**12. Conclusion**

18 Will-be-set-by-IN-TECH

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

1. GANoX algorithm is the same algorithm 2, but without using crossover operator. Single

2. PRRWSGA algorithm is the same algorithm 2, probability of crossover equals to 0.8,

3. MSA-ETC is the same algorithm 3. Initial chromosome can be taken as the best run of 1000 runs of the algorithm 1. Moreover, stopping criterion which is used equals to (*M* × *N* ×

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.

> 0.1 0.2 0.3 0.4 0.5 0.6 0.7

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>10</sup> <sup>11</sup> <sup>12</sup> <sup>0</sup>

Case.No.

(c) Resource Utilization values of ETC model

Load Balancing Factor

Min−Min PRRWSGA MSA GANoX

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>10</sup> <sup>11</sup> <sup>12</sup> <sup>0</sup>

Min−Min PRRWSGA MSA GANoX

Case.No.

(b) LBF values of ETC model

3. yy - is used to indicate the heterogeneity of the tasks(hi-high, lo-low). 4. zz - is used to indicate the heterogeneity of the resources (hi-high, lo-low).

exchange mutation is used at probability of mutation equals to one.

4. Min-Min algorithm is pointed out in section 7.

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>10</sup> <sup>11</sup> <sup>12</sup> <sup>0</sup>

Case.No.

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

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 11. Simulation Results of ETC model

Resource Utilization

5

10

Makespan

<sup>15</sup> x 105

probability of Mutation equals to 0.01, and full chromosome will be altered.

Min−Min PRRWSGA MSA GANoX

algorithms:

20);

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

The initialization of MSA algorithm plays important role to find a good solution and to reduce the time consumed by algorithm.

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 level.

Regarding MSA algorithm for ETC Model, MSA algorithm has superior performance among other algorithms along with resource utilization and load balancing factor values.

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Other benefits of MSA algorithm include robustness and scalability features. the disadvantage of MSA algorithm is that flowtime is higher more than Min-Min, RGSGCS, and GANoX.

It can be concluded that MSA algorithm is a powerful technique to solve problem of minimizing makespan in grid environment with less time to be consumed by the intended algorithm.
