**9. Simulation results Of RGSGCS and MSA**

The simulation results of algorithms RGSGCS, MSA and Min-Min of RM are shown in table 3 for eight different experiments. The reason of testing experimenting is to explore the dynamic behavior of grid environment. For the experiment 1, workloads of tasks are (6, 12, 16, 20, 24, 28, 30, 36, 40, 42, 48, 52, 60) cycles, and the computing capacities of resources are (4, 3, 2) Cycle Per Unit Time(CPUT). The computing capacities of resources, experiments 2 to 8 in the table 3, diverse randomly from 2 to 8 CPUT for each resource. Furthrmore, the workload of tasks ranges randomly from 10 to 150 cycles. The parameters of MSA and RGSGCS are listed in table 2. MSA, Min-Min and RGSGCS are simulated using MATLAB. In table 3, the values of makespan, average time and *LBF* for both algorithms RGSGCS and MSA are compiled together for purpose of comparison. Table 3 and figures( 10 (a), (b) and (c) ) lay out that:

The average gains in time of MSA expressed as percentages are 97.66%, 91.03%, 96.83%, 89.6%, 93.35%, 90.95%, 92% and 92.29% for experiments 1 upto 8 respectively. Hence the total average gain in time for all the experiments is 92.964%.

<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>0</sup>

Expt.No.

<sup>0</sup> <sup>100</sup> <sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>700</sup> <sup>800</sup> <sup>900</sup> <sup>1000</sup> <sup>0</sup>

Min−Min MSA RGSGCS

TasksNo

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

MSA RGSGCS Min−Min

<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>0</sup>

Expt.No.

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

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

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

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

Load Balancing Factor (LBF)

Task Scheduling in Grid Environment Using Simulated Annealing and Genetic Algorithm 103

(a) Makespan values of MSA, Min-Min and

and RGSGCS

Fig. 10. Simulation Results of Random model

Average Utilization of Resource

RGSGCS

RGSGCS.

**11. ETC model**

incompatible with resource *m*.

Makespan

MSA RGSGCS Min−Min


Table 2. Parameters used in RGSGCS/MSA

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

From results discussed above, it can be concluded that MSA algorithm dynamically optimizes output schedule closer to global optimal solution.

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 convergence to the optimal solution.

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 high resource utilization.

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 reasonable and effective.
