 [0502 11187] [0804 17928] 979419 [0284 1087] [0275 10563] 1000020 [0164 2149] [1395 18292] 10000

Task 321 [0164 3594] [0834 18292] 1000022 [0325 9772] [0306 923] 1000023 [0162 3512] [0854 18518] 1000024 [0162 3816] [0786 18518] 1000025 [0345 7115] [0421 8695] 1000026 [017 2066] [1452 17647] 1000027 [0169 2173] [138 17751] 1000028 [017 2349] [1277 17647] 1000029 [0379 14363] [0208 7915] 1000030 [0194 432] [0694 15463] 10000

Task 431 [0195 14418] [0208 15384] 1000032 [0217 13192] [0227 13824] 988233 [02 3272] [0916 150] 988234 [0202 361] [0831 14851] 988235 [0383 19796] [0146 7832] 994136 [0216 5397] [0555 13888] 997137 [0276 11531] [0433 18115] 985338 [0496 16851] [0534 18145] 1000039 [0422 15991] [2814 106635] 1000040 [0343 915] [0546 14577] 10000


1 2 3 4


002040608

11214

Max valueMin value






1= 1205962= 1205963= 13)




4and





























0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10

CS ACS BCS C

(a) Response time

CS ACS BCS C

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10

(b) Throughput




5 Conclusions







Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















119876rt = 119879tran + 119879proc (1)





119876re =119873re119899 (2)







Sequence [119899

sum119894=1

119876rti119899

sum119894=1

(119876rt119894 + Δ119876rt119894)] [min119894

119876tp119894min119894

(119876tp119894 + Δ119876tp119894)]119899

prod119894=1

119876re119894

Selection [119899

sum119894=1

119888119894119876rt119894119899

sum119894=1

119888119894(119876rt119894 + Δ119876rt119894)] [min

119894

119888119894119876tp119894min

119894

119888119894(119876tp119894 + Δ119876tp119894)]

119899

sum119894=1

119888119894119876re119894


re

Parallel [max119894

119876rt119894max119894

(119876rt119894 + Δ119876rt119894)] [min119894

119876tp119894min119894

(119876tp119894 + Δ119876tp119894)]119899

prod119894=1

119876re119894


Web services

Composed service

SC1 SC2 SC3









119894

1198761015840

119894+ Δ1198761015840



Cost type

1198761015840

119894=


119894119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

1198761015840

119894+ Δ1198761015840

119894=

(119876119894+ Δ119876119894) minusmin

119894119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

(3)


Benefit type

1198761015840

119894=

max119894(119876119894+ Δ119876119894) minus 119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

1198761015840

119894+ Δ1198761015840

119894=max119894(119876119894+ Δ119876119894) minus (119876

119894+ Δ119876119894)

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

(4)










119894is theweight

of the QoS and sum119899119894=1120596119894= 1 120596

119894isin [0 1]



119876rt =119899

sum

119894=1

119898119894

sum

119895=1

119876rt (119909119894119895) sdot 119909119894119895 (6)





sum

119895=1

119909119894119895= 1 (7)






119876tp = max119876tp (119909119894119895) sdot 119909119894119895 (8)



119876re = 1 minus119899

prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895 (9)



min

1205961

119899

sum

119894=1

119898119894

sum

119895=1


prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895)

st3

sum

119894=1

120596119894= 1

119899

sum

119894=1

119909119894= 1

119909119894119895isin 0 1

(10)




min

1205961

119899

sum

119894=1

119898119894

sum

119895=1


prod

119894=1

119898119894

prod

119895=1


1205961sum

(119894119895)isin119878


st119899

sum

119894=1

120596119894= 1 120596

119894isin [0 1]

119898119894

sum

119895=1

119909119894119895= 1

119909119894119895isin 0 1

(11)










119866119897

= Γ sdot 119889119897+min119909isin119883

(1198881015840

sdot 119909 +

119897

sum

119895=1

(119889119895minus 119889119897) sdot 119909119895) (12)



119866119897

(3) 119885lowast = 119866119897lowast






Number 119876rt 119876tp 119876re

Task 11 [0432 16523] [002 4629] 97942 [0078 429] [0932 51282] 98233 [0084 13835] [0433 71428] 98534 [0061 3317] [0602 32786] 98535 [0071 3103] [0644 28169] 98536 [0015 6582] [0455 2000] 99717 [0154 9626] [0207 12987] 99718 [022 9552] [11201 486363] 99719 [0115 3726] [0536 17391] 985310 [0169 13237] [0226 17751] 9823

Task 211 [0301 16648] [012 6644] 979412 [0444 15867] [0126 4504] 946913 [1541 16807] [3093 33744] 988214 [0455 9651] [1347 28571] 979415 [0191 19652] [0101 10471] 746316 [0116 15877] [006 17241] 982317 [0466 1127] [0798 19313] 982318 [0502 11187] [0804 17928] 979419 [0284 1087] [0275 10563] 1000020 [0164 2149] [1395 18292] 10000

Task 321 [0164 3594] [0834 18292] 1000022 [0325 9772] [0306 923] 1000023 [0162 3512] [0854 18518] 1000024 [0162 3816] [0786 18518] 1000025 [0345 7115] [0421 8695] 1000026 [017 2066] [1452 17647] 1000027 [0169 2173] [138 17751] 1000028 [017 2349] [1277 17647] 1000029 [0379 14363] [0208 7915] 1000030 [0194 432] [0694 15463] 10000

Task 431 [0195 14418] [0208 15384] 1000032 [0217 13192] [0227 13824] 988233 [02 3272] [0916 150] 988234 [0202 361] [0831 14851] 988235 [0383 19796] [0146 7832] 994136 [0216 5397] [0555 13888] 997137 [0276 11531] [0433 18115] 985338 [0496 16851] [0534 18145] 1000039 [0422 15991] [2814 106635] 1000040 [0343 915] [0546 14577] 10000


1 2 3 4


002040608

11214

Max valueMin value






1= 1205962= 1205963= 13)




4and





























0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10

CS ACS BCS C

(a) Response time

CS ACS BCS C

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10

(b) Throughput




5 Conclusions







Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Sequence [119899

sum119894=1

119876rti119899

sum119894=1

(119876rt119894 + Δ119876rt119894)] [min119894

119876tp119894min119894

(119876tp119894 + Δ119876tp119894)]119899

prod119894=1

119876re119894

Selection [119899

sum119894=1

119888119894119876rt119894119899

sum119894=1

119888119894(119876rt119894 + Δ119876rt119894)] [min

119894

119888119894119876tp119894min

119894

119888119894(119876tp119894 + Δ119876tp119894)]

119899

sum119894=1

119888119894119876re119894


re

Parallel [max119894

119876rt119894max119894

(119876rt119894 + Δ119876rt119894)] [min119894

119876tp119894min119894

(119876tp119894 + Δ119876tp119894)]119899

prod119894=1

119876re119894


Web services

Composed service

SC1 SC2 SC3









119894

1198761015840

119894+ Δ1198761015840



Cost type

1198761015840

119894=


119894119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

1198761015840

119894+ Δ1198761015840

119894=

(119876119894+ Δ119876119894) minusmin

119894119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

(3)


Benefit type

1198761015840

119894=

max119894(119876119894+ Δ119876119894) minus 119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

1198761015840

119894+ Δ1198761015840

119894=max119894(119876119894+ Δ119876119894) minus (119876

119894+ Δ119876119894)

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

(4)










119894is theweight

of the QoS and sum119899119894=1120596119894= 1 120596

119894isin [0 1]



119876rt =119899

sum

119894=1

119898119894

sum

119895=1

119876rt (119909119894119895) sdot 119909119894119895 (6)





sum

119895=1

119909119894119895= 1 (7)






119876tp = max119876tp (119909119894119895) sdot 119909119894119895 (8)



119876re = 1 minus119899

prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895 (9)



min

1205961

119899

sum

119894=1

119898119894

sum

119895=1


prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895)

st3

sum

119894=1

120596119894= 1

119899

sum

119894=1

119909119894= 1

119909119894119895isin 0 1

(10)




min

1205961

119899

sum

119894=1

119898119894

sum

119895=1


prod

119894=1

119898119894

prod

119895=1


1205961sum

(119894119895)isin119878


st119899

sum

119894=1

120596119894= 1 120596

119894isin [0 1]

119898119894

sum

119895=1

119909119894119895= 1

119909119894119895isin 0 1

(11)










119866119897

= Γ sdot 119889119897+min119909isin119883

(1198881015840

sdot 119909 +

119897

sum

119895=1

(119889119895minus 119889119897) sdot 119909119895) (12)



119866119897

(3) 119885lowast = 119866119897lowast






Number 119876rt 119876tp 119876re

Task 11 [0432 16523] [002 4629] 97942 [0078 429] [0932 51282] 98233 [0084 13835] [0433 71428] 98534 [0061 3317] [0602 32786] 98535 [0071 3103] [0644 28169] 98536 [0015 6582] [0455 2000] 99717 [0154 9626] [0207 12987] 99718 [022 9552] [11201 486363] 99719 [0115 3726] [0536 17391] 985310 [0169 13237] [0226 17751] 9823

Task 211 [0301 16648] [012 6644] 979412 [0444 15867] [0126 4504] 946913 [1541 16807] [3093 33744] 988214 [0455 9651] [1347 28571] 979415 [0191 19652] [0101 10471] 746316 [0116 15877] [006 17241] 982317 [0466 1127] [0798 19313] 982318 [0502 11187] [0804 17928] 979419 [0284 1087] [0275 10563] 1000020 [0164 2149] [1395 18292] 10000

Task 321 [0164 3594] [0834 18292] 1000022 [0325 9772] [0306 923] 1000023 [0162 3512] [0854 18518] 1000024 [0162 3816] [0786 18518] 1000025 [0345 7115] [0421 8695] 1000026 [017 2066] [1452 17647] 1000027 [0169 2173] [138 17751] 1000028 [017 2349] [1277 17647] 1000029 [0379 14363] [0208 7915] 1000030 [0194 432] [0694 15463] 10000

Task 431 [0195 14418] [0208 15384] 1000032 [0217 13192] [0227 13824] 988233 [02 3272] [0916 150] 988234 [0202 361] [0831 14851] 988235 [0383 19796] [0146 7832] 994136 [0216 5397] [0555 13888] 997137 [0276 11531] [0433 18115] 985338 [0496 16851] [0534 18145] 1000039 [0422 15991] [2814 106635] 1000040 [0343 915] [0546 14577] 10000


1 2 3 4


002040608

11214

Max valueMin value






1= 1205962= 1205963= 13)




4and





























0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10

CS ACS BCS C

(a) Response time

CS ACS BCS C

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10

(b) Throughput




5 Conclusions







Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Benefit type

1198761015840

119894=

max119894(119876119894+ Δ119876119894) minus 119876119894

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

1198761015840

119894+ Δ1198761015840

119894=max119894(119876119894+ Δ119876119894) minus (119876

119894+ Δ119876119894)

max119894(119876119894+ Δ119876119894) minusmin

119894119876119894

(4)










119894is theweight

of the QoS and sum119899119894=1120596119894= 1 120596

119894isin [0 1]



119876rt =119899

sum

119894=1

119898119894

sum

119895=1

119876rt (119909119894119895) sdot 119909119894119895 (6)





sum

119895=1

119909119894119895= 1 (7)






119876tp = max119876tp (119909119894119895) sdot 119909119894119895 (8)



119876re = 1 minus119899

prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895 (9)



min

1205961

119899

sum

119894=1

119898119894

sum

119895=1


prod

119894=1

119898119894

prod

119895=1

119876re (119909119894119895) sdot 119909119894119895)

st3

sum

119894=1

120596119894= 1

119899

sum

119894=1

119909119894= 1

119909119894119895isin 0 1

(10)




min

1205961

119899

sum

119894=1

119898119894

sum

119895=1


prod

119894=1

119898119894

prod

119895=1


1205961sum

(119894119895)isin119878


st119899

sum

119894=1

120596119894= 1 120596

119894isin [0 1]

119898119894

sum

119895=1

119909119894119895= 1

119909119894119895isin 0 1

(11)










119866119897

= Γ sdot 119889119897+min119909isin119883

(1198881015840

sdot 119909 +

119897

sum

119895=1

(119889119895minus 119889119897) sdot 119909119895) (12)



119866119897

(3) 119885lowast = 119866119897lowast






Number 119876rt 119876tp 119876re

Task 11 [0432 16523] [002 4629] 97942 [0078 429] [0932 51282] 98233 [0084 13835] [0433 71428] 98534 [0061 3317] [0602 32786] 98535 [0071 3103] [0644 28169] 98536 [0015 6582] [0455 2000] 99717 [0154 9626] [0207 12987] 99718 [022 9552] [11201 486363] 99719 [0115 3726] [0536 17391] 985310 [0169 13237] [0226 17751] 9823

Task 211 [0301 16648] [012 6644] 979412 [0444 15867] [0126 4504] 946913 [1541 16807] [3093 33744] 988214 [0455 9651] [1347 28571] 979415 [0191 19652] [0101 10471] 746316 [0116 15877] [006 17241] 982317 [0466 1127] [0798 19313] 982318 [0502 11187] [0804 17928] 979419 [0284 1087] [0275 10563] 1000020 [0164 2149] [1395 18292] 10000

Task 321 [0164 3594] [0834 18292] 1000022 [0325 9772] [0306 923] 1000023 [0162 3512] [0854 18518] 1000024 [0162 3816] [0786 18518] 1000025 [0345 7115] [0421 8695] 1000026 [017 2066] [1452 17647] 1000027 [0169 2173] [138 17751] 1000028 [017 2349] [1277 17647] 1000029 [0379 14363] [0208 7915] 1000030 [0194 432] [0694 15463] 10000

Task 431 [0195 14418] [0208 15384] 1000032 [0217 13192] [0227 13824] 988233 [02 3272] [0916 150] 988234 [0202 361] [0831 14851] 988235 [0383 19796] [0146 7832] 994136 [0216 5397] [0555 13888] 997137 [0276 11531] [0433 18115] 985338 [0496 16851] [0534 18145] 1000039 [0422 15991] [2814 106635] 1000040 [0343 915] [0546 14577] 10000


1 2 3 4


002040608

11214

Max valueMin value






1= 1205962= 1205963= 13)




4and





























0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10

CS ACS BCS C

(a) Response time

CS ACS BCS C

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10

(b) Throughput




5 Conclusions







Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












min

1205961

119899

sum

119894=1

119898119894

sum

119895=1


prod

119894=1

119898119894

prod

119895=1


1205961sum

(119894119895)isin119878


st119899

sum

119894=1

120596119894= 1 120596

119894isin [0 1]

119898119894

sum

119895=1

119909119894119895= 1

119909119894119895isin 0 1

(11)










119866119897

= Γ sdot 119889119897+min119909isin119883

(1198881015840

sdot 119909 +

119897

sum

119895=1

(119889119895minus 119889119897) sdot 119909119895) (12)



119866119897

(3) 119885lowast = 119866119897lowast






Number 119876rt 119876tp 119876re

Task 11 [0432 16523] [002 4629] 97942 [0078 429] [0932 51282] 98233 [0084 13835] [0433 71428] 98534 [0061 3317] [0602 32786] 98535 [0071 3103] [0644 28169] 98536 [0015 6582] [0455 2000] 99717 [0154 9626] [0207 12987] 99718 [022 9552] [11201 486363] 99719 [0115 3726] [0536 17391] 985310 [0169 13237] [0226 17751] 9823

Task 211 [0301 16648] [012 6644] 979412 [0444 15867] [0126 4504] 946913 [1541 16807] [3093 33744] 988214 [0455 9651] [1347 28571] 979415 [0191 19652] [0101 10471] 746316 [0116 15877] [006 17241] 982317 [0466 1127] [0798 19313] 982318 [0502 11187] [0804 17928] 979419 [0284 1087] [0275 10563] 1000020 [0164 2149] [1395 18292] 10000

Task 321 [0164 3594] [0834 18292] 1000022 [0325 9772] [0306 923] 1000023 [0162 3512] [0854 18518] 1000024 [0162 3816] [0786 18518] 1000025 [0345 7115] [0421 8695] 1000026 [017 2066] [1452 17647] 1000027 [0169 2173] [138 17751] 1000028 [017 2349] [1277 17647] 1000029 [0379 14363] [0208 7915] 1000030 [0194 432] [0694 15463] 10000

Task 431 [0195 14418] [0208 15384] 1000032 [0217 13192] [0227 13824] 988233 [02 3272] [0916 150] 988234 [0202 361] [0831 14851] 988235 [0383 19796] [0146 7832] 994136 [0216 5397] [0555 13888] 997137 [0276 11531] [0433 18115] 985338 [0496 16851] [0534 18145] 1000039 [0422 15991] [2814 106635] 1000040 [0343 915] [0546 14577] 10000


1 2 3 4


002040608

11214

Max valueMin value






1= 1205962= 1205963= 13)




4and





























0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10

CS ACS BCS C

(a) Response time

CS ACS BCS C

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10

(b) Throughput




5 Conclusions







Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Number 119876rt 119876tp 119876re

Task 11 [0432 16523] [002 4629] 97942 [0078 429] [0932 51282] 98233 [0084 13835] [0433 71428] 98534 [0061 3317] [0602 32786] 98535 [0071 3103] [0644 28169] 98536 [0015 6582] [0455 2000] 99717 [0154 9626] [0207 12987] 99718 [022 9552] [11201 486363] 99719 [0115 3726] [0536 17391] 985310 [0169 13237] [0226 17751] 9823

Task 211 [0301 16648] [012 6644] 979412 [0444 15867] [0126 4504] 946913 [1541 16807] [3093 33744] 988214 [0455 9651] [1347 28571] 979415 [0191 19652] [0101 10471] 746316 [0116 15877] [006 17241] 982317 [0466 1127] [0798 19313] 982318 [0502 11187] [0804 17928] 979419 [0284 1087] [0275 10563] 1000020 [0164 2149] [1395 18292] 10000

Task 321 [0164 3594] [0834 18292] 1000022 [0325 9772] [0306 923] 1000023 [0162 3512] [0854 18518] 1000024 [0162 3816] [0786 18518] 1000025 [0345 7115] [0421 8695] 1000026 [017 2066] [1452 17647] 1000027 [0169 2173] [138 17751] 1000028 [017 2349] [1277 17647] 1000029 [0379 14363] [0208 7915] 1000030 [0194 432] [0694 15463] 10000

Task 431 [0195 14418] [0208 15384] 1000032 [0217 13192] [0227 13824] 988233 [02 3272] [0916 150] 988234 [0202 361] [0831 14851] 988235 [0383 19796] [0146 7832] 994136 [0216 5397] [0555 13888] 997137 [0276 11531] [0433 18115] 985338 [0496 16851] [0534 18145] 1000039 [0422 15991] [2814 106635] 1000040 [0343 915] [0546 14577] 10000


1 2 3 4


002040608

11214

Max valueMin value






1= 1205962= 1205963= 13)




4and





























0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10

CS ACS BCS C

(a) Response time

CS ACS BCS C

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10

(b) Throughput




5 Conclusions







Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

































0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10

CS ACS BCS C

(a) Response time

CS ACS BCS C

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10

(b) Throughput




5 Conclusions







Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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