## 4 Results
### Study of the Influence of Intensity on the Phenomenon of Ship Delays
An intriguing discovery during the analysis of intensity was the observation that the largest total delay of ships did not occur at the highest intensities of traffic, but at an intensity of 0.42 ships/h, which was an unexpected result (Figure 5). As mentioned earlier, delays occurred in 36 of the observations. The average traffic intensity during this time was 0.59 ships/h (Table 3). During 20 observations (without delay), the average traffic intensity was 0.47 ships/h (Table 2). Results show that 1.75 ships were delayed during each observation and the average delay time was 4.2 h (Table 3). By analysing the average traffic intensity during observations with delays (0.59 ships/h) and without delays (0.47 ships/h), it can be deduced that ships experienced delays at higher traffic intensities. In conclusion, based on the results obtained, there is a correlation between traffic intensity and ship delays (Figure 4). \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Date of Observation**} & **Traffic Intensity** & **No of Delayed Ships for Given** & **Total Delay** \\  & **(Ship/h)** & **Intensity (Ship)** & **(h)** \\ \hline  
*Average intensity** & **0.47** & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Intensity for observations without delay. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Date of Observation**} & **Traffic Intensity** & **No of Delayed Ships** & **Total Delay** \\  & **(Ship/h)** & **for Given Intensity (Ship)** & **(h)** \\ \hline
2 April 2021 & 0.83 & 2 & 6.48 \\
3 April 2021 & 0.92 & 4 & 12.83 \\
7 April 2021 & 0.83 & 3 & 7.68 \\
8 April 2021 & 0.58 & 1 & 0.73 \\
9 April 2021 (night shift) & 0.50 & 2 & 3.52 \\
9 April 2021 (day shift) & 0.33 & 1 & 0.58 \\
10 April 2021 & 0.58 & 2 & 7.67 \\
11 April 2021 & 0.83 & 1 & 1.00 \\
12 April 2021 & 0.83 & 2 & 7.58 \\
13 April 2021 & 0.42 & 2 & 7.42 \\
20 April 2021 & 0.58 & 2 & 3.85 \\
21 April 2021 & 0.58 & 3 & 5.95 \\
22 April 2021 & 0.50 & 2 & 2.63 \\
23 April 2021 & 0.92 & 5 & 7.07 \\
29 April 2021 & 0.58 & 1 & 1.25 \\
4 May 2021 & 0.25 & 1 & 1.73 \\
9 May 2021 & 0.42 & 1 & 4.17 \\
10 May 2021 & 0.42 & 1 & 0.95 \\
11 May 2021 (night shift) & 0.42 & 2 & 4.92 \\
11 May 2021 (day shift) & 0.67 & 2 & 2.58 \\
13 May 2021 & 0.58 & 6 & 12.78 \\
14 May 2021 & 0.92 & 1 & 3.08 \\
15 May 2021 & 0.42 & 1 & 0.50 \\
16 May 2021 & 0.67 & 1 & 0.70 \\
17 May 2021 & 0.50 & 1 & 0.27 \\
21 May 2021 & 1.00 & 1 & 0.53 \\
23 May 2021 & 0.42 & 2 & 1.42 \\
27 May 2021 & 0.33 & 1 & 5.09 \\
27 May 2021 & 0.42 & 1 & 10.05 \\
31 May 2021 & 0.50 & 1 & 0.67 \\
9 June 2021 (night shift) & 0.17 & 1 & 2.92 \\
9 June 2021 (day shift) & 0.67 & 2 & 1.52 \\
18 June 2021 & 1.00 & 1 & 4.00 \\
20 June 2021 & 0.42 & 1 & 2.50 \\
23 June 2022 & 0.50 & 2 & 4.50 \\
24 June 2021 & 0.50 & 1 & 9.50 \\
**Average intensity** & **0.59** & **1.75 (ship/observation)** & **4.20 (h/observation)** \\  & **Total** & **64** & **150.62** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Total ships delay and number for a given intensity. To clarify the impact of intensity variability on the phenomenon of ship delays, a linear regression of summary ship delays as a function of intensity was conducted (Figure 5). The result of the regression analysis showed that the calculated model based on ship flow intensity (I1) explains 44% of the variance in total ships' (S) delays (Figure 6). It can be assumed that 56% of the variance depends on other than intensity factors. Observations with average traffic intensities (0.42-0.67) were analysed to explain the highest number of delays generated in this range. The conclusion that arises is that not only the number of vessels navigating the waterway, but also their parameters and the correlation between them affects the increase in the occurrence of vessel delays. Figure 5: Delay dependence on intensity.