# Analysis of the Macroscopic Behavior of Server Systems in the Internet Environment
## 4 Experiments and Evaluation  
### Setting of Experiments  
The proposed measure, the variance of the fluctuation of the OT of the server system, has the property of rapidly increasing before the system falls into a completely undesirable state, that is, before the degradation of the OT becomes apparent. In this Section, experiments are conducted to confirm that the proposed measure has the same behavioral characteristics as the analysis result described in Figure 5. We evaluate properties of the proposed measure by experiment using an actual server system, and verify its effectiveness as an observation measure of the server system. Figure 6 shows the configuration of the experimental system. In this experiment, we built a server system on the cloud computing virtualization platform VMware vSphere [4]. As a service running on the server system, we prepared a web application that dynamically generated web pages that cooperated with the database system. In the initial state, the server system was composed of a single VM (CPU: 1.795 GHz 4 core, memory: 4.0 GB), and the scaling operation was performed as necessary  
Figure 5: Image of the system’s behavior with respect to input transaction data. As a scaling technique, we used horizontal scaling, which connected replicated VMs in parallel via a load balancer. HTTP requests to this web service were distributed to VMs via the load balancer. The allocation of requests was performed based on the weighted round robin that corresponded to the number of CPU cores of VMs so that the load of each VM was equalized. To observe the temporal transition of the variance of the fluctuation of the activity factor of the server system based on the method formulated in Section 3, we used Apache Bench [30] as an observation tool of the operational status of the server system. Apache Bench is a standard and simple HTTP load generator. We prepared scripts to control the load generator under practical scenarios. The processing load on the server system was controlled by the number of HTTP requests per unit time arriving at the server system. To imitate realistic workloads, the number of HTTP requests was randomly determined and shifted based on the average value specified in experimental scenarios. The activity factor of the server system was observed by the transfer rate that indicated the number of requests processed per unit time. These observations were values that could be acquired by Apache Bench. Then, based on the following procedure, variance \(var(t)\) of the fluctuation of the transfer rate at time \(t\) was calculated every interval \(\Delta T\) seconds. Procedure for calculating the variance of the fluctuation of the activity factor at time \(t\). 1. Calculate fluctuation \(fluc(t)\) of the transfer rate at time \(t\) and obtain the smoothed value \(fluc^{\prime}(t)\):  
\[fluc(t)=v_{t}-\frac{1}{L}\sum_{i=0}^{L-1}v_{t-i}\]  
\[fluc^{\prime}(t)=\frac{1}{M}\sum_{i=0}^{M-1}fluc(t-i).\]  
2. Variance \(var(t)\) of the fluctuation of the transfer rate at time \(t\) is calculated by  
\[var(t)=\frac{1}{N}\sum_{i=0}^{N-1}\left(fluc^{\prime}(t-i)\right)^{2}-\left( \frac{1}{N}\sum_{i=0}^{N-1}fluc^{\prime}(t-i)\right)^{2}.\]  
Figure 6: Configuration of the experimental environment. In this experiment, we set \(\Delta T=1\) for the measurement interval, \(L=10\), \(M=10\) for the moving average data point, and \(N=10\) for the number of data points for the calculation of the variance. To verify the working hypothesis described in the previous section, three experiments were conducted. In order to understand essential features of the proposed measure, the experiments had been done under the following three conditions, i.e., \(x_{0}<x_{p}\), \(x_{0}=x_{p}\) and \(x_{0}>x_{p}\), in the experiments, respectively:  
**Experiment 1. **_For comparison with the results of Experiments 2 and 3, to be shown later, the transfer rate in the normal state of the server system was measured and the variance of the fluctuation was calculated.