Statistical Model of Ship Delays on the Fairway in Terms of Restrictions Resulting from the Port Regulations: Case Study of Świnoujście-Szczecin Fairway

Abstract

The article describes a study of ship delays on the Świnoujście-Szczecin waterway observed by the VTS operator. The research has led to an understanding of the factors that affect delays of ships calling at the ports of Szczecin and Police, as well as the possibilities of predicting and preventing these delays. This article presents the results of the study on the traffic intensity on the investigated waterway and the process of identifying the port regulation that causes the most frequent delays. Based on the obtained results from the statistical analysis and from using multiple regression, a statistical model has been developed that has the ability to estimate expected delays. Additionally, the model has been expanded to calculate financial losses resulting from delays, taking into account the daily cost of maintaining the studied ships. The study took place during ongoing project “Modernization of the Świnoujście-Szczecin waterway to a depth of 12.5 m” but does not include delays resulting from this project.

1. Introduction

The importance of sea transport in international trade has been clearly demonstrated by the recent pandemic. Therefore, maritime transportation continues to grow, bringing record profits to shipowners [1]. New vessels of ever-increasing capacity and dimensions are being constructed. However, port infrastructure, such as berths and fairways, cannot keep up with such dynamic changes. This poses a challenge for almost every port in the world. Additionally, the restrictions and limitations imposed during the pandemic caused delays on an unprecedented scale [2].

The daily cost of maintaining a ship by the shipowner reaches several thousand dollars [3,4]. Financial losses incurred due to delays are therefore severe. Those affected by delays and decreased profits are ports, owners, and companies awaiting to transport essential cargo.

Port congestion is an undesired phenomenon and its negative effects on the national economy have been studied for decades [5]. Delays also have a negative impact on the image of ports and can discourage ship owners from using their services. As a result, they may choose to call at neighbouring countries or look for other transloading solutions.

Both of the mentioned problems and issues lead to the search for tools that can support the marine environment by improving the capacity of waterways [6] and increasing the efficiency of ports.

A possible solution to this situation may be vessel traffic simulation models. A traffic simulation model is a tool that allows for the prediction and understanding of how vessel traffic will change in a specific location, especially on inland waterways or in a port. There are a number of studies based on which port models have been created. These models are often used by port operators and river administrators to better understand and manage vessel traffic in a specific area.

Simulation models differ as to their objectives and purpose. They consist of, but are not limited to, three main elements:

• Vessel traffic model: which determines how vessels will move in a given area, taking into account various factors such as water depth, currents, navigational regulations, etc.
• Met-ocean conditions model.
• Infrastructure model: which determines elements such as channels, berths, loading terminals, etc. that are available to vessels in a given area.
• Loading model: which determines how vessels are loaded and unloaded in a given area, taking under consideration cargo specification.

Bellsolà Olba et al.’s paper [7] reviews and evaluates current port simulation models. The assessment focused on how the models cover processes and how they represent realistic vessel navigation. As assessment criteria, the authors chose nautical infrastructure layout and navigational behaviour.

There are models that are quite detailed in relation to the nautical infrastructure and describe anchorages [8,9], berth allocation [10,11,12], or the berthing process [13,14,15,16]. There are also models related to terminal simulation modelling [17,18], covering a sufficient range of weather conditions [19,20,21] or including different types of vessels [17,19,22,23,24].

The traffic rules are taken into account rarely, are based on collision avoidance, and are simplified to, e.g., minimum headway, overtaking possibility under the right traffic conditions, encountering priority, or speed reduction during encounters [13,15,17,19,22,25].

Relevant improvement in risk assessment evaluation was achieved with a specific course generated for each vessel, based on Automatic Identification System (AIS) data analysis [26,27,28]. This improvement leads to more realistic models in relation to vessel behaviour during navigation.

Pilot and tug assistance availability is also the subject of modelling [17,19,22,28,29]. There are existing models in which the number of pilots and tugs is assumed to be unlimited [23,25]. However, this simplification can lead to unexpected and unrealistic increases in traffic intensity.

Recent studies also focus on the dynamics of flow, considering the need to maintain distances between vessels on inland waterways. The authors of the study propose a model of maintaining distance between vessels which has been shown to accurately reproduce the experimental results [30].

With regard to the topic of ship delay research on the examined waterway, the literature shows only a couple of recent studies. There are also no indications of the costs that these delays can generate.

The topic of ship delays on the Świnoujście-Szczecin waterway was addressed in the study “Stochastic model of ships traffic capacity and congestion—validation by real ships traffic data on Świnoujście–Szczecin waterway” [31,32]. The article presents the results of the validation of a previously created stochastic model of ship traffic flow by comparing it with real data. The total waiting time was adopted as the main parameter of the presented validation. Delayed ships were recorded and averaged. The time defining the delay of the ships was obtained from the Szczecin Vessel Traffic Service (VTS) centre and compared with the model results. The model was then compared and verified with real data obtained from 25 half-day observations (one observation equals 12 h). Data was collected from July to September 2016. During that period, the total ship delay on the Świnoujście-Szczecin waterway was estimated at 125.5 ship-days.

The research for this work was conducted in a way that allows for the estimation of the expected delay of ships, expressed in the paper as ship-days per year.

2. Characteristics of the Świnoujście—Szczecin Waterway

The Świnoujście-Szczecin fairway is an artificial waterway that is 67.35 km long and about 250 m wide. It runs from the approach fairway at the anchorage in the Pomeranian Bay, through the Świna river in Świnoujście, the Mieliński Canal, the Piast Canal, the Szczecin Lagoon, and the Odra River (Szeroki Nurt, Domiąża), to the seaport in Police, and further to Szczecin [33,34] (Figure 1).

The port in Świnoujście can accommodate ships with a draft of up to 13.5 m and a length of up to 270 m. In the southern part of the port, there is a ferry terminal—a leader in ferry connections with Scandinavia. The port in Świnoujście also has a terminal dedicated to handling mainly dry bulk cargo. Meanwhile, the northern part of this port is an outer port with infrastructure for servicing LNG fuel ships.

The port in Szczecin is located over 67 km away from the sea. The passage from the port in Świnoujście to Szczecin takes approximately 4 h. The port can accommodate vessels with a draft of up to 9.15 m and a length of 215 m.

The port in Szczecin has a universal character and serves both general and bulk cargo. The port’s specialization is the handling and storage of containers, steel products, oversized cargo, as well as paper and cellulose. The port in Szczecin is the largest center for handling granite blocks in Poland. It also handles dry bulk cargoes such as coal, coke, aggregates, cereals, fertilizers, and liquid cargoes, including those requiring special storage and handling conditions, such as tar.

The Port of Police is the fourth largest port in Poland in terms of cargo handling volume. Approximately 2.0 million tons of cargo are handled here annually. The Port of Police consists of four terminals for the handling of bulk goods such as phosphates, apatites, ilmenite ore, potash salt, fertilizers, ammonia, and sulfuric acid:

• The Police Port Morski is a two-berth quay with a length of 415 m and a construction depth of 12.5 m, functionally divided into a berth for unloading raw materials equipped with two gantry cranes and a berth for fertilizers. In addition, the quay has a covered warehouse (2000 m²) and storage areas covering an area of 5000 m². The operational depth of the quay is 10.5 m, allowing for the largest ships that can pass through the waterway to Szczecin, i.e., ships with a length of 160 m and a draught of 9.15 m or a length of 206 m and a draught of 8.15 m.
• Port Barkowy has 3 quays with a total length of 791 m and an operational depth of 4.5 m. It serves barges and ships up to 120 m in length and 4 m in draft.
• The “Mijanka” quay has a total length of 286 m (between the outermost dolphins) and a ship depth of up to 9.15 m and is designed for the transshipment of liquid products. It is equipped with an ammonia transfer point with a maximum capacity of 600 t/h.
• The fourth terminal, in Jasienica on the Gunica River, is used for mooring inland vessels, and the waterways leading to it are used for commercial and tourist navigation.

The Świnoujście-Szczecin waterway is a crucial transportation corridor in the Baltic Sea region, linking the coastal city of Świnoujście to the inland city of Szczecin in Poland. This waterway serves as a gateway to the Oder River, which further connects to the Havel and Elbe rivers, forming an extensive network of inland waterways that span across Central and Eastern Europe.

The economic significance of the Świnoujście-Szczecin waterway can be elaborated in several aspects:

• Trade and shipping: As a major navigable route, the waterway facilitates the movement of goods between the Baltic Sea and inland European markets. It supports the export and import of various commodities, including raw materials, agricultural products, and manufactured goods. The Port of Szczecin and the Port of Świnoujście are strategically located along this route, handling millions of tons of cargo annually.
• Industry: The waterway is vital for industrial development in the region. It provides industries with cost-effective and eco-friendly transportation options, enabling them to transport raw materials, finished goods, and waste products efficiently. Key industries such as steel production, shipbuilding, and petrochemicals rely on the Świnoujście-Szczecin waterway for their operations.
• Energy: The waterway is essential for the energy sector in the region, particularly for the transport of coal, oil, and natural gas. The LNG terminal in Świnoujście plays a critical role in Poland’s energy security and diversification by allowing the import of liquefied natural gas from various global sources.
• Tourism: The Świnoujście-Szczecin waterway has great potential for tourism development, attracting tourists with its picturesque landscapes, historical sites, and recreational opportunities. River cruises, boating, and water sports are popular activities, contributing to the growth of the local tourism industry.
• Employment: The waterway generates employment opportunities in various sectors, including port operations, shipping, logistics, and tourism. The growth of industries and businesses reliant on the waterway creates a multiplier effect, generating additional jobs in supporting sectors such as retail, hospitality, and construction.
• Infrastructure development: The Świnoujście-Szczecin waterway has prompted significant investments in infrastructure projects, such as port expansions, navigational improvements, and the construction of roads and railways to support the increased traffic. These investments not only enhance the efficiency of the waterway but also contribute to the overall economic growth of the region.

In conclusion, the Świnoujście-Szczecin waterway plays a pivotal role in the regional economy by supporting trade, industry, energy, tourism, and job creation. The waterway has a wide-reaching impact on the economic development of the Baltic Sea region and beyond, making it a vital component of European transportation infrastructure.

The Vessel Traffic Control System on the Świnoujście-Szczecin Waterway

The VTS (Vessel Traffic Service) in Polish maritime areas, located between the western border of the country and the meridian 15°23′24″ east longitude, performs tasks related to vessel traffic control and monitoring, as well as information dissemination. The organization of the VTS system is based on the work of two centers located in the Maritime Office in Świnoujście and the Harbor Master Office in Szczecin, with strictly defined areas of competence (Figure 2). The VTS Center in Świnoujście serves the area from the outer roadstead to the Brama Torowa no 2 in the Szczecin Lagoon (working channel UKF 12), while the VTS Center in Szczecin serves the area from the Brama Torowa no 2 to the port boundaries in Szczecin (working channel UKF 69). Currently, there are 24 operators employed in the centers, working in a shift system of 24 h/7 days a week/365 days a year.

The VTS service provides information and traffic organization services for ships, particularly concerning:

• any hazards,
• clusters of vessels,
• traffic density,
• meteorological and hydrological conditions of the maritime environment,
• status of navigational aids,
• expected ship encounters,
• names of approaching ships, type, position, dangerous maneuvering conditions if present, and maneuvering intentions if reported,
• local operations and port conditions, such as cross-traffic of ferries, dredgers, and others.
• availability of anchorage areas.

To provide the aforementioned services, the VTS service utilizes available radar systems, communication devices, and the Automatic Identification System (AIS), which is a communication system providing an automatic exchange of data identifying the ship and informing about the parameters of its movement.

VTS operations have an informational and advisory character. The captain of the vessel bears full responsibility for the ship’s navigation.

3. Materials and Methods

Figure 3 presents a visual representation of the research process, highlighting the main steps involved in analysing ship delays and financial losses on the Świnoujście-Szczecin waterway. The subjects of the study are vessels participating in traffic on the Świnoujście-Szczecin waterway calling at the ports of Szczecin and Police. Ships using the port of Świnoujście are subjected to observation only in the situation of direct correlation with ships entering or leaving ports of Szczecin and Police, i.e., having a direct impact on their delay. The study does not include inland traffic and port service (e.g., barges, tugboats). The ongoing project “Modernization of the Świnoujście-Szczecin waterway to a depth of 12.5 m” and any delays resulting from it are not the subject of this research. The study focuses on delays resulting directly from the Port Regulations [36,37]. During the research, the following dependencies and limitations were identified:

• Ships to be provided with one direction of traffic (ODT) on designated sections of the waterway or on the entire route of their passage.
• Ships that cannot pass each other due to exceeding total length.
• Ships that cannot pass each other due to exceeding total width.
• Vessels that cannot pass each other due to exceeding the limit of drafts.
• Ships which cannot enter or leave the port due to the prevailing hydro-meteorological conditions.

Ships with the obligation to maintain one direction of traffic are most commonly oversize vessels, and their case has been studied more extensively in [38]. Those vessels participate in traffic on the studied waterway under special conditions, which will be presented in more detail in the following part of the article.

In this work, a separate category of delays generated by Ro-Pax ferries entering the port of Świnoujście was identified and examined. The exceeding of the technical parameters between ferries and ships from the ports of Szczecin and Police (i.e., total length or/and width or permissible drafts) was treated as an identical cause of delays, referred to as “ferries” in the work.

The research lasted from 1 April to 30 June 2021 and was collected during 12-h shifts taking place between the hours of 8:00 AM and 8:00 PM and 8:00 PM and 8:00 AM. In total, 56 observations were conducted. If, during observation, the ship experienced a delay due to Port Regulations [36], the time of the delay, its duration, and its cause were recorded. It should be noted that the system does not provide an automatic recording of ship delays in the VTS database. All delay measurements and analyses of their causes were observed and recorded in real-time during the service, with a detailed knowledge of the Port Regulations [36] and with the use of database tools. The database provided information on the actual time of passing the breakwater heads in Świnoujście by the vessels being studied. Time stamps of passing the breakwater were used to calculate the intensity on the waterway during one observation. The time of passing the breakwater heads in Świnoujście was also used to calculate the delays of ships entering the ports of Szczecin and Police by comparing the planned time of passing the breakwater heads, based on Estimated Time of Arrival (ETA), with the actual time of passing them. The calculated intensity for each of the 56 observations was analysed to determine the correlation between traffic intensity on the waterway and the resulting delays. In order to understand this correlation, a univariate and multivariate regression analysis was carried out.

The next stage of the research was to isolate the most frequent cause of ship delays resulting directly from the Port Regulations [36]. All the causes of delay that occurred during the research were analysed and seven main regulations were identified as causing ship delays on the studied waterway. The results of this part of the research were presented in the further part of the article.

An important economic aspect directly related to vessel delays is the financial loss due to the daily maintenance of vessels. Ships waiting to enter the port continuously generate costs associated with their maintenance. Also, ships that have completed loading and unloading operations occupy the quay, causing the port to be unable to service another ship. The maintenance cost depends on a number of factors, i.e., the size and age of the vessel, the type of shipping, or the cargo specification. Assessing reliable daily maintenance costs for a ship is not an easy task since shipowners consider this information as highly confidential.

Based on the available literature on the subject [3,4], the daily cost of maintaining each of the ships participating in the study was calculated. In order to get an overview of the scale of the problem of financial losses caused by ship delays in the studied waterway, calculations of expected costs in the annual prediction were carried out.

The results obtained in the process of analysing traffic intensity and causes of delays were subjected to statistical modelling in order to examine the correlation between the studied factors and to assess financial losses.

To analyse the relationship between traffic intensity, ship delays, and the resulting financial losses, univariate and multivariate regression analyses were employed. The univariate regression analysis focused on identifying the individual impact of each factor on ship delays, while the multivariate regression analysis aimed to determine the combined effect of multiple factors on ship delays and financial losses.

The multivariate regression model was chosen for analysis due to its ability to evaluate the combined effect of multiple independent variables on one or more dependent variables, such as ship delays and financial losses. To ensure the robustness and reliability of the statistical models, various validation techniques were employed:

• Model diagnostics: Goodness-of-fit and validity of assumptions were assessed through residual plots, Q-Q plots, and goodness-of-fit statistics such as AIC and BIC.
• Cross-validation: K-fold cross-validation was applied to evaluate model performance on unseen data.
• Out-of-sample testing: Independent datasets were used to validate predictive accuracy and model generalizability.

The constructed multiple regression model was developed by an adopted formula in the following form [39]:

$$y=a_0+a_1{x}_1+a_2{x}_2+\cdots +a_n{x}_n+\epsilon$$

(1)

where:

• y—explained variable (hours)
• a₀—intercept
• x₁…x_n—explanatory variables
• a₁…a_n—coefficients
• ε—error of estimation

A sensitivity analysis was also conducted to evaluate the robustness of findings and assess the impact of changes in input parameters on the results. This involved identifying key parameters, selecting parameter ranges, varying parameter values, and analysing the results. This process provided additional insights into the robustness and reliability of the study’s findings, helping decision-makers better understand potential uncertainties and limitations associated with the multivariate regression models.

4. Results

4.1. 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 Świnoujście (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.

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]:

$$\mathrm{q}=\frac{n}{t}$$

(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 Świnoujście-Szczecin waterway (

Table 1. The intensity of ship traffic in the ports of Szczecin and Police from 2010 to 2019 [34].

Year	No of Ships in Port of Szczecin in Year	No of Ships in Port of Police in Year	No of Ships per Day	Daily Intensity	No of Ships per Day	Daily Intensity
			Szczecin		Police
2019	2891	277	7.92	0.33	0.76	0.03
2018	3043	267	8.34	0.35	0.73	0.03
2017	2975	337	8.15	0.34	0.92	0.04
2016	2939	323	8.05	0.34	0.88	0.04
2015	2823	275	7.73	0.32	0.75	0.03
2014	2619	264	7.18	0.30	0.72	0.03
2013	2872	220	7.87	0.33	0.60	0.03
2012	2822	276	7.73	0.32	0.76	0.03
2011	3084	306	8.45	0.35	0.84	0.03
2010	3185	349	8.73	0.36	0.96	0.04
Average daily intensity				0.33		0.03

). 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. Intensity for observations without delay.

Date of Observation	Traffic Intensity (Ship/h)	No of Delayed Ships for Given Intensity (Ship)	Total Delay (h)
1 April 2021	0.33	0	0.00
4 April 2021	0.25	0	0.00
15 April 2021	0.17	0	0.00
16 April 2021	0.50	0	0.00
19 April 2021	0.33	0	0.00
24 April 2021	0.50	0	0.00
27 April 2021	0.58	0	0.00
28 April 2021	0.67	0	0.00
1 May 2021	0.75	0	0.00
17 May 2021	0.50	0	0.00
18 May 2021	0.08	0	0.00
25 May 2021	0.08	0	0.00
26 May 2021	0.42	0	0.00
29 May 2021	0.83	0	0.00
2 May 2021	0.58	0	0.00
3 June 2021	0.67	0	0.00
19 June 2021	0.50	0	0.00
22 June 2021	0.42	0	0.00
26 June 2021	0.75	0	0.00
27 June 2021	0.42	0	0.00
Average intensity	0.47

) were compared with the intensities from 36 observations during which ships were delayed (

Table 3. Total ships delay and number for a given intensity.

Date of Observation	Traffic Intensity (Ship/h)	No of Delayed Ships for Given Intensity (Ship)	Total Delay (h)
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	0.59	1.75 (ship/observation)	4.20 (h/observation)
Total		64	150.62

). This procedure allowed for obtaining a clear correlation diagram between the intensity and delays of ships (Figure 5).

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).

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.

4.2. Investigating the Causes of Delays in the Context of Port Regulations

As demonstrated by statistical analysis, traffic intensity is not the only factor impacting the delays of ships on the studied fairway. There is also not too high correlation between intensity and the occurrence or duration of delays. Subsequent research has focused on determining the extent to which Port Regulations [36] contribute to ship delays.

In the study, the total delay time of ships during one observation period (12 h) was collected, as well as the number of ships that were delayed during that period of time. Then, it was determined which of the regulations had a direct impact on the delay of a given vessel. For the purpose of the research on Port Regulations, seven main causes of ship delays were identified:

• Oversize vessel on the waterway (one-way traffic during entire transit).

According to Article 56 of the Port Regulations [36], the overall length of ships using the port of Szczecin and the seaport of Police cannot exceed 215 m and the overall width cannot exceed 31 m. The maximum allowable draft is 9.15 m. In the barge port of Police, the overall length of ships cannot exceed 120 m and the overall width cannot exceed 15 m. The current allowable draft of ships is determined each time by the Captain of the Port of Szczecin.

Ships exceeding any of these values are referred to as oversize ships in the workplace. Their movement on the waterway is subject to the consent and conditions specified by the Captain of the Port of Szczecin, after obtaining the opinion of the chief pilots. Their passage through the waterway, provided that they maintain one-direction traffic (ODT), does not result directly from the Port Regulations [36], but rather from additional conditions specified by the port captain to ensure safety on the waterway. Such ships receive one-way traffic along the entire passage route with daytime traffic restrictions [36].

2.

Vessels carrying dangerous cargo (one-way traffic on designated sections of the waterway).

Another group of ships subject to one-way traffic are ships carrying bulk gases, category X harmful liquid chemicals (according to the IBC Code), and tankers carrying flammable or unvaporized liquids and gases.

Under Article 50, point 1 of the Port Regulations [36], these ships cannot pass each other in the basins of ports or on the approach routes to Swinoujscie and the Swinoujscie-Szczecin waterway from buoy pair ‘15–16’ in the Pomorska Bay to the Karsibór bend (10.5 km) and from the Inski Nurt to the Górniczy Basen. In these areas, ships carrying harmful and dangerous cargoes must be provided with one-way traffic [36].

3.

Metocean (wind, wave, visibility etc.) conditions.

The Port Regulations [36] also regulate the hydro-meteorological conditions under which ships can enter or leave the ports of Szczecin and Police. The main factors that affect ship delays are wind force (°B) and visibility (Mm). It should be noted that the permissible wind force and visibility conditions must be ensured for the ships’ movement throughout the waterway.

Ships up to 120 m in length can move along the waterway without restrictions, provided that they have efficient radar equipment. According to Article 56(7) of the Port Regulations [36], ships with an overall length of 120 m, south of the northern tip of Mielin Island, are allowed to move with visibility of not less than 0.5 Mm.

Ships with an overall length of 120 m to 160 m, south of the northern tip of Mielin Island, are allowed to move with visibility less than 0.5 Mm, provided that the conditions for passage in one direction are maintained in the area of limited and poor visibility.

Ships with an overall length of 180 to 200 m, south of the northern tip of Mielin Island, are allowed to move with visibility of not less than 2.0 Mm, and at night, from the Brama Torowa no 1, only with the consent and conditions set by the captain of the port of Szczecin, after consulting the chief pilot.

Ships with an overall length of over 200 m or overall width exceeding 31 m, south of the northern tip of Mielin Island, are allowed to move only during the daytime with visibility of not less than 2.0 Mm.

Ships with a draft exceeding 9.0 m, south of the northern tip of Mielin Island, are allowed to move with visibility of not less than 2.0 Mm, and from the Brama Torowa No 1 only during the daytime.

The movement of tankers with dangerous cargo can be carried out with visibility of not less than 1 Mm.

In addition, another factor that determines safe passage of the ship and can generate delays is the water level in the port. With the water level below the established average water levels, the allowable ship draft at the berth decreases by a correction factor equal to the current difference in water level expressed in centimeters. The established average water level for the port of Szczecin is currently 515 cm and for Police, 507 cm [36].

4.

Ferries at Świnoujście.

In this study, a separate category of delays caused by ferries calling at the port of Świnoujście has been identified. The exceeding of the technical parameters between ferries and ships from the ports of Szczecin and Police (i.e., total length and/or width or permissible drafts) has been treated as an identical cause of delays, referred to as “ferries” in the study. This approach was necessary due to the inability to conduct research in the port of Świnoujście and the impossibility of detailed analyses of the vessels operating there.

5.

Due to exceeded L—length overall.

In accordance with Article 52(2) of the Port Regulations [36], from the pair of buoys ‘15–16’ of the approach channel to Świnoujście to the Orli Przesmyk (63.0 km of the channel), two-way traffic of vessels with a draft of up to 7.40 m is allowed, provided that the sum of the overall lengths of the passing vessels does not exceed 320 m. However, on the stretch from the pair of buoys ‘15–16’ to buoy ‘D’, there is a limitation on the sum of the lengths of passing vessels (Article 52(3)). On this section of the channel, vessels with a draft of up to 9.50 m may be passed by vessels with a draft of up to 6.10 m, provided that the sum of the overall lengths of the passing vessels does not exceed 280 m.

On the stretch from the northern cape of the Kosa Peninsula (3.7 km) to the Karsibór bend (10.5 km), vessels with a draft above 7.40 m, provided their overall length does not exceed 160 m, may be passed by vessels with an overall length of up to 120 m and a draft of up to 6.10 m. Vessels with a draft above 7.40 m and an overall length exceeding 160 m may be passed by vessels with an overall length of up to 120 m and a draft of up to 4.0 m. In both cases, the total length of the passing vessels cannot exceed 280 m.

From the Karsibór bend (10.5 km) to the northern cape of the Chełminek Island (35.0 km), from the Żuławy ponds to the Krępa Dolna pond, and from the Raduń Górna pond to the Iński Nurt, vessels with a draft of up to 9.15 m may be passed by vessels with a draft of up to 7.40 m, provided that the sum of the overall lengths of the passing vessels does not exceed 320 m.

The Port Regulations [36] significantly limit the allowable overall length of vessels in the Mielno Canal. According to Article 52(4), in the area from the Orli Przesmyk to the Basen Górniczy, vessels with a draft greater than 7.40 m or an overall length greater than 160 m may be passed by vessels with an overall length of up to 60 m and a draft of up to 3.0 m. Vessels with a draft of up to 7.40 m and an overall length of up to 160 m may be passed by vessels with a draft of up to 5.50 m, provided that the sum of their lengths does not exceed 240 m [36].

6.

Due to exceeded B—ships breadth.

The Port Regulations [36] also introduce a restriction regarding the width of passing ships. According to Article 52 (4) point 2, from the northern tip of Mielin Island to the Ina River (traversing the Ina S reservoir), ships with a draft greater than 7.40 m may be passed by ships and pusher/tugboat combinations with a draft of 4.0 m and above, provided that the sum of their total widths does not exceed 50 m, with the exception of the section from the northern tip of Chełminek Island (35.0 km) to the Żuławy and the section from the Krępa Dolna to the Raduń Górna, where the sum of the total widths of passing ships cannot exceed 45 m [36].

7.

Due to exceeded T—ships draught.

Article 52(1) of the Port Regulations [36] states that on the approach route to Świnoujście, from the pair of buoys ‘9–10’ to the pair of buoys ‘15–16’, two-way traffic of vessels with a draft of up to 9.15 m is allowed. Vessels with a draft greater than 9.15 m may be overtaken by vessels with a draft of up to 9.15 m, which are obliged to give way to vessels with a draft greater than 9.15 m, within the limits, ensuring that vessels with a greater draft pass in the axis of the waterway. On the sections of the waterways, from the pair of buoys ‘15–16’ of the approach route to Świnoujście to the Orli Przesmyk (63.0 km), two-way traffic of vessels with a draft of up to 7.40 m is allowed, provided that the total length of passing vessels does not exceed 320 m. Vessels with a draft of over 7.40 m may pass each other with vessels with a draft of up to 6.10 m, provided that the total length of passing vessels does not exceed 320 m. Article 52(3) states that on the section from the pair of buoys ‘15–16’ to buoy “D”, the total length of passing vessels is limited, where vessels with a draft of up to 9.50 m may be overtaken by vessels with a draft of up to 6.10 m, provided that the total length of passing vessels does not exceed 280 m. On the section from buoy “D” to the northern cape of the Kosa peninsula (3.7 km), the range of two-way traffic is expanded, where vessels with a draft of up to 7.40 m and a total length of up to 160 m may be overtaken by passenger and cargo ferries, and vessels with a draft of up to 7.40 m may be overtaken by vessels with a draft of up to 9.50 m. On the section from the northern cape of the Kosa peninsula (3.7 km) to the Karsibór bend (10.5 km), the range of two-way traffic is limited, where vessels with a draft above 7.40 m, provided that their total length is not greater than 160 m, may be overtaken by vessels with a total length of up to 120 m and a draft of up to 6.10 m. Vessels with a draft above 7.40 m and a total length above 160 m may be overtaken by vessels with a total length of up to 120 m and a draft of up to 4.0 m [36] (

Table 4. The characteristic points of the Świnoujście- Szczecin waterway with their locations.

Lp	From	km	to	km
1	Glowki	0	Kosa	3
2	Kosa	3	Karsibor	10.5
3	Karsibor	10.5	Mijanka Zalew N	15
4	Mijanka Zalew N	15	Mijanka Zalew S	17
5	Mijanka Zalew S	17	Chełminek	35
6	Chełminek	35	Mankow	41
7	Mankow	41	Mijanka Police N	50.5
8	Mijanka Police N	50.5	Mijanka Police S	51.5
9	Mijanka Police S	51.5	Inski Nurt	56
10	Inski Nurt	56	Orli Przesmyk	63

).

The results of the study showed that the highest total delay time was caused by the regulation requiring one-way traffic for oversize ships (special conditions) or ships carrying hazardous cargo. The requirement to provide the surveyed vessels with a clear waterway along the entire transit route generated 46.84 h of delays. The requirement for one-way traffic on designated sections of the waterway for ships carrying hazardous cargo is responsible for 39.47 h of delays. Hydrometeorological conditions, such as poor visibility or excessive wind, resulted in 24.61 h of delays. The exceeding of technical parameters of the surveyed vessels (total length/width or permissible draft) with ferries calling at Świnoujście caused total 13.63 h of delay (Figure 7).

The restrictions on total length for passing vessels in the waterway are responsible for 21.32 h of delay. The lowest time of delay was generated by restrictions resulting from the exceeded total width of passing ships (3.83 h) and the ratio of their respective drafts (0.93 h) (Figure 7).

The obligation to provide one-way traffic for oversize ships along the entire transit route or on a specified section of the fairway also leads to the highest number of delayed ships (Figure 8). As many as nineteen surveyed vessels were delayed for this reason. Another regulation resulting in ship delays is the requirement to maintain one-way traffic for ships carrying hazardous cargo. This regulation caused a delay for eighteen surveyed vessels. The third most common cause of delay is the exceeded overall length of the vessels. This restriction is responsible for the delay of nine vessels. Exceeding the total length, width, or permissible draft of the surveyed vessels with ships docking in Świnoujście caused a delay for eight ships. Strong wind or wind from the south directions (CPN III quay) and poor visibility were responsible for six delayed vessels. The smallest number of ship delays were caused by the restriction of the total width of passing vessels (two ships) and exceeding the permissible draft (two ships) (Figure 8).

4.3. Financial Losses Resulting from Delays

4.3.1. Analysis of Daily Operating Costs of Ships

In order to answer the question of what kind of costs are generated by each hour of ship delay, the literature on the subject was analysed [3,4]. The collected data was from the year 2011, so it was necessary to take into account the annual percentage change for each type and size of ship. Then the obtained results were averaged.

The annual percentage change for a bulk carrier and general cargo ship was 2.77%. After averaging the daily maintenance rates for each class of ships and the annual percentage change for 10 years, the estimated cost in the year 2021 was USD 7544.1 (

Table 5. Daily operational cost of a bulk carrier/ general cargo ship in 2011.

Bulk/General Cargo Ship Size	L (m)	Daily Rate (USD)	Annual Change (%)
Handysize	170	5278	3.2
Handymax	200	5966	2.5
Panamax	230	6472	3.7
Capesize	290	7437	1.7
Average		7544.1	2.77

). This means that each hour of maintaining a bulk/general cargo ship in that year costs USD 314.3.

For all tanker classes, the average daily maintenance cost in 2011 was USD 8795 (

Table 6. Daily operational cost of a tanker vessel in 2011.

Tanker Size	L (m)	Daily Rate (USD)	Annual Change (%)
Handysize	170	8222	1.8
Handysize Product	200	7670	−0.2
Panamax	220	8346	1.7
Aframax	250	8359	2.8
Suezmax	290	9503	2.6
VLCC	350	10670	0.5
Average		8795	1.53

). It was assessed that since 2011 the average cost of maintaining a 170 m tanker has increased by 18% (annual change of 1.8%). This means an increase of USD 1480.0 in a decade (18% from USD 8222) (Table 6). In the year 2021 it gives a sum of USD 9702.0 (an hourly cost of USD 404.2).

For the purpose of this paper, the calculations of financial losses due to the delay of the investigated tankers used the cost of maintaining vessels with a total length of 170 m, as, during the research, no longer tanker arrived at the ports of Szczecin or Police. Averaging the maintenance costs of tankers and including larger, and therefore more expensive, units in the average would artificially inflate the estimated costs.

The average daily maintenance cost of container ships up to 220 m was estimated at USD 4778.5 (in 2011) (

Table 7. Daily operational cost of a container vessel in 2011.

Container Ship Size	L (m)	Daily Rate (USD)	Annual Change (%)
Feedermax	130	4372	2.1
Container Ship	220	5185	2.4
Average		4778.5	2.25

). The annual percentage change for container ships was 2.25%. After averaging the daily maintenance rates for each ship class and the annual percentage change for 10 years, the estimated cost in 2021 was USD 4778.5. This means that each hour of container ship maintenance in 2021 costs USD 237.6 (Table 7).

These costs increased annually by 2.25%, which, over the last decade, gave a growth amount of USD 1075.2. This means that in 2021 the cost of maintaining this type of ship was USD 5853.7. Each hour is a cost of USD 244.0 (Table 7)

4.3.2. Costs of Delays Generated by the Port Regulations Applicable on the Studied Waterway

The estimated operational costs of the vessels allowed for the calculation of the costs incurred by the shipowners of the delayed vessels during the study. The ships were divided into groups based on their size and type, which allowed for obtaining measurable daily cost results.

The total delay time of 150.62 h was reduced by 2.42 h of delay for the two towing units. This necessity resulted from the inability to estimate the daily maintenance costs of these vessels (data not available). The estimated costs are for bulk/general cargo vessels, containers, and tankers. In total, these vessels generated a delay of 148.20 h (

Table 8. Contribution of various ship types to delays.

LOA (m)	No of Ships	Container (Ship)	Tanker (Ship)	Bulk/General Cargo (Ship)	Delay as per Size (h)
50–100	24	0	9	15	65.97 h
100–150	20	3	5	12	41.55 h
150–230	18	1	0	17	40.68 h
Delay as per type (h)		3.25 h	41.3 h	103.65 h	148.20 h

).

In terms of vessel length, the most delayed ships occurred in the range of up to 100 m. These ships (24 units) also account for the longest delay time of 65.97 h; the majority of them were bulk carriers and general cargo ships. (Table 8). Out of the studied ships, 20 of them were between 100 to 150 m in length. They account for 41.55 h of delay.

The delay of vessels over 150 m in length was 40.68 h and there were a total of 18 vessels. Again, bulk carriers and general cargo ships accounted for the largest delay time of 103.65 h. Tankers and container vessels are responsible for 3.25 h and 41.3 h of delays, respectively (Table 8).

In summary, bulk carriers and general cargo ships are the most frequently delayed units and also account for the highest delay time.

It should be taken under consideration that calculations made above pertain to the duration of current research. To estimate expected financial losses in a longer time frame, calculations of average daily maintenance costs of ships in a yearly prediction were carried out.

A total of 56 12-h observations were conducted. The total duration of the research was 672 h. The average cumulative delay of ships during this time was 150.62 h, meaning an average of 0.22 h of delay per hour of observation. Multiplying this result by 24 h gives an average daily delay of 5.38 h. Similarly, multiplying the average daily delay by the number of days in a year (365) gives an average annual delay in ship-days (

Table 9. Average annual delay.

Total research time (h)	672
Total delay (h)	150.62
Average delay per hour (h)	0.22
Average daily delay (h)	5.38
Average annual delay (h/year)	1963.40
Average annual delay (ship/days)	81.81

).

The result of the calculation of the annual prediction of financial losses in the Świnoujście-Szczecin waterway was 82 ship-days per year (Table 9). For reference, the result obtained in the 2016 study was 125.5 ship-days per year [32]. There are many factors that may contribute to the discrepancy in the results obtained. However, identifying these factors is not the goal of this work, and their examination requires a deeper analysis including economic factors.

In spite of the discrepancies in the results obtained, it can be firmly established that vessel delays that generate significant financial losses occur on the studied fairway.

To estimate the expected annual financial losses the operational costs for each type of ship were averaged and the result of USD 7699.9 was obtained (

Table 10. The daily operational cost per type of vessel in the year 2021.

Type	Bulk/General Cargo	Tanker	Container
Cost USD (day)	7544.1	9702.0	5853.7

).

According to the results obtained, delays of vessels on the Świnoujście-Szczecin waterway may generate annual losses of over USD 630,000 (

Table 11. Average annual financial losses.

Average Costs (USD)	Average Annual Delay (Ship/Days)	Annual Losses (USD)
7699.9	82	631,391.4

). This is an undoubtedly large amount, and every effort should be made to minimize the financial losses resulting from the delays.

4.4. Construction of Regression Model of Ships Delays

The analysis of the data showed that a multivariate regression is necessary to obtain answers to the objectives set in the paper. This will allow us to obtain numerical measures that characterize the correlations between the studied variables. It will provide the ability to prognose the value of delays and the costs resulting from them—with the knowledge of the intensity and number of expected vessels covered by the one-way traffic obligation.

In creating the statistical model, correlations between the intensity of traffic on the waterway and all seven causes of ship delays established during the study were examined.

The extracted causes of delays were modelled sequentially. Then, the correlations between them were studied. The model presented in this paper was selected on the basis of three statistics. These are: the fitted R², the standard error of estimation, and the significance coefficient of the obtained regression equation (p values). In addition, the statistical significance of the coefficients of the variables in the regression model was evaluated (

Table 12. Multivariate regression summary.

Multiple R	0.953004457
R2	0.908217495
Adjusted R2	0.885271868
Standard error	3.503489367

).

Based on the conducted analysis, the variables most strongly associated with the total delays of ships (up to 88.5%) were: traffic intensity, oversize vessels, and vessels carrying dangerous cargo (Table 12). These variables showed statistical significance at the level of α < 0.05 (p-values) (

Table 13. Multivariate regression statistical model for an intensity of 0.52 ships/h.

Variables in Tested Equation [Units]	Coefficients Value	Standard Error	p-Value
Intercept	−2.737	2.214	0.24015
Traffic intensity during tests with/without delay [ship/hour]	21.651	4.852	0.000776
One-way traffic (oversize vessels) [no of ships]	1.861	0.658	0.015257
Dangerous goods [no of ships]	2.867	0.438	2.79 × 10−5

). Other combinations of variables did not allow for achieving such good statistics of the fitted R², for maintaining the significance of the obtained regression model, or for keeping the significance of the variables used to create the model.

When using the model, the expected intensity on the waterway (the number of expected vessels during a 12-h shift) should be entered in the appropriate column. Then, the expected number of oversize vessels and vessels carrying dangerous cargo should be entered into the model sequentially (

Table 14. Results obtained by the statistical model for an intensity of 0.52 ships/h.

Expected intensity	0.52 ship/h
Expected number of oversized vessels	1
Expected number of ships carrying dangerous goods	1
Total delay	13.3 h
Estimated cost	USD 4250.8

).

The constructed multiple regression model confirmed that, with respect to the occurrence of delays in ships on the Świnoujście-Szczecin waterway, the correlation between traffic intensity and vessels subject to a one-way traffic obligation is statistically significant. The multiple factor model, which includes both the intensity on the waterway and vessels subject to one-way traffic, explains up to 88.5% (Table 12) of the total delay (adjusted R²). Additionally, the obtained statistical model can be used to calculate potential financial losses resulting from ship delays.

4.5. Verification of Prognostic Properties of the Model

The verification of the prognostic properties of a model is the process of evaluating how well the model can predict future events based on the data it was trained on. It is a very important step in the development of forecasting models, as it allows for the assessment of the model’s effectiveness and the improvement of its results. In order to determine the forecasting reliability of the created model, the actual total delays of ships were compared with the delays calculated by the model for a given intensity.

The presented computational model explaining the correlation between total delay and intensity, oversized ships, and ships with dangerous cargo, is afflicted with a significant forecasting error—ranging from −4% to as much as 1600%—in relation to actual values (

Table 15. Comparison of real and model-predicted total delay times.

No.	Intensity (Ship/h)	No of Oversize Vessels	No of Vessels with DG Cargo	Real Delay (h)	Model Delay (h)	Δt (h)	% Δt (h)	Costs (USD)
1	0.17	1	0	2.92	2.8	−0.12	−4%	899.8
2	0.42	1	1	4.92	11.1	6.18	126%	3556.2
3	0.42	1	0	4.17	8.2	4.03	97%	2636.3
4	0.42	1	1	7.42	11.1	3.68	50%	3556.2
5	0.5	0	2	2.63	13.8	11.17	425%	4434.8
6	0.5	0	2	3.52	11	7.48	213%	3514.9
7	0.58	2	1	5.95	16.4	10.45	176%	5264.6
8	0.67	1	1	2.58	16.5	13.92	540%	5292.7
9	0.83	0	1	7.68	18.1	10.42	136%	5807
10	0.83	1	0	1	17.1	16.1	1610%	5484.1

). This can be explained by the relatively small amount of collected observations and the number of examined objects. It should also be noted that the calculated model explains the ability to predict total ship delays with an accuracy of 88.5%, and the probability of its reliability is 95%

In order to interpret the calculated costs, the time difference ∆t was also expressed as a percentage (Table 15). This allows for a quick verification of the percentage underestimation or overestimation of the values of financial losses calculated by the model. Further verification of the model was carried out by taking into account the values of traffic intensity that were not used in the model creation process. This was done to test the predictive capabilities of the model in relation to unrealized data, i.e., intensities that did not occur during the research period of this study.

An attempt to apply the model to intensities outside the scope of the research database (

Table 16. Predicted total delays for intensities that were not observed during the research.

No.	Intensity (Ship/h)	No of Oversize Vessels	No of Vessels with DG Cargo	Model Delay (h)	Costs (USD)
1	0.75	0	1	16.4	5251.3
2	0.92	1	0	19	6109.2
3	1	1	1	23.6	7584.9
4	1.08	0	1	23.5	7543.5
5	1.25	1	0	26.2	8401.4

) showed values burdened with significant predictive error (model delay). This can be attributed to the presence of a linear relationship between traffic intensity and delays, resulting in very large predictive errors at high intensity values.

The estimated model in its presented form is not able to successfully predict reliable values of total delays. To confirm the performance of the model, further studies should be conducted, taking into account a larger number of research objects, estimation error, and confidence intervals of dependent variable coefficients sampled to estimate the explained variable (total ship delays).

5. Discussion

Obtained results indicate that vessels entering the port are delayed more often than departing vessels and their delay lasts longer. Vessels calling at the ports of Szczecin and Police obtained a total delay of 104.8 h, while outbound vessels are responsible for 45.8 h of all delays. This means that as much as 70% of delays arise between the time a ship reports to the roadstead and its berthing time.

In the context of ship type, bulk carriers and general cargo ships are delayed most frequently. As many as 44 of the 64 delayed ships (Table 8) were of this type (more than 73%). They account for 103.65 h of delay (Table 8) out of a total delay time of 150.62 h (69%).

The result of the regression analysis showed that intensity only explains 44% of the variability in ship delays (Figure 5). An interesting discovery from our research was that the highest delays were not observed at high traffic intensities, but rather at moderate intensities (0.42–0.67 ships/h) (Figure 4). Using multiple regression analysis, it was shown that the situation is mainly caused by oversize ships subject to a one-way traffic rule throughout the entire passage (accounting for 88.5% of the variability) (Figure 5). Such a ship, which cannot pass any other vessel, can block the waterway for up to 5 h (average time for a ship to enter or leave the Basin Górniczy quays). During this time, the waterway practically comes to a standstill, resulting in a drastic drop in intensity and a sharp increase in delays. This also explains the weak correlation between traffic intensity and the number of delayed ships (32% of the variability) (Figure 5). An oversize ship blocks the waterway, causing a decrease in intensity, while at the same time, more and more ships announcing their readiness to enter or leave experience delays.

The hypothesis stating that delays are dependent on the intensity of traffic on the fairway is in 44% correct (according to the linear regression result). Delays increase drastically to 88.5% reliability (multivariate regression model) when a vessel with one direction of traffic appears on the fairway. With regard to financial losses, an optimistic conclusion can be made that, since intensity does not significantly affect vessel delays, these delays can be considerably minimized by modifying the regulations in the Port Regulations [36], thus achieving a decrease in delay time even at high traffic intensity.

Based on the analysis of daily ship maintenance costs, it was concluded that the cost of maintaining a ship is closely related to its size. The waterway deepening project to a depth of 12.5 m is completed. This will result in the appearance of significantly larger vessels, which also means significantly more expensive maintenance costs and, consequently, an increase in financial losses in the event of their delay.

The conducted research has allowed for establishing the impact of the intensity of traffic on the delays of ships, which was found to be less significant than originally assumed. It has been shown that the correlations between ships resulting from the port regulations are much more important than their quantity on the waterway.

It has also been determined which of the currently applicable Port Regulations [36] is responsible for the largest number of delays. It turned out to be the regulation requiring oversize and dangerous cargo vessels to move in one direction on the entire waterway or its sections. The costs generated by these delays have also been estimated, which clearly demonstrate the scale of the problem (Table 11).

It is likely not possible to completely eliminate the phenomenon of ship delays on the studied waterway. It is not possible to fully predict or prevent the prevailing hydrometeorological conditions or ignore safety conditions and the probability of equipment failure. The creators of new Port Regulations [36], adapted to changes on the waterway after its deepening, face the difficult task of creating regulations that ensure navigation safety while minimizing ship delays.

On the basis of conducted multiple regression analysis, a statistical model was created to calculate the total delay of ships, given the expected intensity and quantity of vessels with the one-way traffic condition. Additionally, the model was extended to estimate financial losses resulting from the calculated delays Tab (14).

Although the multivariate model created in this study cannot be used in its current form for real-world applications, it does demonstrate a strong correlation between traffic intensity and ships subject to a one-way traffic direction. The obtained model provides a basis for conducting further research on a larger scale, which could lead to results confirming the reliability of the model.

Such a model can be used as a tool to support the work of Vessel Traffic Service (VTS) operators, pilots, maritime agents, quay operators, and all authorities interested in port handling effectiveness and traffic efficiency on the Świnoujście-Szczecin waterway.

6. Conclusions

In summary, the results of the conducted research allowed to establish the following conclusions:

• Review and modification of Port Regulations: Our findings suggest that by modifying the existing Port Regulations [36], it may be possible to reduce ship delays and financial losses, even at high traffic intensities. Policymakers should consider revisiting the current regulations and identify areas where adjustments could be made to minimize the impact of traffic intensity on ship delays.
• Prioritization of oversize ships: Given that oversize ships with one direction of traffic account for a significant proportion of ship delays, policymakers should consider implementing strategies to prioritize the passage of these ships or establish dedicated time windows for their movement, thereby minimizing the disruption caused to other vessels on the waterway.
• Infrastructure improvements: To accommodate the expected increase in larger vessels following the completion of the waterway deepening project, policymakers should invest in infrastructure improvements at the ports of Szczecin and Police, such as increasing berth capacity, enhancing port facilities, and improving navigational aids. These improvements will help to reduce delays and financial losses associated with larger ships.
• Enhanced communication and coordination: Our study highlights the importance of effective communication and coordination between port authorities, shipping companies, and other stakeholders involved in the management of the Świnoujście-Szczecin waterway. Policymakers should consider implementing measures to improve information sharing and real-time communication, enabling more efficient scheduling of ship movements and reducing the likelihood of delays.
• Monitoring and evaluation: To ensure the ongoing effectiveness of policies aimed at reducing ship delays and financial losses, policymakers should establish a robust monitoring and evaluation framework. This framework should involve the regular collection and analysis of data on ship delays, traffic intensity, and other relevant factors, allowing for the ongoing assessment of policy effectiveness and the identification of areas for further improvement.