A model of Virtual Resource Scheduling in Cloud Computing and Its

Transcription

1 A model of Virtual Resource Schedulig i Cloud Computig ad Its Solutio usig EDAs 1 Jiafeg Zhao, 2 Wehua Zeg, 3 Miu Liu, 4 Guagmig Li 1, First Author, 3 Cogitive Sciece Departmet, Xiame Uiversity, Xiame, Fujia, Chia; Fujia Key Laboratory of the Brai-like Itelliget Systems(Xiame Uiversity), Xiame, Fujia, Chia, zjfhi2008g@gmail.com liumi_xt@163.com *2,Correspodig Author, 4 Fujia Key Laboratory of the Brai-like Itelliget Systems(Xiame Uiversity), Xiame, Fujia, Chia; Software School of Xiame Uiversity, Xiame, Fujia, Chia, whzeg@xmu.edu.c migmig2633@163.com Abstract Resource schedulig becomes more complex as the itroductio of virtualizatio techology i cloud computig. This paper proposed a resource schedulig model usig the cocept of resource service ratio as a object fuctio ad employig Estimatio of Distributio Algorithms (EDAs) to solve this model. I schedulig model, the resource was abstracted to odes with attributes, the schedulig result was evaluated by resource service ratio istead of the tasks completio time. I EDAs, two ovel factors were itroduced, oe was the iteratio times of best idividual uchaged for reducig the iteratio time, ad aother was share probability for improvig the fitess. I experimet, whe the tasks umber is betwee 5 ad 55 ad the load rate is betwee 0.5 ad 1.5, comparig with Max-mi algorithm, static algorithm ad radom algorithm, the resource service ratio of EDA algorithm is improved o average by at least ad at most times. Keywords: Resource Schedulig, Cloud Computig, Estimatio Of Distributio Algorithms 1. Itroductio Schedulig problem is a widely existed problem i real world, for example, job-shop schedulig problem [1-3], schedulig i heterogeeous distributed systems [4], tasks schedulig i grid eviromet [5-7], vehicle schedulig [8, 9], ad so o. This problem also exists i cloud computig eviromet, which plays a importat role i cloud computig. Cloud computig [10] is a kid of ovel larger-scale distributioal computer ceter i recet year. Although the exactly defiitio is ot clear [11-14], there were hudreds of products amed cloud computig, such as Amazo EC2, IBM smart cloud, Google App Egie ad so o. Differet with the traditioal computer ceter, virtualizatio is putted i cloud computig. The compute is sold as a service ot a product due to the itroductio of virtualizatio, which allows users to purchase compute o-demad. However, the applicatio of virtual techology makes the resource schedulig more complex compared with the traditio distributed computatio. At the same time, the result of resource schedulig is critical for cloud computer i virtue of it decides the complete time of tasks. Therefore, the resource schedulig is a hot topic i cloud computig. How to schedule resource i cloud computig eviromet, differet methods were proposed by scholars. For example, Sotomayor [15] et. al proposed a resource lease maager called Haizea, which ca act as a schedulig back ed for OpeNebula [16]. Itel Corporatio [17] ivestigated the shared resource cotetio problem for virtual machies, modeled the effect o each virtual machies s performace. Kog [18] et. al proposed a efficiet dyamic task schedulig scheme based o fuzzy logic systems for cloud computig, i which the availability ad resposiveess preformace was formulated as a two-objective optimizatio. Sog [19] et. al proposed a multi-tiered resource schedulig scheme which automatically provides o-demad capacities to the hosted services via resource flowig amog VMs. Li [20] et. al propose a hybrid eergy-efficiet schedulig algorithm usig dyamic migratio. All above the schudulig algorithms are the sigle task schedulig algorithm. The advatage of sigle task schedulig algorithm is that it s easy to implemet. The disavatage is that it ca t implemet the global ifromatio. This paper modeled the virtual resource schedulig o accout of Iteratioal Joural of Digital Cotet Techology ad its Applicatios(JDCTA) Volume6,Number4,March 2012 doi: /jdcta.vol6.issue

2 the detailed aalysis for the schedulig process i cloud computig ad the requirmet i reality. A ovel cocept amed resource service rate was proposed ad a optimazatio model was established based o this cocept. The Estimatio of distributio algorithms (EDAs) was used to solve this problem, at the same time, two factors were itroduced i EDAs for reducig the iteratio times ad improvig the solutio fitess. Comparig with the radom algorithm, Static algorithm ad Max-mi algorithm, EDAs ca solve this model ad better resource service ratio was obtaied. 2. Cloud computig ad resource schedulig Cloud computig is a popular ou i recetly year. It was arguably first popularized i 2006 by Amazo s Elastic Compute Cloud (EC2) [15] which is represetative of Cloud computig. However, there is still o a widely accepted cocept about cloud computig. After researchig more tha 20 defiitios, Vaquero [10] et. al provided a defiitio that clouds are a large pool of easily usable ad accessible virtualized resource (such as hardware, developmet platforms ad/or services). Cloud computig becomes the elite amog larger scale distributed computig methods thaks to its low-priced ad usability brought by virtual techology i recet years. Task Task Task Device Device Device a.traditioal distributed eviromet Task Task Task VM VM VM VM VM VM Device Device Device b. Cloud computig eviromet Figure 1. A illustratio of resource schedulig The itroductio of virtualizatio techology brigs huge beefits for cloud computig, whereas the challege of resource schedulig is greater. Differet with the traditioal distributed system, a virtual resource layer is added as show i figure 1. The traditioal distributed schedulig decisio system is illustrated i figure 1.a. At first, a task is received by scheduler, the schedules it to a physical device. It s usually oe-o-oe schedulig, amely whe a task is assiged to a physical device, if this device is buy, the the task waits util other users release this device. The schedulig i cloud computig is explaied i figure 1.b. Whe the user s requiremets are received by system, the decisio system assigs immediately a lot of virtual resource to user, which oe task is assiged usually more tha oe virtual resource. The the scheduler schedules the virtual resource to physical device, which oe physical device is shared by more tha oe virtual resource. Therefore, the schedulig decisio is more complex as the itroductio virtual techology i cloud computig. A mathematic defiitio for resource schedulig i cloud computig is show as followig. Defiitio 1. The resource schedulig i cloud computig is that fid a virtual resource set V = [v i ], i = 1, 2,, m ad a best mappig L = {l 1, l 2,, l m for V to the physical resource set P = [p j ], j = 1, 2,, i a certai time after the tasks set are received. From the defiitio we kow that the key of resource schedulig is to fid a virtual resource set V ad a mappig L. However, this problem is a hard problem. 103

3 3. The resource schedulig model ad its solutio 3.1. The resource schedulig model At first, this paper aalyses the process of schedulig i cloud computig, the model for the virtual resource schedulig i cloud computig. Figure 2 describes the process of resource schedulig i cloud computig. At begi, the users access the cloud computig ceter by explorer or others remote termial, put the tasks to cloud computig ceter. Whe the cloud computig ceter receives the tasks, the virtual resource will be assiged immediately by cloud system. The the virtual resource is scheduled to the physical resource by scheduler. Iteret Figure 2. The process of tasks requiremet i cloud computig I practice, the completio time of task is foremost cocer of users whe a task is put to cloud computig. So, may scholars [18, 19] proposed usig completio time as the evaluatio idex to evaluate the schedulig result. However, the task completio time is related with the resource assiged to it, therefore, if employ the completio time as the evaluatio idex, the relatioship of give resource ad tasks completio time must be established. Whereas, it s a hard work to establish this relatioship thiks to differet kid of tasks has the differet ruig time whe the same resource is obtaied by the differet kid of tasks. Various tasks have to be tested for established this relatioship, it s a hard work ad the result is affected by the elemet of artificiality. From the aalysis we kow that there is a positive correlatio betwee the tasks completio time ad assiged resource, amely, if a task obtai more resource, the the completio time is shorter. Ispired by this opiio, we proposed a cocept called resource service ratio. Defie 2. Resource Service Ratio is the ratio of the assiged resource ad required resource for a give task i cloud computig system. Usig resource service ratio to evaluate the schedulig result, the complexity of schedulig model will be simplified ad the iterferece of experiece fuctio will be reduced. From the cocept, we kow that oly the required resource ad the assiged resource are ecessary. It s easy to obtai those two values i cloud system. I the cloud computig system, the required resource of tasks, virtual resource ad physical resource ca be abstracted some odes with attributes. I the cloud computig system, CPU, RAM ad badwidth are the commo three attributes, this paper uses those three attributes to build model. Set tasks set T = {t i, i = 1, 2,, m, where t i = (c ti, m ti, b ti ), c ti, m ti, b ti is the value of CPU, RAM ad badwidth of task i; A virtual resource set is V = [v i ], i = 1, 2,, m, where, v i = (c vi, m vi, b vi ), c vi, m vi, b vi is the value of CPU, RAM ad badwidth of virtual resource i; Similarly, the physical resource set is P = {p j, j = 1, 2,,, where p j = (c pj, m pj, b pj ), c pj, m pj, b pj is the remat value of CPU, RAM ad badwidth of a physical device ode. A typical example of cloud computig is show as table 1. The formal descriptio of resource service ratio is as followig. 104

4 Table 1. The abstract task ad resource Task set T Virtual resource set V Physical resource set P (1.0, 200, 20) 1.00, 200, 20.0 (3.0, 1000, 80) (0.8, 500, 40) 0.80, 370, 35.1 (20, 700, 20) (2.0,80, 0.5) 0.57, 80, 0.5 (1.0, 400, 20) (0.3, 20, 0.2) 0.30, 20, 0.2 (1.0, 400, 10) (0.4, 50, 0.2) 0.40, 50, 0.2 (0.7, 700, 50) 0.70, 518, 43.7 (1.5, 200, 2) 0.43, 200, 2.0 (1.2, 150, 1) 1.20, 111,0.9 (1.3, 600, 10) 1.30, 600, 10.0 Set S ci is the cpu resource service ratio of task t i, therefore: S c /c (1) Set S c is the total cpu resource service ratio, the: ci vi ci m S s / m (2) c ci Similarly, the RAM resource service ratio S m ad the badwidth resource ratio S b are: m S s / m (3) m mi m S s / m (4) b bi Therefore, the resource service ratio is: S S c S m S b / 3 (5) Set cj is the reality assiged cpu resource o physical device j, the: cj c r (6) vi 1 vi j where, r. The mea of r is that if the task i was assiged to physical device j, the 0 others sum the c vi to cj. Similarly, the reality assiged RAM resource is: mj mvi r (7) the reality assiged badwidth resource is: bj r (8) bbi Therefore, the optimizatio model is: Obtai the best solutio of S ad meet the costraits: cj c j, mj m j, bj b j (9) 3.2. The desig of EDAs EDAs is a ovel evolutioal algorithm i recet years [21]. The mai idea of evolutioal algorithm 105

5 is that fid out the object fuctio extreme value by iteratig people. The object fuctio is formula 5 i this paper ad the extreme value of S is the maximum value of S. People cosist of idividuals, a idividual correspod a solutio of object fuctio. Iteratio is geeratig ext people usig curret people accordig some rules. Differet evolutioal algorithms have differet rules. A whole EDAs evolutioal algorithm flow chart is show as figure 3. At first, geerate the people radomly, the calculate the fitess of idividuals, at last, geerate the ext geeratio based o the probability model, amely sample every code of every idividuals deped o this probability model. Therefore, that there are two key poits i EDAs algorithm: 1) the idividual code; 2) the probability model. We will itroduce these two poits separately The idividual code From the defiite 1 we kow that: the resource schedulig i cloud computig is to fid V ad L. For a give V ad L, firstly it s ecessary to judge whether the V meet the costraits i optimizatio model, the obtai the resource service ratio S by solutio accordig with formula 5. Solvig Costraied optimizatio problems (COPs) has become a importat research area of evolutioary computatio i recet years [22]. This paper uses the followig rule to give the correspodig V: Rule 1. For a give L, the assigmet method of cpu resource is: if cpj cti r, the c vi = c ti ; if pj c c r, the ti cti cvi mi{ cti, cpj, at this time if c pj cvi r, the sort the c r ti tasks accordig to the size of tasks, assig the remaider resource to the smaller tasks. Similarly, the memory resource ad badwidth resource allocatio ca use the same rule to allocatio. Begi Radomly Geerate P idividuals Meet Ls or L? Calculates idividuals fitess Costruct probability model based o statistic method Geerate ext geeratio based o probability model Figure 3. The flow chart of EDA algorithm Usig this rule to assig resource, although the value of S will be affected, the complex degree of algorithm is reduced. The costraits are assured by the rule with less calculatio. O the situatio of usig resource assigmet rule, the schedulig of virtual resource is chaged to fid a mappig L. Therefore, for a give cloud computig system, we idetify each physical ode, there is a ID correspodig with each physical device. Set the ID set is D, the for a task set T, there is a code L = { l i l i D correspodig with it. For example, set T = m, m = 8, the L = {1,3,1,5,9,3,5,7 Ed 106

6 is a mappig of T, which represets that the first task is assiged to physical ode 1, the secod task is assiged to physical ode 3, ad so o The probability model The mai idea of this model i this paper is from Uivariate Margial Distributio Algorithm (UMDA) [21], amely select some best idividuals, the usig those idividuals to costruct probability model. Set P is the umber of idividuals i people, Sp is the selectio possibility, amely how much idividuals should be selected from the people. Therefore the probability model is: S l l l i N S j( Xi xi Dl ) j1 p '( x) p'( x D ) p '( x ) N where, is the umber of object fuctios, as there is oly oe fitess fuctio i this paper, so =1; N P* Sp (11) S 1 X i xi j( Xi xi Dl ) (12) 0 others s D l is the sub-people selected from l geeratio which icludes N idividuals. This paper itroduces a parameter Pm to the EDAs algorithm. The mai purpose of Pm is to avoid the gee with lower possibility beig weeded out too early. From the formula 10 we kow that if a gee does t appear i oce iteratio, the the appearace possibility of this gee i ext geeratio is 0. For avoidig this ureasoable situatio, we itroduce shared factor Pm i EDAs. As show i formula 13, if there is a gee does t appear i oce iteratio, the the appearace possibility of this gee i ext geeratio is Pm/m. pl( x) pm / m(1 pm)* pl '( x) (13) The algorithm of geeratig ext geeratio people is show as followig. Alg. 1 The algorithm of costructig probability model i EDAs cal_poss(selected sub-people D ){ s l for(i<1; i<; i++){ for(j<1; j<m;i++){ possibility_model(i,j)=calculate depedig o formula 10 ad 13; retur possibility_model; Alg. 2 The algorithm of geeratig ext geeratio people i EDAs Eda(People) { Sortig the idividuals accordig with the idividual fitess i people; Select the top Sp*P idividuals to costruct possibility_model = cal_poss( D ); s l D ; for(i=1;i<p;i++){ for(j=1; j<the legth of idividual; i++){ ext_people(i,j) = sample from the probability model; retur ext_people; s l (10) 107

7 The parameters ad their values are show i table 2. Table 2. The parameters, their meaig ad value i EDA Parameters meaig value L The most iteratio time 150 Ls uchaged iteratio umber of best idividual 70 P the umber of people 50 Sp ratio of chose 0.15 Pm miimal possibility shared by all services The experimet ad discussio 4.1. The eviromet of experimet For verifyig the result of algorithms without the iterferece of the oise, this paper uses the simulator to test. How to simulate a cloud computig? I practical, the schedulig result is affected by two poits: oe is the umber of tasks arrived at the same time; aother is ratio of required resource ad physical resource amed load ratio. If the umber of tasks arrived at the same time is large the schedulig will become more complex. Besides if the load ratio is large, it meas there are may tasks ca t be service. I view of those two poits, we give some fixed parameters to represet a existed cloud computig system at first, the we adjust the umber of arrived tasks ad the load ratio to simulate the differet sese of resource schedulig i cloud computig system. I the simulator, the geeratio scopes of physical resource are: CPU (0.5~1.5), RAM (500~1500), badwidth (1~9), the quatity of physical resource is 20. The geeratio of tasks is decided by two poits: oe is the umber of physical resource ad the umber of tasks; aother is the load ratio. So the geeratio method of tasks is show as formula 14. resource radom*( sum( p)* ratio / m)*2 (14) Where, resource is a attribute of the task, such as CPU. radom is a radom. sum(p) is the sum of physical resource correspodig with the attribute of the task, amelysum p = p ( attr). ratio is the ratio of the total required resource ad the total physical resource, m is the umber of tasks. For example, set we wat to radom geerate the CPU attribute of a tasks set. For a give task, set the radom is 0.6, sum(p) is 20.7, which is sum of all physical resource CPU value, the ratio is 0.9, the m is 40, those two parameters value are appoited by experimet, therefore, the CPU value of a task is The desig of other algorithms: 1) Max-mi algorithm Priciple: For a give task, retur the physical resource with the largest resource ratio as the schedulig solutio. The pseudo code is show as followig. Alg. 3 The pseudo code of Max-mi Solutio L Max_mi(t,p){ for (ti t) { for (pi p) { res=ti.cpu/pi.cpu + ti.ram/pi.ram + ti.badwidth/pi.badwidth; Record the largest res as the physical resource assiged to ti; L(i) = ti.serial; retur L; i 108

8 2) Static algorithm Priciple: Assig the task to the physical resource with same ID umber. If the task ID is lager tha the largest physical resource ID, the use the remaider of task ID divided the largest physical resource ID, amely the schedulig solutio is similarly with (1, 2, ). 3) Radom algorithm Priciple: Radomly assig the task to physical resource Experimet result ad discuss Solve a istace Table 3 shows the solutio of the table 1 usig differet algorithms. From the table we kow that the resource service ratio of EDA algorithm is better tha other three algorithms. Table 4 displays the total virtual resource assiged to the tasks set by differet algorithms. From the table 4 we kow that EDA ca maximize the efficiecy of physical resource. Table 3. The solutios of resource the istace i table 1 usig differet algorithms Alg. Solutio s s c s m s b EDA Max-mi Static Radom Table 4. The total virtual resource assiged to tasks set by differet algorithms Attribute EDA Max-mi Static Radom CPU RAM Badwidth Table 5. The cocrete assigmet of each physical device with differet algorithms No. EDA Max-mi Static Radom P set 1 (2.70, , 80.00) (2.50, , 80.00) (2.70, , 30.20) (3.00, , 80.00) (3.0, 1000, 80) 2 (2.00, , 10.40) (2.00, , 2.70) (1.50, , 20.00) (2.00, , 12.20) (2.0, 700, 20) 3 (1.00, , 20.00) (1.00, , 1.20) (1.00, , 2.50) (0.30, 20.00, 0.20) (1.0, 400, 20) 4 (1.00, , 2.50) (1.00, , 10.00) (1.00, , 1.20) (1.00, 80.00, 0.50) (1.0, 400, 10) Table 6. The cocrete assigmet of each task with differet algorithms No. EDA Max-mi Static Radom T set 1 (1.00, , 20.00) (1.00, , 14.55) (1.00, , 20.00) (0.81, , 14.41) (1.0, 200, 20) 2 (0.80, , 35.16) (0.80, , 29.09) (0.80, , 8.89) (0.65, , 28.83) (0.8, 500, 40) 3 (0.57, 80.00, 0.50) (1.05, 80.00, 0.50) (0.57, 80.00, 0.50) (1.00, 80.00, 0.50) (2.0,80, 0.5) 4 (0.30, 20.00, 0.20) (0.16, 20.00, 0.20) (0.20, 20.00, 0.20) (0.30, 20.00, 0.20) (0.3, 20, 0.2) 5 (0.40, 50.00, 0.20) (0.25, 50.00, 0.20) (0.40, 50.00, 0.20) (0.25, 41.18, 0.20) (0.4, 50, 0.2) 6 (0.70, , 43.96) (0.70, , 36.36) (0.70, , 11.11) (0.57, , 36.04) (0.7, 700, 50) 7 (0.43, , 2.00) (0.79, , 2.00) (0.43, , 2.00) (0.94, , 2.00) (1.5, 200, 2) 8 (1.20, , 0.88) (0.75, , 1.00) (0.80, , 1.00) (0.97, 96.77, 0.72) (1.2, 150, 1) 9 (1.30, , 10.00) (1.00, , 10.00) (1.30, , 10.00) (0.81, , 10.00) (1.3, 600, 10) Table 5 shows the cocrete assigmet of physical devices. For physical devices, the max value of assiged resource ca t be over the devices value. If the assiged resource is greater tha devices value, 109

9 the performace of devices will drop dow. From the table 5, all algorithms are t greater tha the devices value. Table 6 shows the cocrete value assiged to each task. Ideally, every task ca obtai the resource they eeds. However, it s hard to reach this goal for the costrait of physical devices. From the table we kow that EDA algorithm is better tha other algorithms due to it ca more fulfill the tasks. Figure 4. The chage of s with the iteratio time i oce solutio of EDA algorithm a. The chage of s c accordig to the umber of tasks b. The chage of s r accordig to the umber of tasks c. The chage of s b accordig to the umber of tasks d. The chage of s accordig to the umber of tasks Figure 5. The chage of object fuctio accordig to the umber of tasks Figure 4 displays oce iteratio process of EDA algorithm. The abscissa axis is iteratio time ad the vertical axis is the value of s, amely the resource service ratio. From the figure we kow that the iteratio time is 20. As the iteratio time icreasig, the average fitess of people icreases rapidly firstly, the icreases slowly with fluctuated. The best idividual fitess always fluctuates as the iteratio time icreasig ad obtais best value at 7 th iteratio time. The reaso is that the problem 110

10 scale is small (9^4), so the iteratio time is small ad the fitess of best idividual is little chaged Algorithm compariso o differet umber of tasks Figure 5 shows the variety of s value as the task set icludig differet umber of tasks. The s value is average value after ruig 25 times. I the experimet, the load ratio is 1.0, the physical resource is geerated radomly ad the task set is geerated depedig o the formula 14. It ca be observed that EDA is better tha other algorithms. Specially, EDA algorithm is obviously better tha other algorithms whe the tasks are small. If the load ratio is fixed, the total required resource is fixed for a give cloud system, therefore, the required resource of sigle task will be larger whe the umber of tasks is small. The schedulig will become more complex ad the advatage of EDA algorithm become more obvious o this situatio. From calculatio it ca be obtaied that the average resource service ratio s of EDA algorithm is 1.060, 1.039, times respectively of Max-mi algorithm, static algorithm ad radom algorithm. a. The chage of s c accordig to the load ratio b. The chage of s r accordig to the load ratio c. The chage of s b accordig to the load ratio d. The chage of s accordig to the load ratio Figure 6. The chage of object fuctio accordig to the load ratio Algorithm compariso o differet load ratio The, we will study the schedulig o differet load ratio. I this situatio, as the tasks umber is ofte more tha devices umber i reality, set m=20, =40. Figure 6 shows the average result of s after ruig 25 times whe the load ratio from 0.5 to 1.5. From the figure we ca see that s of EDA algorithm is 1 whe the load ratio is low, s desceds as the load ratio icreasig. The reaso is there are more tasks ca t be service as the load ratio icreasig. From the figure it also ca be cocluded that EDA algorithm is better tha other algorithms. Accordig the calculatio, the average s of EDA algorithm is better 1.065, 1.004, times tha Max-mi algorithm, static algorithm ad radom algorithm. 111

11 5. Coclusio This paper studies the resource schedulig algorithm i cloud computig, proposes a resource schedulig optimizatio model usig resource service as the object fuctio ad employs EDAs to solve this model. At first, a detail aalysis of resource schedulig o cloud computig eviromet is give, usig resource service replaces completio time to evaluate the schedulig result, models the resource schedulig based o this cocept; the, usig EDA algorithm to solve this problem; at last, a experimet is desiged to verify the feasible of this model. I experimet, a small istatiate is solved to verify the correctess of the model ad lear the solvig process i detail. Besides of those, compares with the Max-mi algorithm, static algorithm ad radom algorithm. The result shows: EDA algorithm is averagely better tha other algorithms at least ad at most whe the umber of tasks from 5 to 55 or the load ratio from 0.5 to Ackowledgmet This work was supported by the Fujia Key Laboratory of the Brai-like Itelliget Systems (Xiame Uiversity), P. R. Chia, the Natioal Natural Sciece Foudatio of Chia (Grat No , , ). 7. Referece [1] Rui Zhag, "A geetic local search algorithm based o isertio eighborhood for the job shop schedulig problem," Advaces i Iformatio Scieces ad Service Scieces, vol. 3, o. 5, pp , [2] Sog Cu-Li, Liu Xiao-Big, Wag Wei,Xi Bai, "A hybrid particle swarm optimizatio algorithm for job-shop schedulig problem," Iteratioal Joural of Advacemets i Computig Techology, vol. 3, o. 4, pp , [3] Zhag Rui, "A particle swarm optimizatio algorithm based o local perturbatios for the job shop schedulig problem," Iteratioal Joural of Advacemets i Computig Techology, vol. 3, o. 4, pp , [4] Jig Weipeg, Liu Yaqiu,Wu Qu, "Commuicatio-aware fault-tolerat schedulig strategy for precedece costraied tasks i heterogeeous distributed systems," Iteratioal Joural of Digital Cotet Techology ad its Applicatios, vol. 5, o. 6, pp , [5] Xu-Yi Re, Zheg-hua Qi, Ru-chua Wag,Xiao-dog Ma, "Rough set ad A* based tasks schedulig i gird eviromet," Iteratioal Joural of Digital Cotet Techology ad its Applicatios, vol. 4, o. 4, pp , [6] Dr.K.Vivekaada, D.Ramyachitra, B.Abu, "Artificial bee coloy algorithm for grid schedulig," Joural of Covergece Iformatio Techology, vol. 6, o. 7, pp , [7] Sog Kufag, Rua Shufe,Jiag Mighua, "A flexible grid task schedulig algorithm based o QoS similarity," Joural of Covergece Iformatio Techology, vol. 5, o. 7, pp , [8] Che Jia-wei, Zhag Yua-Biao,Wag Geg-Jia, "A ew algorithm for a fuzzy vehicle routig ad schedulig problem: Imperialist competitive algorithm," Joural of Covergece Iformatio Techology, vol. 6, o. 7, pp , [9] Wag Geg-jia, Zhag Yua-Biao,Che Jia-Wei, "A ovel algorithm to solve the vehicle routig problem with time widows: Imperialist competitive algorithm," Advaces i Iformatio Scieces ad Service Scieces, vol. 3, o. 5, pp , [10]Luis M. Vaquero, Luis Rodero-Merio, Jua Caceres, Maik Lider, "A break i the clouds: towards a cloud defiitio," ACM SIGCOMM Computer Commuicatio Review, vol. 39, o. 1, pp , [11]Armbrust Michael, Fox Armado, Griffith Rea, Joseph Athoy D., Katz Rady H., Kowiski Adrew, Lee Guho, Patterso David A., Rabki Ariel, Stoica Io, Zaharia Matei, "Above the clouds: A berkeley view of cloud computig," EECS Departmet, Uiversity of Califoria, Berkeley, Tech. Rep. UCB/EECS , [12] Erik Bryjolfsso, Paul Hofma, Joh Jorda, "Cloud Computig ad Electricity: Beyod the Utility Model," Commuicatios of the Acm, vol. 53, o. 5, pp ,

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