Modelling the lateral distribution of ship traffic in traffic separation schemes

Transcription

1 Scientific Journals of the Maritime University of Szczecin Zeszyty Naukowe Akademii Morskiej w Szczecinie 18, 53 (15), ISSN (Printed) Received: ISSN (Online) Accepted: DOI: 1.174/69 Published: Modelling the lateral distribution of ship traffic in traffic separation schemes Agnieszka Nowy, Lucjan Gucma Maritime University of Szczecin 1 Wały Chrobrego St., 7-5 Szczecin, Poland {a.nowy; l.gucma}@am.szczecin.pl corresponding author Key words: vessel traffic streams, ships traffic flow, safety of navigation, probabilistic model, traffic separation 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 historical 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, safety 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 insufficient 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 capabilities emerged with the AIS (Automatic Identification 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 distribution function for the position of a ship were conducted 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 distribution is widely used to calculate the number of encounters in cross-traffic lanes. Pedersen (Pedersen, ) introduced a model to calculate the collision risk in a congested shipping lane and to investigate 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, 1) was based on a dynamic extensive microsimulation of maritime traffic using the Monte Carlo simulation technique in a given area. Detailed studies on vessel Zeszyty Naukowe Akademii Morskiej w Szczecinie 53 (15) 81

2 Agnieszka Nowy, Lucjan Gucma traffic statistics were conducted. The important factor used in the model was the daily variation in traffic (Montewka et al., 11); however, that factor can be applied to particular areas only. A number of studies have been performed in certain waters including the Gulf of Finland (Montewka et al., 11), Japan Strait (Yamaguchi & Sakaki, 1971) and Adriatic (Lušić, Pušić & Medić, 17). Traffic flow in the Istanbul Strait was analysed to improve the safety of navigation (Aydogdu et al., 1). 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, 13). A lot of research on maritime traffic flow was conducted by Chinese colleagues (Feng, 13; Wen et al., 15; Liu et al., 17). A mathematical model was initially developed using classical traffic flow theories (Yip, 13). The combination of an integrated 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, 13). A cellular automaton model that provides the basis for simulation and vessel traffic management was developed (Blokus-Roszkowska & Smolarek, 14). Another approach is to model ship traffic flow in the context of concept drift (Osekowska, Johnson & Carlsson, 17) 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 distribution of ships. The calculations are performed partially with the mathematical software tool IWRAP MK 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 traffic 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, 13). 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, 13). 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 considered 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 random process and probabilistic methods are used for its description. One of the main parameters describing the traffic 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 normal 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 distribution of ship traffic depends largely on the type of route (bend, straight) and its character (Traffic Separation Scheme, narrow channel etc). Preliminary 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 distributions. The most common distributions are the normal distribution, logarithmic distribution, gamma 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, 9). 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 dependent on the ship s length (L). 8 Scientific Journals of the Maritime University of Szczecin 53 (15)

3 Modelling the lateral distribution of ship traffic in traffic separation schemes To create a model for ship route design, different types of waterways and ship types and dimensions (L, T) should be considered. The studies presented 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 applications where a ship is travelling on a given route with coordinate y =, the distribution of the ship s hull position relative to the axis of the lane can be transformed into a conditional distribution of the condition x 1 < X < x, where x 1 and x are considered to be the section range (Gucma, 6). The cumulative distribution function is presented in the form: F Y X (y, x) = P(Y y x 1 < X < x ) () 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 crossing/exit, P C, of the boundary line in position X i as (Gucma, 6): Methods Study area P C 1 F Y X X 1 (3) The Baltic Sea has relatively dense traffic. There are a number of traffic separation schemes established 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 navigation and the protection of the marine environment in most of the major congested shipping areas. There are regulations specifically established for traffic separation schemes. Rule 1 of the COLREGs (Convention, 197) precisely describes how navigators 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 1 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; ) 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 MK software, v5..beta) Data Research has been conducted on the basis of data collected from AIS obtained from the Polish Maritime Administration. Vessel traffic was analysed using data from March to May 17. The two largest groups of ships, general cargo (GC) and oil product tanker (OPT),were considered to be the most common in the given area. AIS raw data was processed using the IWRAP MK application. IWRAP is a modelling tool useful for maritime risk assessment. Using IWRAP, the frequency of collisions and groundings in a given waterway, based on information about traffic volume/composition and route geometry, can be estimated (Engberg, 16). The statistical function can be found using historical AIS data. The traffic patterns 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 histogram for each direction, the mathematical representation 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 Zeszyty Naukowe Akademii Morskiej w Szczecinie 53 (15) 83

4 Agnieszka Nowy, Lucjan Gucma the main parameters describing the traffic flow is the distribution, describing the ship s hull position relative 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 characterisation by means of a single, specific resolution. This research consisted mainly of matching the distribution of traffic in relation 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 ). For subsequent sections, lateral distributions were determined by analysing the number of ship crossings of report lines perpendicular to each route. Figure. 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 determined. The aim of the study was to find a relationship between this standard deviation and the width of the traffic lane. Results Figures 3a and 4a show examples of spatial distributions, 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 modelled by different distributions. This is necessary to calculate collision probability. Their goodness of fit is first determined by performing a Chi-square test (χ). This test determines the degree of agreement between the empirical distribution and the theoretical 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 Information 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., 1). The P-P (Probability-Probability) 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 relation 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 deviation of the lateral distribution for each section 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 1 m, but in the following sections it decreases to 1 m. For N_lane, the differences are comparable for all sections of the track (6 m to over 1 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 statistically 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 <.5 are marked by *. If p is less than.5 then the difference between general cargo vessels and oil product 84 Scientific Journals of the Maritime University of Szczecin 53 (15)

5 Modelling the lateral distribution of ship traffic in traffic separation schemes a) a) 9 Fit Comparison for Distance from center BetaGeneral(1.167;5.3953; 347.8;1993) 5.% 6.5% 35 9.% 87.9% 5.% 5.6% Fit Comparison for Distance from center Logistic(47.99;17.64) 5.% 9.% 5.%.4% 9.7% 6.8% Probability Density, Values Probability Density, Values b) b) Fit Comparison-Probability BetaGeneral(1.167;5.3953; 347.8;1993) Fit Comparison-Probability Logistic(47.99;17.64) 1. 5.% 6.5% 9.% % % 5.6% 1. 5.%.4% 9.% % % 6.8%.8.8 Probability.6.4 Probability Input BetaGeneral Input 1 5 Logistic c) c) Fitted p-value Probability-Probability Plot of Distance from center BetaGeneral(1.167;5.3953; 347.8;1993) Input p-value Figure 3. a) Spatial distribution of ship s hull position relative to the axis of the track at one cross section; b) probability; c) P-P graph. Adlerground TSS. General cargo vessels BetaGeneral Fitted p-value Probability-Probability Plot of Distance from center Logistic(47.99;17.64) Input p-value.7 Logistic Figure 4. a) Spatial distribution of ship s hull position relative to the axis of the track at one cross section; b) probability; c) P-P graph. Adlerground TSS. Oil product tankers tankers within a given variable is statistically significant (Table 1). The U-test statistic for the Mann-Whitney test is given by the smaller of U 1 and U as defined below: U n n n1n R1 (4) n n 1 U n1n R (5) Z n1n U1 3 n 1 1 1n n1 n n n t t 1 1 n n n n 1 (6) 1 1 Zeszyty Naukowe Akademii Morskiej w Szczecinie 53 (15) 85

6 Agnieszka Nowy, Lucjan Gucma a) b) Fit Comparison for GC and OPT Eastbound Traffic Fit Comparison for GC and OPT Westbound Traffic Probability Density Probability Density 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) 65 TSS Słupska Bank "West" 4 TSS Słupska Bank "West" Standard deviation [m] SD S_lane GC SD N_lane GC SD S_lane OPT SD N_lane OPT Mean [m] Mean S_lane GC Mean N_lane GC Mean S_lane OPT Mean N_lane OPT 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 * Gdansk East / M * Eastbound SD * Southbound SD Adlerground M * Bornholmsgat/ M Westbound SD * Southbound SD * Slupska Bank M * Bornholmsgat/ M East /Eastbound SD Northbound SD * Slupska Bank M * Rugen/ M * East /Westbound SD * Eastbound SD * Słupska Bank M * Rugen/ M West /Eastbound SD * Westbound SD * Słupska Bank M * Midsjobankarna/ M West /Westbound SD * Eastbound SD * Gdansk West / M Midsjobankarna/ M * Northbound SD Westbound SD Gdansk West / M * South Hoburgs M Southbank SD Bank/Eastbound SD Gdansk East / M South Hoburgs M Northband SD * Bank/Westbound SD * 86 Scientific Journals of the Maritime University of Szczecin 53 (15)

7 Modelling the lateral distribution of ship traffic in traffic separation schemes where: R 1 rank sum for group 1 (OPT); R rank sum for group (GC); n 1, n sample size; Z value of Mann-Whitney test, when the sample size of both groups is greater than ; p significance level for the test (for the Z test value); U 1 can be replaced by U ; t number of cases included in tied rank. The Mann-Whitney test is a nonparametric equivalent 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-Whitney 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 hypothesis by the t-test (Francuz & Mackiewicz, 7). In Figure 7a, the relationship between the standard 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.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 certain 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 =.1519 D (7) Oil product tankers (OPT): σ =.133 D (8) where: σ is the standard deviation of a ship s distance from the centre [m]; D is the width of the traffic 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 statistically significant difference between samples for general cargo vessels and oil product tankers, there is no distinct difference between the models (Figure 8). Standard deviation σ [m] Width of traffic lane D [m] General cargo vessel Oil product tanker Figure 8. Comparison of two models: general cargo vessels and oil product tankers a) b) Standard Deviation Regression of Standard Deviation by Width of Traffic Lane [m] (R =.731) Width of traffic lane [m] Model (Standard Deviation) Conf. interval (Mean 95%) Conf. interval (Obs 95%) Pred(Standard Deviation) / Standard Deviation 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 <.5, R =.8549, p =. Standard Deviation Zeszyty Naukowe Akademii Morskiej w Szczecinie 53 (15) 87

8 Agnieszka Nowy, Lucjan Gucma In the case of the oil product tankers, where generally the crew is more highly trained and experienced, the deviations are smaller which indicates a more accurate navigational system with compliance to rules. Tankers, as vessels with highly dangerous cargo, 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 distributions are the basis for the development of a mathematical model of traffic. Models for two vessel groups were built (general cargo and oil product tankers). The results show a small difference between these two models, despite there being a statistically significant difference 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 standard 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 accepted interpretation which leads to further research on the topic. The presented method, based on a simple regression model, can be used for designing waterway systems 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 segments and the location-specific results will be generalised 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 simulation of the individual vessel paths. Further studies are planned in this field for other 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 subsidy of the Ministry of Science and Higher Education for statutory activities. References 1. Aydogdu, Y.V., Yurtoren, C., Park, J.S. & Park, Y.S. (1) A study on local traffic management to improve marine traffic safety in the Istanbul Strait. Journal of Navigation 65, pp Blokus-Roszkowska, A. & Smolarek, L. (14) Maritime traffic flow simulation in the intelligent transportation systems theme. Safety and Reliability: Methodology and Applications-Proceedings of the European Safety and Reliability Conference (ESREL 14), pp Convention (197) Convention on the International Regulations for Preventing Collisions at Sea. London, October Dziak, J., Coffman, D., Lanza, S. & Li, R. (1) Sensitivity and specificity of information criteria. Technical Report Series # The Methodology Center of The Pennsylvania State University. 5. Engberg, P.C. (16) IWRAP MK v5.. Manual. Gate- House A/S. 6. Feng, H. (13) Cellular automata ship traffic flow model considering integrated bridge system. International Journal of u- and e- Service, Science and Technology 6, 6, pp Francuz, P. & Mackiewicz, R. (7) 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 4 th International PIANC Congress, Leningrad. 9. Fuji, Y., Yamanouchi, H. & Mizuki, N. (1974) Some Factors Affecting the Frequency of Accidents in Marine Traffic. Journal of Navigation 7(), p Goerlandt, F. & Kujala, P. (1) Modeling of ship collision probability using dynamic traffic simulation. Reliability, Risk and Safety. Ale, Papazoglou & Zio (Eds). London: Taylor & Francis Group, pp Gucma, L. (1999) Kryterium bezpieczeństwa manewru na torze wodnym. Materiały na Konferencję Explo-Ship, WSM, Szczecin. 1. Gucma, L. (6) The method of navigation risk assessment on waterways based on generalised real time simulation data. Proc. of International MARSIM Conference, Terschelling. 13. Gucma, L., Perkovic, M. & Przywarty, M. (9) Assessment of influence of traffic intensity increase on collision probability in the Gulf of Trieste. Annual of Navigation 15, pp Gucma, S. (13) Optimization of sea waterway system parameters in marine traffic engineering. Journal of KONBiN (6), pp Scientific Journals of the Maritime University of Szczecin 53 (15)

9 Modelling the lateral distribution of ship traffic in traffic separation schemes 15. Gucma, S., Ślączka, W. & Zalewski, P. (13) Parametry torów wodnych i systemów nawigacyjnych wyznaczane przy wykorzystaniu bezpieczeństwa nawigacji. Monography edited 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 Dimensions of Ship Manoeuvering Areas. PIANC Bulletin No. 1, Bruxelles. 19. Liu, Z., Liu, J., Li, Z., Liu, R.W. & Xiong, N. (17) Characteristics analysis of vessel traffic flow and its mathematical model. Journal of Marine Science and Technology 5(), pp Lušić, Z., Pušić, D. & Medić, D. (17) 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 Infrastructure and Systems. Dell Acqua G. & Wegman F. (Eds) pp MacDuff, T. (1974) The Probability of Vessel Collisions. Ocean Industry.. Montewka, J., Krata, P., Goerlandt, F., Mazaheri, A. & Kujala, P. (11) Marine traffic risk modeling an innovative approach and a case study. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 5 (3). pp Osekowska, E., Johnson, H. & Carlsson, B. (17) Maritime vessel traffic modeling in the context of concept drift. Transportation Research Procedia 5, pp Pedersen, P.T. () Collision risk for fixed offshore structures close to high density shipping lanes. Journal of Engineering for the Maritime Environment 16 (1), pp Puszcz, A. & Gucma, L. (11) Towards the Model of Traffic Flow on the Southern Baltic Based on Statistical Data. Proc. of the 9 th International Trans-Nav Conference, Vol. 5, Gdynia. 6. Silveira, P.A.M., Teixeira, A.P. & Guedes Soares, C. (13) Use of AIS Data to Characterise Marine Traffic Patterns and Ship Collision Risk off the Coast of Portugal. The Journal of Navigation, 66, pp Wen, Y.Q., Huang, Y.M., Zhou, C.H., Yang, J.L., Xiao, C.S. & Wu, X.C. (15) Modelling of marine traffic flow complexity. Ocean Engineering 14, pp Yamaguchi, A. & Sakaki, S. (1971) Traffic surveys in Japan. Journal of Navigation 4, pp Yip, T.L. (13) A marine traffic flow model. International Journal on Marine Navigation and Safety of Sea Transportation 7, 1, pp Zeszyty Naukowe Akademii Morskiej w Szczecinie 53 (15) 89