Modelling the lateral distribution of ship traffic in traffic separation schemes
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Scientific Journals Zeszyty Naukowe
of the Maritime University of Szczecin Akademii Morskiej w Szczecinie
2018, 53 (125), 81–89
ISSN 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 Studies on the most adequate probability distribu-
tion function for the position of a ship were con-
A proper understanding of traffic stream ducted on restricted waters (Iribarren, 1999). The
behaviour is necessary for risk analysis and efficient author proposed the use of Weibull, Rayleigh or
design of sea routes and traffic facilities. Research Gaussian type distributions to describe the location
work on ship traffic analysis has been conducted for of a ship on the.
many years. These analyses were limited by insuf- Using radar data, offshore collision risk studies
ficient sample size, position accuracy ship course were performed. One of the conclusions was the
and speed accuracy resulting from the need for correlation between standard deviation and route
expensive measuring equipment and data collection length (Haugen, 1991). Prediction of ship traffic dis-
equipment. An additional problem was the difficulty tribution is widely used to calculate the number of
of obtaining data for all ships in the area. New capa- encounters in cross-traffic lanes. Pedersen (Peders-
bilities emerged with the AIS (Automatic Identifi- en, 2002) introduced a model to calculate the colli-
cation System) which enables not only vessel traffic sion risk in a congested shipping lane and to investi-
monitoring but also studies on the basic processes gate the distribution of different categories of traffic.
that govern the movement of vessels in a given area. Using AIS data, it is possible to conduct more
The research on traffic flow is conducted in terms investigations on the actual behaviour of vessels.
of risk analysis. Early models assumed the random Numerous collision risk and traffic studies have been
spatial distribution of ships and the same speed for conducted in the past few years. A model introduced
each ship without regard for the vessel type (Fuji, by Goerlandt and Kujala (Goerlandt & Kujala, 2010)
Yamanouchi & Mizuki, 1974; MacDuff, 1974). In was based on a dynamic extensive microsimulation
coastal areas, a normal and uniform distribution of maritime traffic using the Monte Carlo simulation
was used as the theoretical distribution (Fuji, 1977). technique in a given area. Detailed studies on vessel
Zeszyty Naukowe Akademii Morskiej w Szczecinie 53 (125) 81Agnieszka Nowy, Lucjan Gucma
traffic statistics were conducted. The important fac- (Gucma, Ślączka & Zalewski, 2013). Characteristic
tor used in the model was the daily variation in traf- sections are based on:
fic (Montewka et al., 2011); however, that factor can • parameters of the individual section (available
be applied to particular areas only. depth and width);
A number of studies have been performed in cer- • type of manoeuvres performed in these sections;
tain waters including the Gulf of Finland (Montew- • hydrometeorological conditions prevailing in
ka et al., 2011), Japan Strait (Yamaguchi & Sakaki, these sections;
1971) and Adriatic (Lušić, Pušić & Medić, 2017). • type of aids to navigation in each section.
Traffic flow in the Istanbul Strait was analysed to To define the width of a sea waterway, ship traffic
improve the safety of navigation (Aydogdu et al., flow has to be investigated.
2012). Using AIS data, statistical analysis of marine The ship traffic along a definite route is con-
traffic patterns and a risk of collision model off the sidered to be a process affected by numerous
coast of Portugal have been developed (Silveira, factors that change with time, as well as the route
Teixeira & Guedes Soares, 2013). length and type. These factors make the traffic a ran-
A lot of research on maritime traffic flow was dom process and probabilistic methods are used for
conducted by Chinese colleagues (Feng, 2013; Wen its description.
et al., 2015; Liu et al., 2017). A mathematical model One of the main parameters describing the traf-
was initially developed using classical traffic flow fic flow is the spatial distribution, describing the
theories (Yip, 2013). The combination of an inte- ship’s hull position relative to the axis of the track.
grated bridge system with a microcosmic cellular In ship traffic modelling it is common practice to
automata (CA) model was proposed to simulate the model transverse ship traffic distribution by a nor-
vessel traffic flow by taking the ship identity, type, mal distribution (Guziewicz, 1996; Iribaren, 1999;
position, course, speed and navigation status into Gucma, 1999). This is based on the assumption that
account (Feng, 2013). A cellular automaton mod- most ships try to follow the official route as close
el that provides the basis for simulation and vessel as possible and are thus normally distributed across
traffic management was developed (Blokus-Rosz- the route. These assumptions, however, do not fully
kowska & Smolarek, 2014). Another approach is to describe the behaviour of the traffic. Transverse dis-
model ship traffic flow in the context of concept drift tribution of ship traffic depends largely on the type
(Osekowska, Johnson & Carlsson, 2017) where the of route (bend, straight) and its character (Traffic
fluctuations of traffic relative to time are subject to Separation Scheme, narrow channel etc). Prelimi-
studies. nary research on traffic flow in the Southern Baltic
This article presents studies on traffic streams in Sea shows that the centre of gravity of a ship relative
the TSS to develop a general mathematical model of to a given route can be modelled by a number of dis-
vessel traffic flows by using the distance to danger as tributions. The most common distributions are the
one of the main factors influencing the spatial distri- normal distribution, logarithmic distribution, gam-
bution of ships. The calculations are performed par- ma distribution, logistic distribution and Weibull
tially with the mathematical software tool IWRAP distribution.
MK2 recommended by IALA. AIS data are used for The following step is to describe the standard
the studies. Results for the TSS in the Baltic Sea are deviation (SD), σ, of ship traffic flow. Studies on this
presented. topic carried out on the Baltic Sea (real traffic) and
on the restricted area (simulation studies) lead to the
Spatial ships traffic model assumption that the standard deviation of ship traffic
is mostly dependent on the distance to danger and
A system of sea waterways from the marine traf- size of ships (Gucma, Perkovic & Przywarty, 2009).
fic engineering perspective consists of a number of The following relationship can be used to define the
separate sections. Each waterway section features standard deviation of ship routes:
two basic components: a waterway subsystem and
σ = aD + b (1)
a ship position determination system (navigational
subsystem) (Gucma, 2013). where: a and b are coefficients of regression, D is
The stage preceding the optimisation of the the distance to navigational danger (safety contour,
parameters of the sea waterway system determines boundary of traffic lane).
the conditions for safe operation of the system In the above formula, the coefficient a is depen-
and divides the waterway into distinctive sections dent on the ship’s length (L).
82 Scientific Journals of the Maritime University of Szczecin 53 (125)Modelling the lateral distribution of ship traffic in traffic separation schemes
To create a model for ship route design, different at as small an angle to the general direction of traffic
types of waterways and ship types and dimensions flow as practicable.
(L, T) should be considered. The studies present- The authors analysed the movement of ships in
ed in this paper relate to TSSs where the boundary the following TSSs established in the Baltic Sea
of the traffic lane can be considered as a “virtual (Figure 1):
danger”. 1) TSS Adlergrund;
In most maritime traffic engineering applica- 2) TSS North of Rugen;
tions where a ship is travelling on a given route with 3) TSS Bornholmsgat;
coordinate y = 0, the distribution of the ship’s hull 4) TSS Słupska Bank;
position relative to the axis of the lane can be trans- 5) TSS in the Gulf of Gdańsk;
formed into a conditional distribution of the condi- 6) TSS Midsjöbankarna;
tion x1 < X < x2, where x1 and x2 are considered to 7) TSS South Hoburgs Bank.
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):
Figure 1. Analysed TSSs in the Baltic Sea (picture made by
PC 1 FY X X1 (3) IWRAP MK2 software, v5.2.0BETA)
Data
Methods
Study area Research has been conducted on the basis of data
collected from AIS obtained from the Polish Mari-
The Baltic Sea has relatively dense traffic. There time Administration. Vessel traffic was analysed
are a number of traffic separation schemes estab- using data from March to May 2017. The two largest
lished and adopted by the International Maritime groups of ships, general cargo (GC) and oil product
Organization (IMO) in the Baltic Sea. These are tanker (OPT),were considered to be the most com-
commonly used in areas difficult to navigate where mon in the given area.
corridors for shipping are narrow and winding. The AIS raw data was processed using the IWRAP
reason for this is to enhance the safety of naviga- MK2 application. IWRAP is a modelling tool use-
tion and the protection of the marine environment in ful for maritime risk assessment. Using IWRAP, the
most of the major congested shipping areas. frequency of collisions and groundings in a given
There are regulations specifically established for waterway, based on information about traffic vol-
traffic separation schemes. Rule 10 of the COLREGs ume/composition and route geometry, can be esti-
(Convention, 1972) precisely describes how naviga- mated (Engberg, 2016). The statistical function can
tors should behave when they navigate through TSSs be found using historical AIS data. The traffic pat-
adopted by the IMO. It can be assumed that the edge terns are illustrated in a density plot, which helps to
of the traffic lane is a virtual boundary for the vessel. identify the location of navigational routes (legs).
Crossing of this lane/boundary does not pose a direct Making a cross-section of the leg and creating a his-
risk of collision or grounding but navigation in TSSs togram for each direction, the mathematical repre-
gives a good overview of a navigator’s behaviour on sentation using a number of probability functions is
limited waters. According to Rule 10 of COLREG, prepared.
the ships should proceed in the appropriate traffic
lane in the general direction of traffic flow for that Statistical model of the spatial
distribution of ship traffic streams
lane; so far as practicable to keep clear of a traffic
separation line or separation zone; normally join or The theory of traffic flow of ships involved
leave a traffic lane at the termination of the lane, but describes the movement of many vessels through the
when joining or leaving from either side shall do so traffic lane in the some chosen period of time. One of
Zeszyty Naukowe Akademii Morskiej w Szczecinie 53 (125) 83Agnieszka Nowy, Lucjan Gucma
the main parameters describing the traffic flow is the between the empirical distribution and the theoret-
distribution, describing the ship’s hull position rel- ical distribution. The hypothesis is that there is no
ative to the axis of the track. Information about the significant difference between those distributions.
position of the vessel’s centre of gravity and course The confidence level (answering the question “what
is used to define the distribution. A simple approach is significant?”) is set at 95%. Also, Kolmogorov–
to describing traffic streams is their characterisa- Smirinov and Anderson–Darling tests have been
tion by means of a single, specific resolution. This performed. The K–S statistic and A–D statistic do
research consisted mainly of matching the distribu- not require binning. But unlike the K–S statistic,
tion of traffic in relation to the axis and obtaining the which focuses on the middle of the distribution, the
mean and standard deviation of the traffic lane for A–D statistic highlights differences between the tails
two groups of ships. of the fitted distribution and input data. Also, Akaike
For each TSS, the centre of the traffic lane was Information Criterion (AIC) and Bayesian Infor-
established. To describe changes in traffic flow, each mation Criterion (BIC) were taken into account.
lane has been divided into the number of sections, The AIC and BIC statistics are calculated from
each section of 1 Nm wide (Figure 2). For subse- the log-likelihood function and take into account
quent sections, lateral distributions were determined the number of parameters of the fitted distribution
by analysing the number of ship crossings of report (Dziak et al., 2012). The P-P (Probability-Probabili-
lines perpendicular to each route. 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-
Figure 2. TSS Slupska Bank, West part. Lanes divided into
sections, with section histograms, for general cargo vessels tion of the lateral distribution for each section were
(picture made by IWRAP software) determined. In Figures 6a and 6b, example results
for TSS Slupska Bank “West” are shown.
In a further step, the mean and standard deviation It can be seen that there is a difference between
of the lateral distribution for each section were deter- the mean and standard deviation for the two chosen
mined. The aim of the study was to find a relation- groups of ships. For S_lane, differences in the first
ship between this standard deviation and the width sections for SD are approximately 100 m, but in the
of the traffic lane. following sections it decreases to 10 m. For N_lane,
the differences are comparable for all sections of the
Results track (60 m to over 100 m). In the same way, the
means of the lateral distribution can be compared.
Figures 3a and 4a show examples of spatial dis- This shows that the type of ship is a factor affecting
tributions, derived from the empirical data collected the distribution of a vessel’s position in relation to
in a certain section. On the X-axis, a value of zero the track axis.
correspondents to the middle of the traffic lane. Consequently, it was decided to compare these
A positive value for X means that the vessel sails two groups and to check whether there was a statisti-
more to the starboard side. cally significant difference in the results.
Transverse ship traffic distribution can be mod- To compare two independent groups in terms
elled by different distributions. This is necessary to of quotient variables, a Mann-Whitney U test was
calculate collision probability. Their goodness of fit performed. Significant differences at p < 0.05 are
is first determined by performing a Chi-square test marked by “*”. If p is less than 0.050 then the differ-
(χ2). This test determines the degree of agreement ence between general cargo vessels and oil product
84 Scientific Journals of the Maritime University of Szczecin 53 (125)Modelling the lateral distribution of ship traffic in traffic separation schemes
a) Fit Comparison for Distance from center a) Fit Comparison for Distance from center
BetaGeneral(10.167;5.3953;–2347.8;1993) Logistic(247.99;217.64)
5.0% 90.0% 5.0% 5.0% 90.0% 5.0%
6.5% 87.9% 5.6% 2.4% 90.7% 6.8%
–325 1251 –555 817
9 14
8
12
7
10
Probability Density,
Probability Density,
6
Values × 10–4
Values × 10–4
5 8
4 6
3
4
2
2
1
0 0
–2000
–1500
–1000
–500
0
500
1000
1500
–2000
–1500
–1000
–500
0
500
1000
1500
2000
Distance from center [m] Distance from center [m]
b) Fit Comparison-Probability b) Fit Comparison-Probability
BetaGeneral(10.167;5.3953;–2347.8;1993) Logistic(247.99;217.64)
5.0% 90.0% 5.0% 5.0% 90.0% 5.0%
6.5% 87.9% 5.6% 2.4% 90.7% 6.8%
–325 1251 –555 817
1.0 1.0
0.8 0.8
0.6 0.6
Probability
Probability
0.4 0.4
0.2 0.2
0.0 0.0
–2000
–1500
–1000
–500
0
500
1000
1500
2000
–2000
–1500
–1000
–500
0
500
1000
1500
Distance from center [m] Distance from center [m]
Input BetaGeneral Input Logistic
c) Probability-Probability Plot of Distance from center c) Probability-Probability Plot of Distance from center
BetaGeneral(10.167;5.3953;–2347.8;1993) Logistic(247.99;217.64)
1.0 1.0
0.9 0.9
0.8 0.8
0.7 0.7
0.6 0.6
Fitted p-Value
Fitted p-Value
0.5 0.5
0.4 0.4
0.3 0.3
0.2 0.2
BetaGeneral Logistic
0.1 0.1
0.0 0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Input p-Value Input p-Value
Figure 3. a) Spatial distribution of ship’s hull position rela- Figure 4. a) Spatial distribution of ship’s hull position rel-
tive to the axis of the track at one cross section; b) probabil- ative to the axis of the track at one cross section; b) proba-
ity; c) P-P graph. Adlerground TSS. General cargo vessels bility; c) P-P graph. Adlerground TSS. Oil product tankers
tankers within a given variable is statistically signif- n2 n2 1
U 2 n1n2 R2 (5)
icant (Table 1). 2
The U-test statistic for the Mann-Whitney test is nn
given by the smaller of U1 and U2 as defined below: U1 1 2
Z 2
(6)
U1 n1n2
n1 n1 1
R1 (4)
n1n2 n1 n2 1
n1n2 t 3 t
2 12 12 n1 n2 n1 n2 1
Zeszyty Naukowe Akademii Morskiej w Szczecinie 53 (125) 85Agnieszka Nowy, Lucjan Gucma
a) Fit Comparison for GC and OPT b) Fit Comparison for GC and OPT
Eastbound Traffic Westbound Traffic
0.0012 0.0014
0.0012
0.0010
0.0010
Probability Density
0.0008
Probability Density
0.0008
0.0006
0.0006
0.0004
0.0004
0.0002
0.0002
0.0000 0.0000
–2000
–1500
–1000
–500
0
500
1000
1500
2000
–2000
–1500
–1000
–500
0
500
1000
1500
2000
Distance from center [m] Distance from center [m]
Logistic OPT Persons GC 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" TSS Słupska Bank "West"
650 400
300
Standard deviation [m]
SD S_lane GC
600
SD N_lane GC 200 Mean S_lane GC
Mean N_lane GC
Mean [m]
SD S_lane OPT
100 Mean S_lane OPT
550 SD N_lane OPT
Mean N_lane OPT
0
–100
500
–200
450 –300
1 3 5 7 9 11 1 3 5 7 9 11
Section of traffic lane Section of traffic lane
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
Vari- Rank Sum Vari- Rank Sum
TSS U Z p TSS U Z p
able OPT GC able OPT GC
Adlerground M 197.0 103.0 25.0 2.685 0.007* Gdansk „East”/ M 204.0 391.0 51.0 –3.203 0.001*
Eastbound SD 91.0 209.0 13.0 –3.377 0.001* Southbound SD 288.0 307.0 135.0 –0.310 0.757
Adlerground M 79.0 221.0 1.0 –4.070 0.000* Bornholmsgat/ M 855.0 1098.0 359.0 –1.704 0.088
Westbound SD 78.0 222.0 0.0 –4.128 0.000* Southbound SD 706.0 1247.0 210.0 –3.801 0.000*
Slupska Bank M 341.0 124.0 4.0 4.478 0.000* Bornholmsgat/ M 912.0 1041.0 416.0 –0.901 0.367
“East”/Eastbound SD 261.0 204.0 84.0 1.1614 0.245 Northbound SD 524.0 1429.0 28.0 –6.364 0.000*
Slupska Bank M 106.0 300.0 1.0 –4.434 0.000* Rugen/ M 15.0 40.0 0.0 –2.507 0.012*
„East”/Westbound SD 152.0 254.0 47.0 –2.320 0.020* Eastbound SD 15.0 40.0 0.0 –2.507 0.012*
Słupska Bank M 55.0 155.0 0.0 –3.742 0.000* Rugen/ M 132.0 121.0 55.0 0.328 0.743
„West”/Eastbound SD 143.0 67.0 12.0 2.835 0.005* Westbound SD 89.0 164.0 23.0 –2.430 0.015*
Słupska Bank M 147.0 63.0 8.0 3.137 0.002* Midsjobankarna/ M 75.0 61.0 25.0 0.683 0.495
„West”/Westbound SD 155.0 55.0 0.0 3.742 0.00* Eastbound SD 36.0 100.0 0.0 –3.308 0.001*
Gdansk„West”/ M 261.0 204.0 84.0 1.161 0.245 Midsjobankarna/ M 101.0 52.0 7.0 2.742 0.006*
Northbound SD 267.0 198.0 78.0 1.410 0.158 Westbound SD 56.5 96.5 20.5 –1.443 0.149
Gdansk „West”/ M 184.0 281.0 64.0 –1.991 0.046* South Hoburgs M 177.0 123.0 45.0 1.530 0.126
Southbank SD 275.0 190.0 70.0 1.742 0.081 Bank/Eastbound SD 145.0 155.0 67.0 –0.260 0.795
Gdansk „East”/ M 284.0 311.0 131.0 –0.448 0.654 South Hoburgs M 132.0 121.0 55.0 0.328 0.743
Northband SD 214.0 381.0 61.0 –2.859 0.004* Bank/Westbound SD 89.0 164.0 23.0 –2.430 0.015*
86 Scientific Journals of the Maritime University of Szczecin 53 (125)Modelling the lateral distribution of ship traffic in traffic separation schemes
where: • Oil product tankers (OPT):
R1 – rank sum for group 1 (OPT);
R2 – rank sum for group 2 (GC); σ = 0.1332·D + 96.888 (8)
n1, n2 – sample size;
Z – value of Mann-Whitney test, when the sample where: σ is the standard deviation of a ship’s dis-
size of both groups is greater than 20; tance from the centre [m]; D is the width of the traf-
p – significance level for the test (for the Z test fic lane [m].
value); By building individual sub-models for distinct
U1 can be replaced by U2; types of ship, waterway and navigational conditions,
t – number of cases included in tied rank. etc. it is possible to create a general model of ship
The Mann-Whitney test is a nonparametric equiv- traffic flows. The aim of the model is to determine
alent of the t-test for independent data. According to the standard deviation according to the mentioned
the results of the Monte Carlo test in some cases, this parameters and the distance to danger. The results
test is even stronger than the t-test. When the test obtained can be implemented in navigation risk
feature has no normal distribution, the Mann-Whit- assessment models.
ney test can be safely used because the chance of It can be seen that, despite there being a statisti-
accepting the alternative hypothesis, if it is true, it is cally significant difference between samples for gen-
not less than the chance of rejecting the null hypoth- eral cargo vessels and oil product tankers, there is
esis by the t-test (Francuz & Mackiewicz, 2007). no distinct difference between the models (Figure 8).
In Figure 7a, the relationship between the stan-
1400
dard deviation of a ship’s distance from the centre
and the width of the traffic lane, D,is shown. It can 1200
be seen that there is a linear correlation between
Standard deviation σ [m]
1000
these parameters with a correlation coefficient of
more than 0.8. This seems to be a very important 800
conclusion in the scope of traffic model creation.
600
This is due to the way the navigator navigates in cer-
tain areas. The more difficult (the narrower) the area 400
for navigation, the more accurately the steering of
200
the vessel is performed.
These results allowed a linear regression model 0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
to be built for the standard deviation of ship tracks in Width of traffic lane D [m]
the TSS for two groups of analysed ships: General cargo vessel Oil product tanker
• General cargo vessels (GC):
Figure 8. Comparison of two models: general cargo vessels
σ = 0.1519·D + 87.291 (7) and oil product tankers
a) Regression of Standard Deviation by Width of Traffic Lane b) Pred(Standard Deviation) / Standard Deviation
[m] (R2 = 0.731) 1400
1400
1200
1200
Standard Deviation
1000 1000
Standard Deviation
800
800
600
600
400
200 400
0
0 1000 2000 3000 4000 5000 6000 7000 200
–200
Width of traffic lane [m] 0
–200 0 200 400 600 800 1000 1200 1400
Model (Standard Deviation) Conf. interval (Mean 95%)
–200
Conf. interval (Obs 95%) Pred(Standard Deviation)
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
Zeszyty Naukowe Akademii Morskiej w Szczecinie 53 (125) 87Agnieszka Nowy, Lucjan Gucma
In the case of the oil product tankers, where general- Further studies are planned in this field for oth-
ly the crew is more highly trained and experienced, er traffic routes. The influence of vessel size (L, T),
the deviations are smaller which indicates a more type, and distance to danger will be determined.
accurate navigational system with compliance to
rules. Tankers, as vessels with highly dangerous car- Acknowledgments
go, keep away from other vessels and navigate with
extra caution. This research outcome has been achieved under
the grant No. 11/MN/IIRM/17 financed from a sub-
Conclusions sidy of the Ministry of Science and Higher Educa-
tion for statutory activities.
This paper presents the results of research into
ship traffic flow models in the Baltic Sea. Vessel References
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matical model of traffic. tion 65, pp. 99–112.
Models for two vessel groups were built (gen- 2. Blokus-Roszkowska, A. & Smolarek, L. (2014) Maritime
eral cargo and oil product tankers). The results traffic flow simulation in the intelligent transportation sys-
tems theme. Safety and Reliability: Methodology and Appli-
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