**10. Improvment in time consumed by algorithm of RGSGCS and MSA**

According to the table 3, two genes exchanged in single exchange mutation has shown good performance in both algorithms RGSGCS and MSA. Moreover, the times taken by both algorithms RGSGCS and MSA are still big, and it is useful to get reasonable results along with less time consumed by algorithms RGSGCS and MSA. One way to do this is to assign

(a) Makespan values of MSA, Min-Min and RGSGCS (b) *LBF* values of MSA, Min-Min and RGSGCS

(c) Utilization of Resource of MSA, Min-Min and RGSGCS

Fig. 10. Simulation Results of Random model

probability of crossover, probability of mutation, ppopulation size and maximum generations number to the values 1 , 1, 50 and 1000, respectively in the experiments in table 3. Table 4 dispays new values of solution for both algorithms MSA and RGSGCS. This table provides the results of MSA algorithm for two different termination criterions, namely *T < e*−<sup>300</sup> for MSA(1) and *T < e*−<sup>50</sup> for MSA(2). Note that, in tables 3, 4, *MR* denotes reduction in makespan, which is difference between makespan values for both algorithms RGSGCS and MSA. Two experiments 9 and 10 are added to ensure scalability of both algorithms MSA and RGSGCS.

#### **11. ETC model**

14 Will-be-set-by-IN-TECH

RGSGCS algorithm Parameters Crossover Rate 0.8 Mutation Rate 0.1 Population Size for experiment 1 20 Population Size for experiment 2 80 Population Size for experiment 3 150 Population Size for experiment 4 250 Maximum Generations for experiments from 1 up to 3 1000 Population Size for experiments from 5 up to 8 TasksNo. Maximum Generations for experiments from 4 up to 8 1500

Stopping Criterion for experiments 1 and 2 *M* ∗ *N*\*100 Stopping Criterion for experiment 3 *M* ∗ *N*\*20 Stopping Criterion for experiment 4 *M* ∗ *N*\*10 Stopping Criterion for experiments 5 up to 8 *M* ∗ *N*\*5 Initial Temperature 1000 Cooling rate 0.99

MSA algorithm has reduction in makespan value equals to eighteen (18) when it is compared with algorithm Min-Min and equals to three (3) when it is compared with algorithm RGSGCS. Moreover, *LBF* values of algorithms MSA, Min-Min and RGSGCS are in ranges [0–1.53],

From results discussed above, it can be concluded that MSA algorithm dynamically optimizes

Note that the MSA algorithm outperforms RGSGCS algorithm within very less time to run the algorithm. Depending on SA algorithm and random-MCT heuristic, MSA algorithm is powerful when it is compared with RGSGCS algorithm, while RGSGCS algorithm has less

The results of the comparison among algorithms RGSGCS , Min-Min and MSA in each experiment in the table 3, prove that MSA algorithm provides an effective way to enhance the search performance, because it obtains an optimal schedule within a short time along with

Notably, the solutions of MSA algorithm are high quality and can be used for realistic scheduling in grid environment. The simulation results are consistent with the performance analysis in section 8, which clarifies that the improvement to the evolutionary process is

According to the table 3, two genes exchanged in single exchange mutation has shown good performance in both algorithms RGSGCS and MSA. Moreover, the times taken by both algorithms RGSGCS and MSA are still big, and it is useful to get reasonable results along with less time consumed by algorithms RGSGCS and MSA. One way to do this is to assign

**10. Improvment in time consumed by algorithm of RGSGCS and MSA**

MSA algorithm

Table 2. Parameters used in RGSGCS/MSA

output schedule closer to global optimal solution.

[6.4–29.56] and [0–8.12] respectively.

convergence to the optimal solution.

high resource utilization.

reasonable and effective.

The Expected Time to Compute (ETC) model is another model can also test performance of MSA algorithm. Interestingly, ETC matrix model allows to capture important characteristics of task scheduling. For example, ETC model introduces possible inconsistencies among tasks and resources in grid system by assigning a large value to *ETC*(*t*, *m*) to indicate that task *t* is incompatible with resource *m*.

Moreover, ETC matrix considers three factors: task heterogeneity, resource heterogeneity and consistency. The task heterogeneity depends upon the various execution times of the

Algo. *Makespan* Time *LBF MR Utilization*

Task Scheduling in Grid Environment Using Simulated Annealing and Genetic Algorithm 105

MSA(1)/MSA(2) 46/46.5 5.49/0.964 0/1.45 100/98.57 RGSGCS 46 5.84 0 0/0.5 100

MSA(1)/MSA(2) 94/94 7.277/1.31 0.34/0.32 99.63/99.68 RGSGCS 94 10.28 0.33 0/0 99.67

MSA(1)/MSA(2) 135.5/135.5 9.33/1.64 0.05/04 99.95/99.96 RGSGCS 136 16.39 0.38 0.5/0.5 99.63

MSA(1)/MSA(2) 61.5/64 31.66/5.587 2.66/6.37 97.79/94.01 RGSGCS 65 42.46 7.7 3.5/1 92.285

MSA(1)/MSA(2) 123.33/126 57.92/10.167 0.97/2.76 99.04/97.31 RGSGCS 127.75 76.01 2.42 4.42/1.75 95.46

MSA(1)/MSA(2) 188/192.5 84.02/14.78 0.66/2.86 99.34/97.22 RGSGCS 190.62 107.44 3.12 2.62/-1.88 97.89

MSA(1)/MSA(2) 255/261 109.9/19.23 0.69/2.86 99.32/97.22 RGSGCS 259 139.41 5.83 4/-2 97.52

MSA(1)/MSA(2) 316/319 136.23/23.876 0.4/1.3 99.6/98.69 RGSGCS 318 170.81 1.13 2/-1 98.88

MSA(1)/MSA(2) 629/635 268.23/46.94 0.37/1.1 99.63/98.9 RGSGCS 630 329.36 0.63 1/-5 99.38

MSA(1)/MSA(2) 948/953 402.8/70.62 0.47/0.84 99.53/99.17 RGSGCS 947.33 488.68 0.48 -0.67/-5.67 99.52

Table 4. Simulation Results of MSA and RGSGCS with probability of crossover, probability of mutation, population size and maximum generations number equal to 1 , 1, 50 and 1000,

instances depend upon the above three factors as task heterogeneity, resource heterogeneity

(a) c - consistent. An ETC matrix is said to be consistent if a resource *Ri* execute a task Ti

(b) s - semi consistent. A semiconsistent ETC matrix is an inconsistent matrix which has a

(c) i - inconsistent. An ETC matrix is said to be inconsistent if a resource Ri executes some

faster than the resource *Rk* and *Ri* executes all other tasks faster than *Rk*.

and consistency. Instances are labeled as u-x-yyzz where: 1. u - is a uniform distribution, used to generate the matrix.

respectively.

2. x - is a type of consistency.

sub matrix of a predefined size.

tasks faster than Rj and some slower.

experiment 1 (13 tasks,3 resources)

experiment 2 (50 tasks,10 resources)

experiment 3 (100 tasks, 10 resources)

experiment 4 (200 tasks, 50 resources)

experiment 5 (400 tasks, 50 resources)

experiment 6 (600 tasks, 50 resources)

experiment 7 (800 tasks, 50 resources)

experiment 8 (1000 tasks, 50 resources)

experiment 9 (2000 tasks, 50 resources)

experiment 10 (3000 tasks, 50 resources)


Table 3. Simulation Results of MSA, Min-Min and RGSGCS with probability of crossover, probability of mutation, population size and maximum generations number values taken from table 2.

tasks. The two possible values are defined high and low. Similarly the resource heterogeneity depends on the running time of a particular task across all the resources and again has two values: high and low.

In the real scheduling, three different ETC consistencies are possible. They are consistent, inconsistent and semi-consistent. The instances of benchmark problems are classified into twelve (12) different types of ETC matrices, they are generated from model of Braun (Braun et al., 2001). Each type is obtained by calculating the average value of makespan of ten runs of each algorithm except Min-Min algorithm which it runs just once by default. The


Table 4. Simulation Results of MSA and RGSGCS with probability of crossover, probability of mutation, population size and maximum generations number equal to 1 , 1, 50 and 1000, respectively.

instances depend upon the above three factors as task heterogeneity, resource heterogeneity and consistency. Instances are labeled as u-x-yyzz where:


16 Will-be-set-by-IN-TECH

Algo. *Makespan* Time *LBF MR Utilization*

MSA 46 0.43 0 100 Min-Min 56 0.012 29.56 10 77.18 RGSGCS 46 18.38 0 0 100

MSA 94 5.78 0.317 99.68 Min-Min 112 0.072 27.35 18 78.5 RGSGCS 94.33 64.44 0.81 0.33 99.196

MSA 135.5 4.5 0.063 99.94 Min-Min 149.5 0.077 10.35 14 90.62 RGSGCS 136.5 142.1 0.75 1 99.25

MSA 61.14 41.12 1.53 98.49 Min-Min 72.5 0.36 27.87 11.36 78.2 RGSGCS 64 395 8.12 2.86 92.49

MSA 123.33 67.86 0.823 99.18 Min-Min 137.2 2.92 14.62 13.87 87.24 RGSGCS 125.75 1021 3.32 2.42 96.78

MSA 187.5 142.58 0.452 99.55 Min-Min 201 8.92 8.98 13.5 91.76 RGSGCS 190.5 1575 2.54 3 97.52

MSA 253.167 248.7 0.235 99.76 Min-Min 267.37 21.66 7.6 14.203 92.94 RGSGCS 255 2826 1.33 1.833 98.69

MSA 315 380.14 0.108 99.89 Min-Min 329.5 41.46 6.4 14.5 93.98 RGSGCS 317.6 4928 1.19 2.6 98.82

Table 3. Simulation Results of MSA, Min-Min and RGSGCS with probability of crossover, probability of mutation, population size and maximum generations number values taken

tasks. The two possible values are defined high and low. Similarly the resource heterogeneity depends on the running time of a particular task across all the resources and again has two

In the real scheduling, three different ETC consistencies are possible. They are consistent, inconsistent and semi-consistent. The instances of benchmark problems are classified into twelve (12) different types of ETC matrices, they are generated from model of Braun (Braun et al., 2001). Each type is obtained by calculating the average value of makespan of ten runs of each algorithm except Min-Min algorithm which it runs just once by default. The

from table 2.

values: high and low.

experiment 1 (13 tasks,3 resources)

experiment 2 (50 tasks,10 resources)

experiment 3 (100 tasks, 10 resources)

experiment 4 (200 tasks, 50 resources)

experiment 5 (400 tasks, 50 resources)

experiment 6 (600 tasks, 50 resources)

experiment 7 (800 tasks, 50 resources)

experiment 8 (1000 tasks, 50 resources)


Furthermore, the resource utilization value in range [0.9975-0.9999], and *LBF* value in range [0.0025-0.000085]. From the analysis of time complexity of RGSGCS algorithm in the table 1, ETC matrix / Algo. Min-Min MSA-ETC GANoX PRRWSGA *u* − *c* − *hihi* 1462108.59 1407383.05 1408816.72 1423161.96 *u* − *i* − *hihi* 534521.65 517909.73 518207.61 522950.76 *u* − *s* − *hihi* 1337720.25 1295674.81 1297192.19 1311406.26 *u* − *c* − *hilo* 114600.52 110549.32 110774.58 110661.56 *u* − *i* − *hilo* 250758.61 243168.05 243295.24 244844.35 *u* − *s* − *hilo* 83094.47 80568.32 80680.07 81423.61 *u* − *c* − *lolo* 47104.35 45800.13 45822.55 46398.43 *u* − *i* − *lolo* 8659.29 8422.85 8430.91 8483.34 *u* − *s* − *lolo* 23337.57 22546.96 22561.49 22841.92 *u* − *c* − *lohi* 51556.38 49786.42 49907.59 50254.31 *u* − *i* − *lohi* 452016.81 438583.36 438728.74 443424.34 *u* − *s* − *lohi* 445906.75 431898.36 432666.09 437031.44 *LBF* 0.5379-0.0385 0.0025-0.000085 0.03-0.0008 0.14-0.002 *ResourceUtilization* 0.8365-0.963 0.9975-0.9999 0.971-0.999 0.876-0.99

Task Scheduling in Grid Environment Using Simulated Annealing and Genetic Algorithm 107

Table 5. Simulation Results of ETC Model of Min-Min, MSA-ETC, GANoX, and PRRWSGA the time complexity of GANoX algorithm and PRRWSGA algorithm is O(*Q*.*PS*.*M*.*N*), and for

As a result, MSA-ETC has less time complexity when it is compared with both algorithms GANoX and PRRWSGA. In the study, the algorithm is designed and compared to different

The proposed MSA-ETC algorithm can consistently find better schedules for several

This chapter studies problem of minimizing makespan in grid environment. The MSA algorithm introduces a high throughput computing scheduling algorithm. Moreover, it provides solutions for allocation of independent tasks to grid computing resources, and speeds up convergence. As a result load balancing for MSA algorithm is higher than RGSGCS algorithm, and the gain of MSA algorithm in average time consumed by an algorithm is higher than RGSGCS algorithm for both RM and ETC models, which makes MSA algorithm very

The initialization of MSA algorithm plays important role to find a good solution and to reduce

Furthermore, the improvments on the performance of MSA algorithm, and RGSGCS, give another salient feature, which reduces the time consumed by algorithm to the low reasonable

Regarding MSA algorithm for ETC Model, MSA algorithm has superior performance among

other algorithms along with resource utilization and load balancing factor values.

grid environments. Using MSA-ETC it can get good workload balancing results.

benchmark problems as compared to other techniques in the literature.

high QoS and more preferable for realistic scheduling in grid environment.

MSA-ETC algorithm is O(*Q*.*M*.*N*).

the time consumed by algorithm.

**12. Conclusion**

level.


All the instances consist of 512 tasks and 16 resources. This Model is studied for the following algorithms:


Maximum Generation is 1000 and Population Size is 50 for both algorithms GANoX and PRRWSGA. It can be seen from figures 11 (a), (b) and (c), and table 5, that MSA-ETC has superior performance on all remaining algorithms, namely, Min-Min, GANoX, and PRRWSGA, in terms of *LBF*, *Makespan*, *ResourceUtilization*, and time taken by the algorithm. Saving in average time is about 90%, except when it is compared with Min-Min.

(a) Makespan values of ETC model (sec.)

(b) LBF values of ETC model

(c) Resource Utilization values of ETC model

Fig. 11. Simulation Results of ETC model


Furthermore, the resource utilization value in range [0.9975-0.9999], and *LBF* value in range [0.0025-0.000085]. From the analysis of time complexity of RGSGCS algorithm in the table 1,

Table 5. Simulation Results of ETC Model of Min-Min, MSA-ETC, GANoX, and PRRWSGA

the time complexity of GANoX algorithm and PRRWSGA algorithm is O(*Q*.*PS*.*M*.*N*), and for MSA-ETC algorithm is O(*Q*.*M*.*N*).

As a result, MSA-ETC has less time complexity when it is compared with both algorithms GANoX and PRRWSGA. In the study, the algorithm is designed and compared to different grid environments. Using MSA-ETC it can get good workload balancing results.

The proposed MSA-ETC algorithm can consistently find better schedules for several benchmark problems as compared to other techniques in the literature.
