## 4 Verification of the Method
### Determining the Quality of Operations and Messages
Operation \(b_{1}\) is performed within 0.35 h (21 min) to 1.22 h (73 min), while the dispatchers supplement the data on average in \(\overline{x}_{b_{1}}=0.74\) h. The values of the standard deviation and the coefficient of variation indicate that the values of the feature are slightly different from the mean value. The average time to supplement the data in the system with a probability of 95% ranges from 0.72 h (43 min) to 0.76 h (46 min). For the results of the operation performance time \(b_{1}\), a histogram was drawn up (Figure 7), in which the interval was assumed to be 0.1 h, which resulted in 13 intervals. The dispatchers supplemented the data in the system 22 times in less than 0.5 h. The operation of supplementing the data in the system most often (51 times) took between 0.6 h (36 min) and 0.7 h (42 min) as well as 0.7 h and 0.8 h (48 min). The time to supplement the data in the system that took over 1 h was exceeded 18 times. The gamma distribution density function was also matched with the histogram. At the test significance level of \(\alpha=0.05\ \chi^{2}\), the statistical value was obtained, \(\chi^{2}=3.47\), and it does not exceed the critical value of the \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**The Operation of Supplementing the Data in the System**} \\ \hline Number of observations & 255 \\ \hline Mean (h) & 0.74 \\ \hline Confidence interval dg 95\% (h) & 0.72 \\ \hline Confidence interval gg 95\% (h) & 0.76 \\ \hline Min (h) & 0.35 \\ \hline Max (h) & 1.22 \\ \hline Standard deviation & 0.17 \\ \hline Coefficient of variation (\%) & 23.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Basic statistics on the time of the execution of operation \(b_{1}\). gamma distribution; for the 5 th degree of freedom, at the significance level of \(\alpha\) = 0.05, the value of the statistics is equal to \(\chi^{2}_{4,5}=11.07\). Based on this, it can be concluded that there are no grounds to reject the zero hypothesis that the data takes the character of a gamma distribution; therefore, the formula of the gamma distribution density function is:  
\[f\left(x\right)=\frac{1}{\Gamma(18.04)*0.04^{18.04}}\chi^{18.04-1}e^{-\frac{x }{0.04}}\;for\;x\;e<0,\infty) \tag{16}\]  
From the analysis of results (Figure 7) and observation of the time of operation \(b_{1}\) as performed by the dispatcher, it was established that 90% of all results were performed in a timely manner; therefore, the value of the 9 th decile was calculated, which amounted to 0.98 h (59 min). The values of the operation execution above this decile are treated as untimely performed operations. At the container terminal, operation \(b_{1}\), which took more than 0.98 h to complete, is an operation in which other disruptions were being clarified or other tasks were performed by the road dispatcher. On the basis of the adopted distribution, the probability of a delay of 0.98 h can be calculated, which is equal to:  
\[P(X\geq 0.98)=1-0.93=0.07 \tag{17}\]  
The probability of an occurrence of a delay in operation \(b_{1}\) for the value of 0.98 h is equal to 0.07. From the sample studied for operation \(b_{1}\), no case was noted in which there was a failure to perform this operation. The finding of the analysis of the results of operation \(b_{1}\) is also the fact that there is a high repeatability of results could be found. This is due to the fact that one person is responsible for supplementing these data in the system, the road dispatcher; other dispatchers do not provide these data. The probability of an occurrence of a delay in operation \(b_{2}\) for the value of 0.98 h is equal to 0.18. From the sample studied for operation \(b_{2}\), no case was noted in which there was a failure to perform this operation. The finding of the analysis of the results of operation \(b_{2}\) is also the fact that there is a high repeatability of results could be found.