## 4 Results
### Experiment One: Test the Performance of the Proposed Model in Terms of Load Balancing  
Objective: To validate the benefits of implementing the proposed DR-tree model for grid computing networks; this experiment compares it with related load balancing algorithms discussed in [11]. The aim is to decrease the mean job response time and consequently increase the number of jobs/s.  
Observation: Figure 3 shows the load balance of the grid network at different arrival rates. The mean job response time for different random distributions, such as random (Rand-Dist), exponential (Exp-Dist), normal (Norm-Dist), uniform (Unif-Dist), and Poisson (Poiss-Dist) are calculated and, after many trials, it can be shown that the same results were obtained for all distributions. The results confirm that the mean job response time increases approximately in a linear way as the arrival rate increases. Figure 4 shows the comparison between the load balance of the proposed model and the traditional algorithm mentioned in [11]. The results from Figure 4 prove the superiority of the proposed model. The suggested model improves the mean job response time by decreasing it with a ratio of  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Node\_id** & **Q\_Size** & **Task Time (sec)** & **CPU Speed (GHz)** & **Memory Size (GB)** \\ \hline
1 & 90.73618432 & 453.0043176 & 67.84965223 & 84.77457651 \\
2 & 95.28959685 & 689.9301012 & 124.7546078 & 62.6737682 \\
3 & 56.34934081 & 254  
26% (gain) as compared to the traditional one. Additionally, it can be observed from the table that the different distributions of mean job response times do not affect the stability of the model.  
Figure 5 shows the improvement ratio of the suggested model as a function of the arrival rates. The suggested model improves the load balance by 98% from a configuration with an arrival rate of 400 jobs/s to a configuration with an arrival rate of 1690 jobs/s in the different distributions.  
Figure 4: Load balance estimation with the traditional algorithm.  
Figure 3: Load balance estimation.  
Discussion: One possible explanation of these results is that the load balancing achieved by the proposed model is asymptotically optimal because its saturation point intensity \(\approx 1\) is very close to the saturation level of the grid computing model [11]. Furthermore, the suggested model is more stable at different arrival rate distributions because of the utilized DR-tree properties that mainly depend on the reduction version of the tree. This reduction version of the grid network tree mainly improves the load balancing policy as compared to the alternative model in [11] that depend on the whole grid network tree. Moreover, within the suggested model, the information of any processing element joining or leaving the grid system is collected at the associated site manager which in turn transmits it to its parent local grid manager. This means that communication is needed only if a processing element joins or leaves its site. All of the collected information is used in balancing the system workload between the processing elements to efficiently utilize the whole system resources, aiming to minimize user job response time. This policy minimizes the communication overhead involved in capturing system information before making a load balancing decision that improves the system performance.