# Low-Cost Software Evaluation of Communication Delays in Networked Industrial Systems
## 6 Baseline Topology Evaluation  
### Baseline Characterization  
The \(\mathcal{T}_{base}\) topology can be characterized by using the Rtgen generator under experimental conditions similar to those described in Section 5. As before, test streams consist of \(m_{\omega}=10^{5}\) UDP packets per experiment, but the inter-packet interval has been increased to \(\omega=150\) \(\upmu\)s to accommodate larger values of \(l\) without overloading the links. Various Ethernet packet lengths have been used, from \(l=64\) B to 1472 B in 64 B steps. For each packet, we measured the difference \(u_{R}(t_{R})-u_{M}(t_{M})\). As explained in Section 4, this difference is the packet delay plus the fixed timestamp counter offsets \(c_{R}\) and \(-c_{M}\). The mean differences are plotted in Figure 4 as a function of \(l\) and the corresponding summary statistics are listed in Table 3, with a larger step size for conciseness. With \(c_{R}\) and \(c_{M}\) being unknown, the absolute values of the mean differences are of no particular significance--albeit their relationship with \(l\) definitely is. For this reason, they have not been shown in the table.  
For all values of \(l\) but two, the frequency distribution of \(u_{R}(t_{R})-u_{M}(t_{M})\) was found to be light-tailed, as also confirmed by the values of Pearson's kurtosis being less than 3, the kurtosis of a normal distribution. Actually, measurements only comprised two or three discrete values. Consistently with a measured range of 80 ns or 160 ns, these discrete values are exactly 80 ns apart. This corresponds to 8 bit times at 100 Mb/s and suggests that the only source of delay variability in the \(\mathcal{T}_{base}\) topology is due to byte-wide serialization/deserialization, which occurs at the MAC/PHY interface of the two Ethernet links used for communication. The skewness varied, suggesting that the frequency proportion  
\begin{table}
\begin{tabular}{r r r r r} \hline \hline \(l\) (B) & \(s_{\omega}\) (\(\upmu\)s) & Range (\(\upmu\)s) & Skewness & Kurtosis \\ \hline
64 & 0.032 & 0.160 & 1.043 & 4.777 \\
192 & 0.037 & 0.080 & \(-\)0.792 & 1.627 \\
320 & 0.033 & 0.160 & 1.352 & 3.004 \\
448 & 0.034 & 0.160 & 1.216 & 2.492 \\
576 & 0.035 & 0.080 & 1.052 & 2.107 \\
704 & 0.036 & 0.080 & 0.900 & 1.811 \\
832 & 0.037 & 0.080 & 0.763 & 1.582 \\
960 & 0.038 & 0.080 & 0.632 & 1.399 \\
1088 & 0.039 & 0.080 & 0.509 & 1.259 \\
1216 & 0.039 & 0.080 & 0.388 & 1.151 \\
1344 & 0.040 & 0.080 & 0.274 & 1.075 \\
1472 & 0.040 & 0.160 & 0.163 & 1.027 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary statistics of \(\mathcal{T}_{base}\) delay for varying \(l\), \(m_{\omega}=10^{5}\) nominal samples; \(\omega=150\) \(\upmu\)s.  
among discrete values may shift from one experiment to another, but it was found to still be compatible with the other summary statistics listed in Table 3. Among them, the most relevant one is \(s_{\omega}\), which affects the width of the confidence intervals that the measurement system can determine for DUT delay and variance.  
As shown in Figure 4, which contrasts experimental data with a linear interpolation, the mean delay increases linearly with \(l\), by \(160\,\mathrm{ns}\) for each additional byte in the packet. This is consistent with the physical setup of \(\mathcal{T}_{\text{base}}\) shown in the upper half of Figure 2, in which the store-and-forward switch \(SW\) receives and transmits each packet twice. Thus, each byte in the packet needs to be stored (and then forwarded) twice, which indeed takes exactly \(80+80=160\,\mathrm{ns}\). Furthermore, this result confirms that, as expected, \(SW\) does not introduce any additional, unexplained packet length-dependent delay.