Influence of maritime traffic organization at waterways crossings on the safety level of navigation

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1 BLOKUS-ROSZKOWSKA Agnieszka 1 SMOLAREK Leszek 2 Influence of maritime traffic organization at waterways crossings on the safety level of navigation INTRODUCTION Maritime transport is of great importance as it is the basis of international trade. Cargo transport is increasing rapidly and the waterways are more congested. To overcome challenges in modern maritime transportation and face the logistical organization it is necessary to apply new alternative solutions for operational optimization [7, 12, 13]. The permanent increase of the ship s traffic density causes the growth of collision. Therefore, potential collision prevention and evaluation of ship-ship collision is important task for vessel navigational systems, as well as vessel traffic monitoring and information systems, to improve maritime safety. The paper introduces model of cellular automaton allowing to emulate vessels flows. We focus on waterway crossings simulation in restricted area, specifically estimation of risk collision at a simple crossing and at a roundabout. Simulation program based on the cellular automaton model allows not only for estimation of of ship collision s risk but also of occurrence of potentially dangerous situation. Considered priority scenarios and performed traffic simulation at waterways crossing are not devoted to change rules on the level of vessels navigation. They can be applied during creating concepts of maritime traffic organization and management in restricted area with developed Vessel Traffic Management (VTM) system including Vessel Traffic Services (VTS), especially in ports area in order to increase safety of navigation. 1. A CELLULAR AUTOMATON MODEL FOR MARITIME TRAFFIC Cellular automata (CA) are very efficient way to implement not only traffic flow, but also in other fields such as pedestrian behaviour, escape and panic dynamics, the spreading of forest fires, material properties etc. [8, 17]. In this paper CA are applied to vessels flow modeling in VTS area. Cellular automata models could give us an idea of how risk of collision influence on navigation safety even if they emulate nature in more than a rough way. In basic cellular automaton traffic flow model four main rules are usually applied to all cars. These are: acceleration, braking (deceleration), randomization (of velocity) and driving (car movement) [1, 1]. The cellular automaton model can be proposed for description of single-lane traffic, multi-lane traffic, ramps or roundabout, however four basic rules, mentioned above are necessary to reproduce the basic phenomena encountered in real traffic. For description of more complex situation some additional rules can be added or the basic rules can be modified [15]. Some modifications of Nagel- Schrekenberg model are based on implementing so called slow-to-start rules, where standing cars accelerate with lower (slower) than moving cars. Such a modification of the acceleration rule is introduced in Takayasu and Takayasu (T 2 ) model [16] or in Benjamin-Johnson-Hui (BJH) model [2]. Other models propose for example modification of randomization rule by adding velocitydependent randomization [1]. Most of rules describing vehicles motion can not be easily imported to vessels movement as vessels usually move with constant velocity so acceleration, deceleration and velocity randomization rules have no application on waterways. An exception to this rule is vessel s acceleration in restricted area in order to avoid collision. Similarly as in multi-lane models we provide rules for lane changes, however in vessels movement these rules are usually used for describing collision avoidance instead of slowing down 1 Akademia Morska w Gdyni, Wydział Nawigacyjny; Gdynia, ul. Morska Tel: , a.blokus-roszkowska@wn.am.gdynia.pl 2 Akademia Morska w Gdyni, Wydział Nawigacyjny; Gdynia, ul. Morska Tel: , leszsmol@ am.gdynia.pl 553

2 or acceleration. The specification of vessels movement and behaviour is quite different than drivers behaviour. The lane-changing behaviour of vehicles is usually concerned with local density and is based on three criteria: incentive criterion, improvement criteria and safety criteria [14]. Thus to initiate lane change the situation on the other lane must be more convenient (the number of empty cells in the other lane must be grater than the number of empty cells before the vehicle) and the safety rule must be followed (the number of empty cells between the vehicles and its neighbor vehicle in the other lane back must be grater than maximum vehicle velocity). In maritime traffic distance between a vessel and other vessel being on collision course (the number of empty cells between two vessels) must be know in order to perform the collision avoidance manoeuvre. The necessary distance to take evasive action depends on vessel s size, velocity and maneuverability. Thus it is clear that vessel motivation for lane-changing manoeuvre is quite different than in description of road traffic and can not be expressed with the same rules. In this paper we use cellular automaton for describing maritime traffic in separation area of lanes crossing (a simple crossing or a roundabout) in a distance of 6 nm (nautical miles). A crossing s geometry for considered situation is widely described in [4, 5]. Taking this into account while implementing vessel motion in this area we do not consider overtaking rule. First we propose following modification of movement rule from the Nagel-Schrekenberg model: ( t t) ( t) x i xi vi, if ith vessel in not performing an avoidance manoeuvre, where: x the position of ith vessel at a time t, (t) i v i velocity of ith vessel, t a time step. The velocity of a vessel do not depend on parameter t as we assume that in the considered distance of lanes crossing vessels move with constant velocity. In separation area vessels move with limited velocity usually form interval 1-15 knots. The second rule of cellular automaton model of maritime traffic is collision avoidance. In cellular automaton traffic flow model, presented in [11], collision avoidance rule is concerned with assumption that a car does not overtake its preceding car, including anticipation. Here for vessels performing an avoidance manoeuvre we can implement some collision avoidance rules depending on vessels size, velocity, type (maneuverability) and distance to the lanes crossing. We distinguish two types of collision avoidance rule. First case performing an avoidance manoeuvre by course changing and second possibility avoiding collision by change of velocity i.e. significant acceleration. Some types of vessels can reach much higher velocities that limit value in restricted area and in collision situation they can speed up to 2 knots, in case of fast ferry can reach speed even over 3 kn. A collision avoidance manoeuvre should be preceded by starting evasive action rule that determine whether a vessel starts collision avoidance manoeuvre taking into account distance between vessels and of taking evasive action by give-way and stand-on vessel. Described rules can be applied for all vessels, however for different type of vessels rules are used with different parameters affecting of taking evasive action, time of performing collision avoidance manoeuvre as well as velocity in movement rule. Another factor that influence the decision of taking evasive action and its performance is vessel s priority. 2. SIMULATION PROGRAM AND RESULTS Cellular automaton model is able to describe different types of vessels evolving different type of intersections. In simulation we consider a simple crossing with distinguished main flow having priority and a roundabout with three different priority scenarios [6]. First case, when a vessel having other vessel on her own starboard side shall keep out of the way. Second scenario when a vessel being on a roundabout-lane has priority and vessel entering roundabout crossing is directed to keep out of the way. And third case a roundabout with distinguished main flow having priority. 554

3 An example of area with high maritime traffic intensity, where one of solutions of waterways crossing organization is a roundabout can be the port of Rotterdam area. VTS plan of the port of Rotterdam is given in figure 1. Fig. 1. VTS plan of the port of Rotterdam. Source: In safety analysis we distinguish four states corresponding to risk levels and their critical distances. As proposed model is applied to safety analysis of maritime traffic in restricted area we assume following criteria in defining safety states: state 3 (negligible risk of collision), when both vessels being on collision course are in a safety distance defined as 1 nm (d 3 ); state 2 (low risk of collision corresponding to a safety distance), when both vessels being on collision course are in a distance,5 nm (d 2 ); state 1 (high risk of collision), when both vessels being on collision course are in a distance of double length of larger vessel (d 1 ); state (collision alert), when two vessels are in a distance shorter than d 1. To present all possible scenarios included in safety analysis at the waterways crossing we use event tree analysis. The event tree, presented in figure 2, start with an initiating event that is vessels starting on the main and lateral waterways. Presented event tree identify possible transitions between safety states of the system of waterways crossing. In order not to take into account the same transition twice we observe the situation at crossing from the point of view of vessels on main waterway. The final outcome of a sequence of events is a collision alert, however it is not an absorbing state. We define a state that is collision alert as a situation when two vessels on collision courses are in a distance shorten than d 1 corresponding to the situation of two vessels domains overlapping. We do not verify whether the vessel managed to avoid collision or estimate the of vessels collision occurrence. In simulation we assume a vessel even in situation of collision alert moves further. We analyze transitions between states till passing all collision points by the vessel on main waterway in the observed restricted area. 555

4 Fig. 2. Event tree for analysis of possible transitions between safety states of the system of waterways crossing. 556

5 2.1. Sensitivity analysis of traffic intensity In simulation program we consider major ship types dividing them into two groups. First group constitute vessels that can reach large speed that is can avoid collision in VTS area by significant acceleration: a container carrier, a RoPax, a passenger ship, reefer and fast ferry. The second group of vessels is made by a tanker, a bulk carrier and general cargo ships. The simulation is carried out with randomly generated initial configuration on vessels parameters and behaviour (vessel s type, size and speed, of taking evasive action, of choosing destination waterway) and traffic flows parameters (flows intensities, distributions). We assume weather conditions are tolerable. For each class of vessel on main and lateral route vessel velocity is taken into the model by random sampling according to fitted, on basis of data recorded in Gulf of Finland, distribution [9]. As input length of ship we assumed the mode for considered types of vessel using collected data. The input data of traffic flows parameters for performed simulation are randomly chosen with assumed mean value and standard deviation for each flow, on the basis of system flows analysis presented in [3]. Analyzing outcomes of the simulation program we have observed sensitivity of value of traffic intensity and other vessels parameters. Taking into account the of vessels collision depending on mean time period between consecutive vessels departures on main route that is value of parameter T 1 we obtain following results of average value, lower bound (smallest value) and upper bound (largest value). We assume that vessels start according to fixed distribution with fixed mean time and standard deviation. The results for a simple crossing with distinguished main route having priority of of collision alert, high risk of collision, low and negligible risk of collision are presented in figures 3a-d, equivalently. 1a),2 1b),4,18,16,14,12,35,3,25,1,2,8,15,6,4,2,1,5,4,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5,4,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5 1c),45 1d) 1,4,9,35,3,25,2,15,8,7,6,5,4,3,1,2,5,1,4,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5,4,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5 Fig. 3. Bounds for of a) collision alert, b) high risk, c) low risk, d) negligible risk of collision in case maritime traffic scenario: a simple crossing with distinguished main flow having priority. 557

6 The average of collision alert is placed on the level between,2,4 with highrisk time interval,8,9 h and 1,2 1,3 h. In a case of a roundabout the of vessels collision is much lower for larger values of parameter T 1. A variable T 1 denotes the main time between consecutive vessels departures on main route. The simulation both for a simple crossing and a roundabout have been performed under the same conditions and parameters values. Considering a roundabout we observe results for a priority scenario referring to priority scenario in a case of a simple crossing. That mean there is distinguished main route for example East-West with stand-on vessels and vessels being on other two lanes entering a roundabout for example North- South are give-way vessels. The results for a roundabout traffic scenario of are equivalently depicted in figures 4a-d. 2a),14 2b),8,12,7,1,6,8,5,6,4,3,4,2,2,1,4,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5,4,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5 2c),12 2d) 1,2,1 1,98,8,96,94,6,92,4,9,88,2,86,84,4,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5,82,4,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5 Fig. 4. Bounds for of a) collision alert, b) high risk, c) low risk, d) negligible risk of collision in case maritime traffic scenario: a roundabout with distinguished main flow having priority. Analyzing simulation results obtained in a case of a roundabout we can conclude that average of collision does not differ very much and falls noticeably over value 1,1 h of parameter T 1. However taking into account maximum values of of collision and high risk of collision we can observe a high-risk area under value,6 h and for value interval 1 1,1 h of parameter T 1. It can be noticed that of occurrence of low risk of collision is significantly lower in a case of a roundabout than for a simple crossing s geometry. The simulation output indicates that variability of parameter T 1 value in traffic flow has more significant effect on of collision s risk for a roundabout than for a simple crossing Analysis of crossing s geometry and priority scenarios The simulation results for different crossing s geometry and priority scenarios have been analyzed graphically and presented in figures 5a-d. Simulation run under various crossing s geometric 558

7 conditions for fixed, on the basis of results presented in [3] and [9], traffic flow s parameters. For the simulation need we assume the ships starting times on the main waterway follow normal distribution with mean value 2,21 h and standard deviation,52 h. On the lateral waterways we assume Erlang distribution with the mean time between ships departing equal to 1,21 h and standard deviation,95 h and 1,3 h, equivalently for both directions. of collision alert of high risk of collision,45,8,4,7,35,3,25,2,15,1,5,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 distance between collision points (nm) rondo 1 way priority rondo right-way priority rondo rondo-way priority,6,5,4,3,2,1,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 distance between collision points (nm) rondo 1 way priority rondo right-way priority rondo rondo-way priority,4,35,3,25,2,15,1,5 of low risk of collision,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 distance between collision points (nm) rondo 1 way priority rondo rondo-way priority rondo right-way priority,96,95,94,93,92,91,9,89,88,87,86 of negligible risk of collision,5,6,7,8,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 distance between collision points (nm) rondo 1 way priority rondo rondo-way priority rondo right-way priority Fig. 5. Probability of a) collision alert, b) high risk of collision, c) low risk of collision, d) negligible risk of collision depending on distance between collision points for different priority scenarios of a roundabout. From the analysis of ships collision, with respect to the distance between collision points i.e. the roundabout-lane size, we can distinguish lower-risk area for distance interval,6,8 nm and 1,4 1,6 nm. A detailed comparison of simulation output for various priority scenarios of roundabout traffic does not result in any regularity observation for of occurrence of collision s risk. This indicates that for example larger roundabout-lane size does not assure more safety of waterways crossing. Moreover it seems that of collision alert for larger values of distance between collision points can be even higher. This conclusion can arise due to the fact that for larger distances between collision points vessels moving on the roundabout-lane cross each collision point as a single collision risk area. Whereas in case collision points are located close to each other vessels cross a roundabout as one large collision risk area without taking unnecessary additional evasive action at each collision point. As a next step we plan to analyze situation when a vessel priority is not concerned with course direction or traffic lane on which vessel move but each vessel has defined priority concerned with unit specification. Then we will compare this model with traffic scheme scenarios presented above in this paper in terms of navigation safety. 559

8 2.3. Sensitivity analysis of waterways crossing angle In the paper we consider crossing situation in which an angle of intersection α of two vessels courses falls in the range 1º-17º. Below in figures 6 and 7 there are presented the results for a simple crossing with distinguished main route having priority of of collision alert, high risk of collision, low and negligible risk of collision depending on angle of waterways intersection.,5,45,4,35,3,25,2,15,1, of collision alert angle of intersection of vessels courses of high risk of collision,6,5,4,3,2, angle of intersection of vessels courses of collision alert of high risk of collision Fig. 6. Probability of collision alert and high risk of collision depending on an angle of intersection of vessels courses in case of maritime traffic scenario: a simple crossing with distinguished main flow having priority. We can notice that the of collision alert is on the similar level (between,5 and,15) for crossing angle between 5º and 12º. Moreover this is the lowest for angle of waterways intersection equal to 95º and 15º and amounts about,6. The of negligible risk of collision is the highest for 8º and 1º value of waterways crossing angle. 1,9,8,7,6,5,4,3,2, of low risk of collision 9 angle of intersection of vessels courses of negligible risk of collision 1,9,8,7,6,5,4,3,2, of low risk of collision angle of intersection of vessels courses of negligible risk of collision Fig. 7. Probability of low and negligible risk of collision depending on an angle of intersection of vessels courses in case of maritime traffic scenario: a simple crossing with distinguished main flow having priority. CONCLUSION We have introduced the cellular automaton model that is able to reproduce some of maritime traffic features such as vessels movement and collision avoidance manoeuvre. The presented model describes motion of different types of vessels evolving in different types of intersections (a roundabout crossing and a simple crossing) and priority scenarios. We studied via simulation sensitivity of vessels collision risk depending on the distance between collision points and mean time between consecutive vessels departures on main route. The relationship between these 56

9 parameters and of occurrence of high, low or negligible risk of collision can be used for design and analysis of maritime traffic at waterways crossing in VTS area. We also compared the obtained results for various priority scenarios of a roundabout i.e. when a vessel having the other vessel on its own starboard side shall keep out of the way, when a vessel being on a roundabout-lane has priority and a roundabout with distinguished main flow having priority. In the scope of the ITS theme the proposed cellular automaton model can be helpful in maritime transport both on the level of waterways crossing s planning and traffic management and control. Further investigation on this topic can potentially affect the tasks and decisions of various authorities related to maritime transport and traffic. Abstract Dynamic development of maritime transport in context of navigation safety has influence on the need of introducing new solutions of maritime traffic organization and future development of systems of vessels traffic control. Intelligent Transportation Systems using a wide range of new information and communication technologies can improve effectiveness of management and influence on safety improvement of maritime traffic. The crucial issue of vessels traffic safety is reducing risk of occurrence of vessels collisions at waterways crossings. In this paper there is presented analysis of various scenarios of traffic organization at waterways crossings in area controlled by Vessel Traffic Management (VTM) or Vessel Traffic Services (VTS). With this aim there is applied a cellular automaton model. Among the scenarios of traffic organization in VTS area there is presented a classical waterways crossing and a roundabout in three different cases of vessels traffic priority. There is considered classical priority rule according to the COLREGS, priority of vessel being at a roundabout-lane and distinguishing main lane with priority. Applied simulation program allowed for estimation of of collision risk and analysis of occurrence of potential threat situation. Obtained estimation of of collision in restricted area of waterways crossing can be used in traffic control systems for evaluation of maritime traffic safety. Wpływ organizacji ruchu skrzyżowań dróg morskich na poziom bezpieczeństwa żeglugi Streszczenie Dynamiczny rozwój transportu morskiego w kontekście bezpieczeństwa żeglugi skutkuje koniecznością wprowadzenia nowych rozwiązań organizacji ruchu morskiego oraz dalszego rozwoju systemów nadzoru ruchu statków. Inteligentne Systemy Transportowe, wykorzystując w szerokim zakresie nowoczesne technologie informacyjne i komunikacyjne, mogą podnieść efektywność zarządzania i wpłynąć na poprawę bezpieczeństwa ruchu morskiego. Kluczowym zagadnieniem bezpieczeństwa ruchu statków jest zmniejszenie ryzyka wystąpienia kolizji na skrzyżowaniach tras morskich. W artykule przedstawiona została analiza różnych scenariuszy organizacji ruchu na skrzyżowaniach dróg morskich nadzorowanych przez systemy rozgraniczenia ruchu z zastosowaniem modelu automatu komórkowego. Wśród różnych scenariuszy organizacji ruchu w obszarach zarządzania ruchem przedstawione zostało klasyczne skrzyżowanie dróg morskich oraz rondo w trzech różnych przypadkach pierwszeństwa ruchu dla statków t.j. klasyczna reguła pierwszeństwa zgodnie z przepisami MPDM, pierwszeństwo statku znajdującego się na rondzie oraz wyróżnienie głównej trasy z pierwszeństwem. Prezentowany program symulacyjny pozwolił na oszacowanie prawdopodobieństwa ryzyka kolizji oraz zbadanie prawdopodobieństwa wystąpienia sytuacji potencjalnego zagrożenia. Uzyskane oszacowanie prawdopodobieństwa wystąpienia kolizji w obrębie skrzyżowań może być wykorzystane w systemach nadzoru ruchu do oceny bezpieczeństwa ruchu morskiego. REFERENCES 1. Barlovic R. Santen L. Schadschneider A. & Schreckenberg M.: Metastable states in cellular automta for traffic flow, The European Physical Journal B, Vol. 5, pp , Benjamin S.C. Johnson N.F. & Hui P.M.: Cellular automata models of traffic flow along a highway containing a junction, J. Phys. A: Math. Gen. Vol. 29, pp ,

10 3. Blokus-Roszkowska A. Montewka J. Smolarek L.: Modelling the accident in largescale, maritime transportation system, Journal of Polish Safety and Reliability Association, Summer Safety and Reliability Seminars, Vol. 3, No. 2, pp , Blokus-Roszkowska A. & Smolarek L.: Application of simulation methods for evaluating the sea waterways traffic organisation, ISRN Applied Mathematics, Blokus-Roszkowska A. Smolarek L.: Collision risk estimation for motorways of the sea, Reliability: Theory & Applications, Vol. 1, No. 2(25), pp , Blokus-Roszkowska A. & Smolarek L.: Influence of traffic schemes on the level of vessels safety, Journal of KONBiN, No. 4(24), pp.5-12, Jamroz K. & Krystek R.: Inteligentne Systemy Transportu rozwój i struktura. Transport Miejski i Regionalny, 26, nr Maerivoet S. De Moor B.: Cellular automata models of road traffic, Physics Reports, Vol. 419, pp. 1-64, Montewka, J., Hinz T., Kujala, P., Matusiak, J.: Probability modeling of vessel collisions. Reliability Engineering and System Safety Vol. 95, pp , Nagel K. Schreckenberg M.: A cellular automaton model for freeway traffic, Journal de Physique I France Vol. 2, No. 12, pp , Nishinari K. Fukui M. & Schadschneider A.: A stochastic cellular automaton model for traffic flow with multiple metastable states, J. Phys. A: Math Gen. Vol. 37, pp , Pietrzykowski Z.: Maritime Intelligent Transport Systems. Transport Systems Telematics, Communications in Computer and Information Science, Vol. 14, pp , Planning a modern transport system. A guide to Intelligent Transport System architecture. European Communities, Rawat K. Katiyar V.K. & Gupta P.: Two-lane traffic flow simulation model via cellular automaton, International Journal of Vehicular Technology, Schadschneider A. & Schreckenberg M.: Traffic flow models with slow-to-start rules, Ann. Phys. Vol. 6, No. 7, pp , Takayasu M. & Takayasu H.: 1/f noise in a traffic model, Fractals Vol. 1, No. 4, pp , Wolfram S.: Theory and Application of Cellular Automata, World Scientific, Singapore,