## 4 Results  
### Study of the Influence of Intensity on the Phenomenon of Ship Delays  
During the research, a total of 56 observations lasting 12 h each were conducted. Delays occurred during 36 observations. Altogether, 64 delayed ships were observed with a total delay of 150.62 h.  
Most of the observed vessels were delayed in the time range of up to 2 h. A similar frequency of delay times persists in the 2 h to 8 h interval, while delays lasting longer are already much less frequent (Figure 4). The impact of traffic intensity on the occurrence of delays seems to be quite obvious. The more ships on the waterway, the greater the probability of correlations and limitations between them, which may eventually lead to delay, due to the necessity of keeping the ship in the roadstead or at the quay. In the next step of the work, the intensity was determined by the ratio of the number of ships passing the breakwater head in Swinoujscie (a designated track point) to the duration of observation (12 h). To determine if the delay may depend on intensity, a multiple linear regression analysis was conducted. To determine whether the experimental data set studied contained extremes, a Grubbs test for deviations was performed. The result of this test showed that there were no statistical reasons to reject any of the results. The influence of the traffic intensity on the occurrence of delays seems to be an obvious assumption. The more ships on the waterway, the greater the probability of dependencies and constraints between them, which may eventually lead to the need to stop a ship at an anchorage/roadstead or berth. The traffic intensity analysis included all 56 observations. For each observation, the traffic intensity was compared with the time and number of delayed ships to determine whether there is a relationship between the intensity and the occurrence of delays. Figure 4: The histogram of ship delays. Intensity can be defined as the number of ships passing a designated point on the waterway (often a section understood as a perpendicular section at a specific point) in a specified period of time. The unit of intensity is the number of ships appearing in a unit of time (minute, hour, day). The characteristic feature of traffic intensity is its daily, weekend, and seasonal fluctuations [37]. The hourly intensity can be calculated by dividing the number of ships in a given port by the number of days in a year (365). For research purposes, the traffic intensity was calculated using the equation [32]:  
\[\mathrm{q}=\frac{n}{t} \tag{2}\]  
where:  
\(n\)--number of ships;  
\(t\)--time (hours)  
The aim of this procedure was to establish the average annual intensity of ship traffic calling at the surveyed ports. This intensity is a significant factor in the analysis and research of the flow of ship traffic in the surveyed waterway. After analysing the statistical data on the number of ships and calculating the daily intensities for each investigated year, no significant changes in intensity trends were observed on the Swinoujscie-Szczecin waterway (Table 1). The intensity for the port of Szczecin fluctuates in the range of 0.30-0.36 ships per day and for Police it is 0.03-0.04 ships per day. The statistical data from the last decade show insignificant changes in the intensity of vessel traffic on the investigated waterway. By dividing the number of delayed ships by the duration of the observation period (12 h), the traffic intensity on the waterway was obtained for all 56 observations. To analyse the relationship between the delay phenomenon and traffic intensity, the intensities from 20 observations during which no ship was delayed (Table 2) were compared with the intensities from 36 observations during which ships were delayed (Table 3). This procedure allowed for obtaining a clear correlation diagram between the intensity and delays of ships (Figure 5).