of the Maritime University of Szczecin
Akademii Morskiej w Szczecinie
2018, 53 (125), 81–89ISSN 1733-8670 (Printed) Received: 24.10.2017
ISSN 2392-0378 (Online) Accepted: 26.02.2018
DOI: 10.17402/269 Published: 16.03.2018
Modelling the lateral distribution of ship
traffic in traffic separation schemes
Agnieszka Nowy
, Lucjan Gucma
Maritime University of Szczecin
1–2 Wały Chrobrego St., 70-500 Szczecin, Poland e-mail: {a.nowy; l.gucma}@am.szczecin.pl
corresponding author
Key words: vessel traffic streams, ships’ traffic flow, safety of navigation, probabilistic model, traffic
separa-tion scheme, modelling
Abstract
This paper presents the method used for the creation of ship traffic models in Southern Baltic Traffic Separation Schemes (TSS). The analysis of ship traffic was performed by means of statistical methods with the use of his-torical AIS data. The paper presents probabilistic models of ship traffic’s spatial distribution and its parameters. The results showed that there is a correlation between the standard deviation of traffic flow and TSS lane width that can be used in practical applications to ensure the safety of navigation; improve navigation efficiency, safe-ty and risk analysis in given area, and for the creation of a general model of ship traffic flow.
Introduction
A proper understanding of traffic stream behaviour is necessary for risk analysis and efficient design of sea routes and traffic facilities. Research work on ship traffic analysis has been conducted for many years. These analyses were limited by insuf-ficient sample size, position accuracy ship course and speed accuracy resulting from the need for expensive measuring equipment and data collection equipment. An additional problem was the difficulty of obtaining data for all ships in the area. New capa-bilities emerged with the AIS (Automatic Identifi-cation System) which enables not only vessel traffic monitoring but also studies on the basic processes that govern the movement of vessels in a given area.
The research on traffic flow is conducted in terms of risk analysis. Early models assumed the random spatial distribution of ships and the same speed for each ship without regard for the vessel type (Fuji, Yamanouchi & Mizuki, 1974; MacDuff, 1974). In coastal areas, a normal and uniform distribution was used as the theoretical distribution (Fuji, 1977).
Studies on the most adequate probability distribu-tion funcdistribu-tion for the posidistribu-tion of a ship were con-ducted on restricted waters (Iribarren, 1999). The author proposed the use of Weibull, Rayleigh or Gaussian type distributions to describe the location of a ship on the.
Using radar data, offshore collision risk studies were performed. One of the conclusions was the correlation between standard deviation and route length (Haugen, 1991). Prediction of ship traffic dis-tribution is widely used to calculate the number of encounters in cross-traffic lanes. Pedersen (Peders-en, 2002) introduced a model to calculate the colli-sion risk in a congested shipping lane and to investi-gate the distribution of different categories of traffic. Using AIS data, it is possible to conduct more investigations on the actual behaviour of vessels. Numerous collision risk and traffic studies have been conducted in the past few years. A model introduced by Goerlandt and Kujala (Goerlandt & Kujala, 2010) was based on a dynamic extensive microsimulation of maritime traffic using the Monte Carlo simulation technique in a given area. Detailed studies on vessel
traffic statistics were conducted. The important fac-tor used in the model was the daily variation in traf-fic (Montewka et al., 2011); however, that factor can be applied to particular areas only.
A number of studies have been performed in cer-tain waters including the Gulf of Finland (Montew-ka et al., 2011), Japan Strait (Yamaguchi & Sa(Montew-kaki, 1971) and Adriatic (Lušić, Pušić & Medić, 2017). Traffic flow in the Istanbul Strait was analysed to improve the safety of navigation (Aydogdu et al., 2012). Using AIS data, statistical analysis of marine traffic patterns and a risk of collision model off the coast of Portugal have been developed (Silveira, Teixeira & Guedes Soares, 2013).
A lot of research on maritime traffic flow was conducted by Chinese colleagues (Feng, 2013; Wen et al., 2015; Liu et al., 2017). A mathematical model was initially developed using classical traffic flow theories (Yip, 2013). The combination of an inte-grated bridge system with a microcosmic cellular automata (CA) model was proposed to simulate the vessel traffic flow by taking the ship identity, type, position, course, speed and navigation status into account (Feng, 2013). A cellular automaton mod-el that provides the basis for simulation and vessmod-el traffic management was developed (Blokus-Rosz-kowska & Smolarek, 2014). Another approach is to model ship traffic flow in the context of concept drift (Osekowska, Johnson & Carlsson, 2017) where the fluctuations of traffic relative to time are subject to studies.
This article presents studies on traffic streams in the TSS to develop a general mathematical model of vessel traffic flows by using the distance to danger as one of the main factors influencing the spatial distri-bution of ships. The calculations are performed par-tially with the mathematical software tool IWRAP MK2 recommended by IALA. AIS data are used for the studies. Results for the TSS in the Baltic Sea are presented.
Spatial ships traffic model
A system of sea waterways from the marine traf-fic engineering perspective consists of a number of separate sections. Each waterway section features two basic components: a waterway subsystem and a ship position determination system (navigational subsystem) (Gucma, 2013).
The stage preceding the optimisation of the parameters of the sea waterway system determines the conditions for safe operation of the system and divides the waterway into distinctive sections
(Gucma, Ślączka & Zalewski, 2013). Characteristic sections are based on:
• parameters of the individual section (available depth and width);
• type of manoeuvres performed in these sections; • hydrometeorological conditions prevailing in
these sections;
• type of aids to navigation in each section.
To define the width of a sea waterway, ship traffic flow has to be investigated.
The ship traffic along a definite route is con-sidered to be a process affected by numerous factors that change with time, as well as the route length and type. These factors make the traffic a ran-dom process and probabilistic methods are used for its description.
One of the main parameters describing the traf-fic flow is the spatial distribution, describing the ship’s hull position relative to the axis of the track. In ship traffic modelling it is common practice to model transverse ship traffic distribution by a nor-mal distribution (Guziewicz, 1996; Iribaren, 1999; Gucma, 1999). This is based on the assumption that most ships try to follow the official route as close as possible and are thus normally distributed across the route. These assumptions, however, do not fully describe the behaviour of the traffic. Transverse dis-tribution of ship traffic depends largely on the type of route (bend, straight) and its character (Traffic Separation Scheme, narrow channel etc). Prelimi-nary research on traffic flow in the Southern Baltic Sea shows that the centre of gravity of a ship relative to a given route can be modelled by a number of dis-tributions. The most common distributions are the normal distribution, logarithmic distribution, gam-ma distribution, logistic distribution and Weibull distribution.
The following step is to describe the standard deviation (SD), σ, of ship traffic flow. Studies on this topic carried out on the Baltic Sea (real traffic) and on the restricted area (simulation studies) lead to the assumption that the standard deviation of ship traffic is mostly dependent on the distance to danger and size of ships (Gucma, Perkovic & Przywarty, 2009). The following relationship can be used to define the standard deviation of ship routes:
σ = aD + b (1)
where: a and b are coefficients of regression, D is the distance to navigational danger (safety contour, boundary of traffic lane).
In the above formula, the coefficient a is depen-dent on the ship’s length (L).
To create a model for ship route design, different types of waterways and ship types and dimensions (L, T) should be considered. The studies present-ed in this paper relate to TSSs where the boundary of the traffic lane can be considered as a “virtual danger”.
In most maritime traffic engineering applica-tions where a ship is travelling on a given route with coordinate y = 0, the distribution of the ship’s hull position relative to the axis of the lane can be trans-formed into a conditional distribution of the condi-tion x1 < X < x2, where x1 and x2 are considered to
be the section range (Gucma, 2006). The cumulative distribution function is presented in the form:
FY|X (y, x) = P(Y ≤ y|x1 < X < x2) (2)
where X and Y give the vessel’s position coordinates in relation to the track axis.
This distribution can be used in a simple way to calculate the probability of a safe waterway cross-ing/exit, PC, of the boundary line in position Xi as
(Gucma, 2006): 1 1 YX X C F P (3) Methods Study area
The Baltic Sea has relatively dense traffic. There are a number of traffic separation schemes estab-lished and adopted by the International Maritime Organization (IMO) in the Baltic Sea. These are commonly used in areas difficult to navigate where corridors for shipping are narrow and winding. The reason for this is to enhance the safety of naviga-tion and the protecnaviga-tion of the marine environment in most of the major congested shipping areas.
There are regulations specifically established for traffic separation schemes. Rule 10 of the COLREGs (Convention, 1972) precisely describes how naviga-tors should behave when they navigate through TSSs adopted by the IMO. It can be assumed that the edge of the traffic lane is a virtual boundary for the vessel. Crossing of this lane/boundary does not pose a direct risk of collision or grounding but navigation in TSSs gives a good overview of a navigator’s behaviour on limited waters. According to Rule 10 of COLREG, the ships should proceed in the appropriate traffic lane in the general direction of traffic flow for that lane; so far as practicable to keep clear of a traffic separation line or separation zone; normally join or leave a traffic lane at the termination of the lane, but when joining or leaving from either side shall do so
at as small an angle to the general direction of traffic flow as practicable.
The authors analysed the movement of ships in the following TSSs established in the Baltic Sea (Figure 1):
1) TSS Adlergrund; 2) TSS North of Rugen; 3) TSS Bornholmsgat; 4) TSS Słupska Bank;
5) TSS in the Gulf of Gdańsk; 6) TSS Midsjöbankarna; 7) TSS South Hoburgs Bank.
Figure 1. Analysed TSSs in the Baltic Sea (picture made by IWRAP MK2 software, v5.2.0BETA)
Data
Research has been conducted on the basis of data collected from AIS obtained from the Polish Mari- time Administration. Vessel traffic was analysed using data from March to May 2017. The two largest groups of ships, general cargo (GC) and oil product tanker (OPT),were considered to be the most com-mon in the given area.
AIS raw data was processed using the IWRAP MK2 application. IWRAP is a modelling tool use-ful for maritime risk assessment. Using IWRAP, the frequency of collisions and groundings in a given waterway, based on information about traffic vol-ume/composition and route geometry, can be esti-mated (Engberg, 2016). The statistical function can be found using historical AIS data. The traffic pat-terns are illustrated in a density plot, which helps to identify the location of navigational routes (legs). Making a cross-section of the leg and creating a his-togram for each direction, the mathematical repre-sentation using a number of probability functions is prepared.
Statistical model of the spatial distribution of ship traffic streams
The theory of traffic flow of ships involved describes the movement of many vessels through the traffic lane in the some chosen period of time. One of
the main parameters describing the traffic flow is the distribution, describing the ship’s hull position rel-ative to the axis of the track. Information about the position of the vessel’s centre of gravity and course is used to define the distribution. A simple approach to describing traffic streams is their characterisa-tion by means of a single, specific resolucharacterisa-tion. This research consisted mainly of matching the distribu-tion of traffic in reladistribu-tion to the axis and obtaining the mean and standard deviation of the traffic lane for two groups of ships.
For each TSS, the centre of the traffic lane was established. To describe changes in traffic flow, each lane has been divided into the number of sections, each section of 1 Nm wide (Figure 2). For subse-quent sections, lateral distributions were determined by analysing the number of ship crossings of report lines perpendicular to each route.
Figure 2. TSS Slupska Bank, West part. Lanes divided into sections, with section histograms, for general cargo vessels (picture made by IWRAP software)
In a further step, the mean and standard deviation of the lateral distribution for each section were deter-mined. The aim of the study was to find a relation-ship between this standard deviation and the width of the traffic lane.
Results
Figures 3a and 4a show examples of spatial dis-tributions, derived from the empirical data collected in a certain section. On the X-axis, a value of zero correspondents to the middle of the traffic lane. A positive value for X means that the vessel sails more to the starboard side.
Transverse ship traffic distribution can be mod-elled by different distributions. This is necessary to calculate collision probability. Their goodness of fit is first determined by performing a Chi-square test (χ2). This test determines the degree of agreement
between the empirical distribution and the theoret-ical distribution. The hypothesis is that there is no significant difference between those distributions. The confidence level (answering the question “what is significant?”) is set at 95%. Also, Kolmogorov– Smirinov and Anderson–Darling tests have been performed. The K–S statistic and A–D statistic do not require binning. But unlike the K–S statistic, which focuses on the middle of the distribution, the A–D statistic highlights differences between the tails of the fitted distribution and input data. Also, Akaike Information Criterion (AIC) and Bayesian Infor-mation Criterion (BIC) were taken into account. The AIC and BIC statistics are calculated from the log-likelihood function and take into account the number of parameters of the fitted distribution (Dziak et al., 2012). The P-P (Probability-Probabili- ty) graph plots the p-value of the fitted distribution versus the p-value of the input data. If the fit is good, the plot will be nearly linear (Figure 3c and 4c).
Studies have shown that the distribution of a ship’s position in relation to the centre of the traffic lane is not right-sided or centrally located in rela-tion to the track axis. Figures 5a and 5b show that ship positions are located port from the centre of the track. The results relate both type of TSSs: with and without separation zones. Such distributions show that the navigators move away from the centre of the lane; for general cargo vessels, this deviation is significant.
In a further step, the mean and standard devia-tion of the lateral distribudevia-tion for each secdevia-tion were determined. In Figures 6a and 6b, example results for TSS Slupska Bank “West” are shown.
It can be seen that there is a difference between the mean and standard deviation for the two chosen groups of ships. For S_lane, differences in the first sections for SD are approximately 100 m, but in the following sections it decreases to 10 m. For N_lane, the differences are comparable for all sections of the track (60 m to over 100 m). In the same way, the means of the lateral distribution can be compared. This shows that the type of ship is a factor affecting the distribution of a vessel’s position in relation to the track axis.
Consequently, it was decided to compare these two groups and to check whether there was a statisti-cally significant difference in the results.
To compare two independent groups in terms of quotient variables, a Mann-Whitney U test was performed. Significant differences at p < 0.05 are marked by “*”. If p is less than 0.050 then the
tankers within a given variable is statistically signif-icant (Table 1).
The U-test statistic for the Mann-Whitney test is given by the smaller of U1 and U2 as defined below:
1 1 1 2 1 1 nn n n2 1 R U (4)
2 2 2 2 1 2 nn n n2 1 R U (5)
1
12 12 1 2 2 1 2 1 3 2 1 2 1 2 1 2 1 1
n n n n t t n n n n n n n n U Z (6)Fit Comparison for Distance from center
BetaGeneral(10.167;5.3953;–2347.8;1993) 5.0%
6.5% 5.0%5.6%
–325 1251
Distance from center [m]
–2000 –1500 –1000 –500 0 500 1000 1500 2000 Probability Density , Values × 10 –4 9 8 7 6 5 4 3 2 1 0 90.0% 87.9%
Figure 3. a) Spatial distribution of ship’s hull position rela-tive to the axis of the track at one cross section; b) probabil-ity; c) P-P graph. Adlerground TSS. General cargo vessels
Fit Comparison for Distance from center
Logistic(247.99;217.64) 5.0%
2.4% 5.0%6.8%
–555 817
Distance from center [m]
–2000 –1500 –1000 –500 0 500 1000 1500 Probability Density , Values × 10 –4 14 12 10 8 6 4 2 0 90.0% 90.7% Fit Comparison-Probability BetaGeneral(10.167;5.3953;–2347.8;1993) 5.0% 6.5% 5.0%5.6% –325 1251
Distance from center [m]
–2000 –1500 –1000 –500 0 500 1000 1500 2000 Probability 1.0 0.8 0.6 0.4 0.2 0.0 90.0% 87.9% Input BetaGeneral Fit Comparison-Probability Logistic(247.99;217.64) 5.0% 2.4% 5.0%6.8% –555 817
Distance from center [m]
–2000 –1500 –1000 –500 0 500 1000 1500 Probability 1.0 0.8 0.6 0.4 0.2 0.0 90.0% 90.7% Input Logistic
Probability-Probability Plot of Distance from center
BetaGeneral(10.167;5.3953;–2347.8;1993) Input p-Value 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fitted p-V alue 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 BetaGeneral
Probability-Probability Plot of Distance from center
Logistic(247.99;217.64) Input p-Value 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fitted p-V alue 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Logistic a) a) b) b) c) c)
Figure 4. a) Spatial distribution of ship’s hull position rel-ative to the axis of the track at one cross section; b) proba-bility; c) P-P graph. Adlerground TSS. Oil product tankers
Probability Density 0.0012 0.0010 0.0008 0.0006 0.0004 0.0002 0.0000
Distance from center [m]
–2000 –1500 –1000 –500
0
500 1000 1500 2000
Fit Comparison for GC and OPT
Eastbound Traffic
Logistic OPT Persons GC
Probability Density 0.0014 0.0012 0.0010 0.0008 0.0006 0.0004 0.0002 0.0000
Distance from center [m]
–2000 –1500 –1000 –500
0
500 1000 1500 2000
Fit Comparison for GC and OPT
Westbound Traffic
Logistic OPT BetaGeneral GC
Figure 5. Distribution over the waterway at one cross section. Adlerground TSS: a) eastbound traffic; b) westbound traffic
a) b)
TSS Słupska Bank "West"
1 3 5 7 9 11
Section of traffic lane
Standard deviation [m] 650 600 550 500 450 SD S_lane GC SD N_lane GC SD S_lane OPT SD N_lane OPT
TSS Słupska Bank "West"
1 3 5 7 9 11
Section of traffic lane
400 300 200 100 0 –100 –200 –300 Mean [m] a) b)
Figure 6. a) Standard deviation for general cargo (GC) vessels and oil product tankers (OPT) for subsequent sections of the lanes; b) Mean for general cargo (GC) vessels and oil product tankers (OPT) for subsequent sections of the lanes; SD – standard deviation, S_lane – eastbound vessels, N_lane – westbound vessels
Table 1. Mann-Whitney U test results for Traffic Separation Schemes
TSS Vari- able Rank SumOPT GC U Z p TSS Vari- able Rank SumOPT GC U Z p
Adlerground Eastbound M 197.0 103.0 25.0 2.685 0.007 * Gdansk „East”/ Southbound M 204.0 391.0 51.0 –3.203 0.001 * SD 91.0 209.0 13.0 –3.377 0.001* SD 288.0 307.0 135.0 –0.310 0.757 Adlerground Westbound M 79.0 221.0 1.0 –4.070 0.000 * Bornholmsgat/ Southbound M 855.0 1098.0 359.0 –1.704 0.088 SD 78.0 222.0 0.0 –4.128 0.000* SD 706.0 1247.0 210.0 –3.801 0.000* Slupska Bank “East”/Eastbound M 341.0 124.0 4.0 4.478 0.000 * Bornholmsgat/ Northbound M 912.0 1041.0 416.0 –0.901 0.367 SD 261.0 204.0 84.0 1.1614 0.245 SD 524.0 1429.0 28.0 –6.364 0.000* Slupska Bank „East”/Westbound M 106.0 300.0 1.0 –4.434 0.000 * Rugen/ Eastbound M 15.0 40.0 0.0 –2.507 0.012 * SD 152.0 254.0 47.0 –2.320 0.020* SD 15.0 40.0 0.0 –2.507 0.012* Słupska Bank „West”/Eastbound M 55.0 155.0 0.0 –3.742 0.000 * Rugen/ Westbound M 132.0 121.0 55.0 0.328 0.743 SD 143.0 67.0 12.0 2.835 0.005* SD 89.0 164.0 23.0 –2.430 0.015* Słupska Bank „West”/Westbound M 147.0 63.0 8.0 3.137 0.002 * Midsjobankarna/ Eastbound M 75.0 61.0 25.0 0.683 0.495 SD 155.0 55.0 0.0 3.742 0.00* SD 36.0 100.0 0.0 –3.308 0.001* Gdansk„West”/
Northbound M 261.0 204.0 84.0 1.161 0.245 Midsjobankarna/ Westbound M 101.0 52.0 7.0 2.742 0.006
* SD 267.0 198.0 78.0 1.410 0.158 SD 56.5 96.5 20.5 –1.443 0.149 Gdansk „West”/ Southbank M 184.0 281.0 64.0 –1.991 0.046 * South Hoburgs Bank/Eastbound M 177.0 123.0 45.0 1.530 0.126 SD 275.0 190.0 70.0 1.742 0.081 SD 145.0 155.0 67.0 –0.260 0.795 Gdansk „East”/
Northband SD 214.0 381.0 61.0 –2.859 0.004M 284.0 311.0 131.0 –0.448 0.654* Bank/WestboundSouth Hoburgs SD 89.0 164.0 23.0 –2.430 0.015M 132.0 121.0 55.0 0.328 0.743*
Mean S_lane GC Mean N_lane GC Mean S_lane OPT Mean N_lane OPT
where:
R1 – rank sum for group 1 (OPT);
R2 – rank sum for group 2 (GC);
n1, n2 – sample size;
Z – value of Mann-Whitney test, when the sample
size of both groups is greater than 20;
p – significance level for the test (for the Z test
value);
U1 can be replaced by U2;
t – number of cases included in tied rank.
The Mann-Whitney test is a nonparametric equiv-alent of the t-test for independent data. According to the results of the Monte Carlo test in some cases, this test is even stronger than the t-test. When the test feature has no normal distribution, the Mann-Whit-ney test can be safely used because the chance of accepting the alternative hypothesis, if it is true, it is not less than the chance of rejecting the null hypoth-esis by the t-test (Francuz & Mackiewicz, 2007).
In Figure 7a, the relationship between the stan-dard deviation of a ship’s distance from the centre and the width of the traffic lane, D,is shown. It can be seen that there is a linear correlation between these parameters with a correlation coefficient of more than 0.8. This seems to be a very important conclusion in the scope of traffic model creation. This is due to the way the navigator navigates in cer-tain areas. The more difficult (the narrower) the area for navigation, the more accurately the steering of the vessel is performed.
These results allowed a linear regression model to be built for the standard deviation of ship tracks in the TSS for two groups of analysed ships:
• General cargo vessels (GC):
σ = 0.1519·D + 87.291 (7)
• Oil product tankers (OPT):
σ = 0.1332·D + 96.888 (8)
where: σ is the standard deviation of a ship’s dis-tance from the centre [m]; D is the width of the traf-fic lane [m].
By building individual sub-models for distinct types of ship, waterway and navigational conditions, etc. it is possible to create a general model of ship traffic flows. The aim of the model is to determine the standard deviation according to the mentioned parameters and the distance to danger. The results obtained can be implemented in navigation risk assessment models.
It can be seen that, despite there being a statisti-cally significant difference between samples for gen-eral cargo vessels and oil product tankers, there is no distinct difference between the models (Figure 8).
Figure 7. a) Linear correlation between the width of traffic lane D and standard deviation of distance from the centre σ; b) prediction of standard deviation vs. standard deviation. Marked correlations are significant at p < 0.05000, R = 0.8549,
p = 0.00
Regression of Standard Deviation by Width of Traffic Lane [m] (R2 = 0.731)
Width of traffic lane [m]
1400 1200 1000 800 600 400 200 0 –200 Standard Deviation 0 1000 2000 3000 4000 5000 6000 7000
Model (Standard Deviation) Conf. interval (Mean 95%) Conf. interval (Obs 95%)
Pred(Standard Deviation) / Standard Deviation
Pred(Standard Deviation) 1400 1200 1000 800 600 400 200 Standard Deviation 0 200 400 600 800 1000 1200 1400 a) b) –200 –200 0
Width of traffic lane D [m]
General cargo vessel Oil product tanker
Standard deviation σ [m] 1400 1200 1000 800 600 400 200 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000
Figure 8. Comparison of two models: general cargo vessels and oil product tankers
In the case of the oil product tankers, where general-ly the crew is more highgeneral-ly trained and experienced, the deviations are smaller which indicates a more accurate navigational system with compliance to rules. Tankers, as vessels with highly dangerous car-go, keep away from other vessels and navigate with extra caution.
Conclusions
This paper presents the results of research into ship traffic flow models in the Baltic Sea. Vessel traffic in Traffic Separation Schemes was taken into consideration. The presented samples of distribu-tions are the basis for the development of a mathe-matical model of traffic.
Models for two vessel groups were built (gen-eral cargo and oil product tankers). The results show a small difference between these two models, despite there being a statistically significant differ-ence between these two groups. This issue needs to be investigated more thoroughly. It is necessary to continue research in other waters in to expand and verify the model. It was noticed that navigators do not always navigate on the centre or right-hand side of the traffic lane as was previously suggested.
There is a linear correlation between the stan-dard deviation of a ship’s distance from the centre and the width of the traffic lane. The coefficient of determination is satisfactory according to the accept-ed interpretation which leads to further research on the topic.
The presented method, based on a simple regres-sion model, can be used for designing waterway sys-tems and calculating the probability of crossing the boundary line. The developed model will allow the design of sea routes during the development of wind farms and other marine constructions and facilities that affect the nature of vessel traffic flow. Using this approach, it is possible to obtain generic rules that describe the vessel path in many different areas. To do so, the case study area (Southern Baltic) will be split into several characteristic waterways and seg-ments and the location-specific results will be gener-alised to their specific segments.
It can be concluded that by using an analysis of historical AIS data, clearly more insight is obtained into detailed individual vessel behaviour. This understanding of the behaviour can be formulated into generic rules. These rules can be implemented in the maritime model, which improves the simula-tion of the individual vessel paths.
Further studies are planned in this field for oth-er traffic routes. The influence of vessel size (L, T), type, and distance to danger will be determined.
Acknowledgments
This research outcome has been achieved under the grant No. 11/MN/IIRM/17 financed from a sub-sidy of the Ministry of Science and Higher Educa-tion for statutory activities.
References
1. Aydogdu, Y.V., Yurtoren, C., Park, J.S. & Park, Y.S. (2012) A study on local traffic management to improve ma-rine traffic safety in the Istanbul Strait. Journal of
Naviga-tion 65, pp. 99–112.
2. Blokus-Roszkowska, A. & Smolarek, L. (2014) Maritime
traffic flow simulation in the intelligent transportation sys-tems theme. Safety and Reliability: Methodology and
Appli-cations-Proceedings of the European Safety and Reliability Conference (ESREL 2014), pp. 265–274.
3. Convention (1972) Convention on the International
Regula-tions for Preventing Collisions at Sea. London, 20 October
1972.
4. Dziak, J., Coffman, D., Lanza, S. & Li, R. (2012)
Sensitiv-ity and specificSensitiv-ity of information criteria. Technical Report
Series #12-119. The Methodology Center of The Pennsylva-nia State University.
5. Engberg, P.C. (2016) IWRAP MK2 v5.2.0 Manual. Gate-House A/S.
6. Feng, H. (2013) Cellular automata ship traffic flow model considering integrated bridge system. International Journal
of u- and e- Service, Science and Technology 6, 6, pp. 121–
132.
7. Francuz, P. & Mackiewicz, R. (2007) Liczby nie wiedzą
skąd pochodzą. Przewodnik po metodologii i statystyce nie tylko dla psychologów. Wydawnictwo KUL.
8. Fuji, Y. (1977) The behavior of ships in limited waters. Proc. of the 24th International PIANC Congress, Leningrad.
9. Fuji, Y., Yamanouchi, H. & Mizuki, N. (1974) Some Fac-tors Affecting the Frequency of Accidents in Marine Traffic.
Journal of Navigation 27(2), p. 239–247.
10. Goerlandt, F. & Kujala, P. (2010) Modeling of ship colli-sion probability using dynamic traffic simulation.
Reliabil-ity, Risk and Safety. Ale, Papazoglou & Zio (Eds). London:
Taylor & Francis Group, pp. 440–447.
11. Gucma, L. (1999) Kryterium bezpieczeństwa manewru
na torze wodnym. Materiały na Konferencję Explo-Ship,
WSM, Szczecin.
12. Gucma, L. (2006) The method of navigation risk
assess-ment on waterways based on generalised real time simu-lation data. Proc. of International MARSIM Conference,
Terschelling.
13. Gucma, L., Perkovic, M. & Przywarty, M. (2009) Assess-ment of influence of traffic intensity increase on collision probability in the Gulf of Trieste. Annual of Navigation 15, pp. 41–48.
14. Gucma, S. (2013) Optimization of sea waterway system pa-rameters in marine traffic engineering. Journal of KONBiN 2(26), pp. 51–60.
15. Gucma, S., Ślączka, W. & Zalewski, P. (2013) Parametry
torów wodnych i systemów nawigacyjnych wyznaczane przy wykorzystaniu bezpieczeństwa nawigacji. Monography
edi-ted by Stanisław Gucma. Szczecin: Wydawnictwo Naukowe Akademii Morskiej w Szczecinie.
16. Guziewicz, J. (1996) Model manewrowania statkiem na
wybranych basenach portowych Świnoujścia i Szczecina.
Rozprawa doktorska, Wydział Budownictwa Wodnego, PW, Gdańsk.
17. Haugen, S. (1991) Probabilistic Evaluation of Frequency of
Collision Between Ships and Offshore Platforms. Doctoral
dissertation, University in Trondheim.
18. Iribarren, J.R. (1999) Determining the Horizontal
Dimen-sions of Ship Manoeuvering Areas. PIANC Bulletin No.
100, Bruxelles.
19. Liu, Z., Liu, J., Li, Z., Liu, R.W. & Xiong, N. (2017) Char-acteristics analysis of vessel traffic flow and its mathemati-cal model. Journal of Marine Science and Technology 25(2), pp. 230–241.
20. Lušić, Z., Pušić, D. & Medić, D. (2017) Analysis of the maritime traffic in the central part of the Adriatic. In:
Transport Infrastructure and Systems. Proceedings of
the AIIT International Congress on Transport Infrastruc-ture and Systems. Dell’Acqua G. & Wegman F. (Eds) pp. 1013–1020.
21. MacDuff, T. (1974) The Probability of Vessel Collisions. Ocean Industry.
22. Montewka, J., Krata, P., Goerlandt, F., Mazaheri, A. & Kujala, P. (2011) Marine traffic risk modeling – an inno-vative approach and a case study. Proceedings of the
Institu-tion of Mechanical Engineers, Part O: Journal of Risk and Reliability 225 (3). pp. 307–322.
23. Osekowska, E., Johnson, H. & Carlsson, B. (2017) Mar-itime vessel traffic modeling in the context of concept drift.
Transportation Research Procedia 25, pp. 1457–1476.
24. Pedersen, P.T. (2002) Collision risk for fixed offshore struc-tures close to high‐density shipping lanes. Journal of
Engi-neering for the Maritime Environment 216 (1), pp. 29–44.
25. Puszcz, A. & Gucma, L. (2011) Towards the Model of
Traf-fic Flow on the Southern Baltic Based on Statistical Data.
Proc. of the 9th International Trans-Nav Conference, Vol. 5,
Gdynia.
26. Silveira, P.A.M., Teixeira, A.P. & Guedes Soares, C. (2013) Use of AIS Data to Characterise Marine Traffic Pat-terns and Ship Collision Risk off the Coast of Portugal. The
Journal of Navigation, 66, pp. 879–898.
27. Wen, Y.Q., Huang, Y.M., Zhou, C.H., Yang, J.L., Xiao, C.S. & Wu, X.C. (2015) Modelling of marine traffic flow complexity. Ocean Engineering 104, pp. 500–510.
28. Yamaguchi, A. & Sakaki, S. (1971) Traffic surveys in Ja-pan. Journal of Navigation 24, pp. 521–534.
29. Yip, T.L. (2013) A marine traffic flow model. International
Journal on Marine Navigation and Safety of Sea Transpor-tation 7, 1, pp. 109–113.
