# Analysis of the Macroscopic Behavior of Server Systems in the Internet Environment
## 4 Experiments and Evaluation
### Experiment 3  
In Experiment 3, the OT of the server system when recovering from the overloaded state to the normal state was measured and the variance of the fluctuation of the OT was calculated. Then, we verified the behavioral property of the variance of the fluctuation of the transfer rate when the load decreased and the server system recovered from the overloaded state to the normal state. According to the analysis result, it was expected that the variance of the fluctuation of the transfer rate would rapidly increase just before the server system returned to the normal state. In this experiment, the overloaded state was caused by gradually increasing the server load, and then the load was gradually decreased to restore it to the normal state again. Table 1 shows the setting of the temporal transition of the server load (the number of requests) in this experiment. The server load was an average of 13 requests per second at the start of the measurement, and thereafter every 300 s, the average number of requests per second was increased by two. Then, the number of requests was decreased from time 900 s, when it was assumed that the server system was in an overloaded state. Figure 8: Results of measurements of the changed test bed system (to the abnormal state); (**a**) Server load (requests per second); (**b**) transfer rate; (**c**) variance of the fluctuation of the transfer rate. Figure 9 shows the results of Experiment 3. Figure 9a shows the transition of the server load, Figure 9b shows the measured transfer rate, and Figure 9c shows the variance of the fluctuation of the transfer rate. As shown in Figure 9b, it can be confirmed that the server system catastrophically became overloaded in the period of 600-899 s because of the increase in server load. Then, as the load decreased, the server system began to recover in the period of 1200-1499 s, and after 1500 s, the normal state was restored. By contrast, it can be seen that the variance of the fluctuation of the transfer rate shown in Figure 9c increased in the period of 0-599 s. This phenomenon, by which the variance of the fluctuation of the transfer rate increased as a sign of the overload condition, is equal to the result of Experiment 2. In the period of 600-1199 s, while the server system was in the overloaded state, the variance of the fluctuation of the OT was in the vicinity of zero. It can be confirmed that the variance of the fluctuation increased again in the period of 1200-1499 s. After 1500 s, the variance of the fluctuation converged to almost zero as the server system recovered to the normal state. From these results, it was confirmed that the variance of the fluctuation of the transfer rate increased immediately before the server system returned from the overloaded state to the normal state. Therefore, we confirmed the behavioral property as suggested in the proposed method concerning the variance of the fluctuation of the server system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Time Period (s)** & **Number of Request (Re/s)** \\ \hline
0–299 & 13 \\
300–599 & 15 \\
600–899 & 17 \\
900–1199 & 15 \\
1200–1499 & 13 \\
1500–1799 & 11 \\
1800–2099 & 10 \\
2100–2699 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Setting of the processing load of the test bed system. Figure 9: _Cont._  
From the results of Experiments 1-3 using the experimental server system, it is confirmed that the proposed measure, that is, \"variance of the fluctuation of OT,\" has the same behavioral characteristics as the analysis result described in Section 3. In Experiment 1, it was confirmed that the variance of the fluctuation of the transfer rate took a value close to zero when the server system was in a normal state (\(x_{0}<x_{p}\)).