# Influence of Model and Traffic Pattern on Determining the Self-Similarity in IP Networks
## 7 Comparison of Results
The SSDP protocol increased the empirical Hurst exponent as opposed to high traffic. Hurst values for \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Protocol** & **ARP** & **DNS** & **SSDP** & **IGMP** & **DHCP** & **HTTP** & **TCP** & **UDP** \\ \hline \multicolumn{8}{c}{High intensity of network traffic} \\ \hline R/S estmation & 0.45 & 0.59 & 0.38 & 0.42 & 0.52 & 0.57 & 0.77 & 0.85 \\ \hline R/S improved estmation & 0.41 & 0.70 & 0.32 & 0.15 & 0.27 & 0.76 & 0.88 & 0.99 \\ \hline Empirical exponent H & 0.45 & 0.63 & 0.29 & 0.12 & 0.71 & 0.66 & 0.85 & 1.03 \\ \hline Improved empirical H & 0.44 & 0.62 & 0.27 & 0.12 & 0.70 & 0.65 & 0.85 & 1.02 \\ \hline Theoretical exponent H & \multicolumn{8}{c}{0.54} \\ \hline \multicolumn{8}{c}{Low intensity of network traffic} \\ \hline R/S estmation & 0.40 & 0.51 & 0.39 & 0.41 & 0.49 & 0.55 & 0.50 & 0.69 \\ \hline R/S improved estmation & 0.34 & 0.53 & 0.32 & 0.13 & 0.28 & 0.72 & 0.48 & 0.72 \\ \hline Empirical exponent H & 0.35 & 0.62 & 0.33 & 0.11 & 0.47 & 0.70 & 0.50 & 0.80 \\ \hline Improved empirical H & 0.33 & 0.61 & 0.31 & 0.11 & 0.46 & 0.69 & 0.49 & 0.78 \\ \hline Theoretical exponent H & \multicolumn{8}{c}{0.54} \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Average Hurst coefficients for selected protocols for two types of network traffic. Figure 15: Detailed comparison of the value of the H exponent for the time window size 1024.  
the ARP, SSDP, and IGMP had values in the range of 0-0.5, which indicated antipersistent traffic and a low level of self-similarity. The DNS protocol adopted Hurst exponent in the range of 0.5-1, which confirmed the nature of the persistent movement. DHCP had similar properties for R/S estimation and improved R/S estimation for both types of traffic. The Hurst exponent for the empirical method increased for high network traffic intensity, while for low traffic, the value decreased. The HTTP protocol had a similar Hurst exponent to the DNS protocol, which indicated that these protocols are closely related. They are necessary for correctly opening websites and web address translation. For both types of traffic, the Hurst coefficient values were in the range of 0.5-1. Hurst exponent for TCP and UDP depends on the number of packets. These protocols represent the largest number of packages in comparison with all other protocols. For high-intensity traffic, the Hurst exponent for the improved R/S estimation was higher than for standard R/S estimation. The values of the empirical and improved Hurst exponents were similar. The values were in the range of 0.5-1, and even for the empirical exponent, they went above the value of 1. For low traffic, the TCP protocol reached values close to 0.5, which indicates the randomness of the traffic. The UDP protocol assumed values in the range of 0.5-1 and value characteristics similar to the UDP protocol with high traffic. It has been observed that the values of the Hurst exponent of the method of improved R/S estimation were lower than the usual R/S estimation for most protocols. The values of the corrected empirical Hurst exponent were not much smaller than the empirical values. This was due to the method of the calculated exponent and also to the data itself.