# A model of Virtual Resource Scheduling in Cloud Computing and Its

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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

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

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

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