## 5 Simulation and Results Analysis  
CloudSim 3.0 [35] is chosen as the simulation toolkit for cloud computing, which is easily used to test and verify the feasibility and stability of the proposed load balancing approach. Windows XP (professional, Microsoft, Los Angeles, CA, US, 2010) OS with 2.53 Ghz CPU, 2 GB of memory, JDK (7.0, Sun Microsystems, Palo Alto, CA, US, 2009) and Ant (1.8.4, Apache Software Foundation, Forest Hill, MD, US, 2011) are employed to run the simulations. First of all, we test different combinations of the parameters in order to find out the optimal parameters setting. Generally, the CPU has the highest importance in hardware resources [14,16], so we set \(\psi_{\text{i}}:\psi_{\text{j}}:\psi_{\text{j}}:\psi_{\text{4}}:\psi_{\text{s}}= 12:7:7:7:7\). As [34], the coefficient of evaporation for slave node is set \(\rho=0.5\) while the coefficient of evaporation for backward ant is set \(\pi=0.5\). We arrange 10,000 slave nodes in the cloud platform and each node is set with different processing capabilities randomly. The pheromone initialization of each node is calculated after randomly setting slave nodes. Each iteration is regarded as a unit time in our experiment. In a unit time, a new job with 10,000 tasks is distributed to 10,000 slave nodes at random. Each task can be finished within [1,3] unit time. All ants can only move one edge from one slave node to the other and the pheromone update is carried out once in a unit time. During the process, 50 slave nodes that the task number is bigger than nine are selected as overload nodes and 50 slave nodes that the task number is smaller than two are selected as underload nodes at random. If there are not enough slave nodes that can satisfy such conditions, the actual number of overload nodes and underload nodes are chosen. The forward ants are generated from both the overload nodes and underload nodes in order to accelerate searching process. The load balancing is performed when reaching the maximum searching step. The maximum search step stands for the maximum distance the ant can reach within one unit time. After load balancing operations, the cloud platform goes into the next unit time and a new job with 10,000 tasks comes. Table 1 gives the experimental results for the number of iterations (Num) and the convergence time (CT) with diverse parameters when reaching load balancing state. For each group of parameters, we carry out the simulation 20 times and the results of Num and CT are the average values. It can be seen from Table 1 that the result in row 6 has the minimum number of iterations and convergence time to achieve load balancing, which means the presented approach can reach an optimal state by these parameter settings. Thus, this group of parameter settings are used for the following simulations. Since the number of ants has an impact on the results, we perform the study by using different number of ants with 50 (Ant-50), 100 (Ant-100), and 200 (Ant-200) ants. The maximum searching step for each ant is set to 10. We adopt the degree of load balancing to describe the results, which stands for the balance level of the virtual machine in the cloud platform. The degree of load balancing is defined as:  
\[LB=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(Load_{{}_{i}}-Load_{{}_{avg}}\right)^ {2}} \tag{20}\]