1131

1 INTRODUCTION

The Baltic Sea connects all the countries in the Baltic

region, including, among others, Finland, Sweden, and

Estonia. The location makes its maritime routes vital in

supporting reliable and sustainable transportation in

Europe [1-3]. Sea ice dynamics challenges shipping in

the Baltic Sea. Several countries in the region have

established centralized systems providing icebreaking

assistance, including the most northern Finnish–

Swedish Winter Navigation System (FSWNS),

maintaining safe and efficient year-round navigation

in the Gulf of Bothnia [4, 5].

A typical winter navigation system (WNS) consists

of ship traffic, icebreakers, and an organizing

framework setting up the principles of their operation.

The required icebreaking assistance (i.e., number,

location of icebreakers, and their characteristics) in

specific ice conditions depends on the icebreaking

capabilities of the ship traffic: the less ice-strengthened

the ships, the more icebreaker resource is needed. The

winter navigation system is developed to guarantee

safe and reliable shipping throughout the winter. It

also imposes some minimum size and ice class

requirements on the ships to ensure safe and efficient

operations. Moreover, ships must be built and

operated following the corresponding ice-class rules

applied in the region [5, 6].

Climate change will affect future ice conditions, so

the maximum ice extent and average ice thickness

might decrease [7]. At the same time, climate change

might result in more stormy winds and waves,

increasing ice movements. This makes the ice more

dynamic, results in a higher possibility of forming

ridged ice, and makes the ice conditions more spatially

heterogeneous and less predictable. Offshore wind

farms affect the local ice conditions so that the typical

ice patterns and related ice parameter statistics may no

System-level Simulation for Sustainable Winter

Navigation

A. Kondratenko

1,2

, K. Kulkarni

3,4

, L. Lu

, C. Winberg

, F. Li

, P. Kujala

4,6

, K. Kamberov

R. Leiger

Technical University of Sofia, Sofia, Bulgaria

Chalmers University of Technology, Gothenburg, Sweden

Hanken School of Economics, Helsinki, Finland

Aalto University, Espoo, Finland

Shanghai Jiao Tong University, Shanghai, China

Estonian Maritime Academy, Tallinn University of Technology, Tallinn, Estonia

ABSTRACT: Many European countries are connected to the Baltic Sea, making it vital for transporting goods and

passengers in the region. Because of its northern location, a significant part of the Baltic Sea is ice-covered in

winter, resulting in complications for ship navigation. Icebreakers may allow for safe and efficient transportation

in ice conditions, which requires their organizing in a centralized system aimed at efficient and sustainable

navigation. It is vital to analyze maritime traffic in ice to understand better the future need for icebreakers in the

Baltic Sea. The paper applies agent-based simulation to enhance the performance of winter navigation and

icebreaking assistance in the Bay of Bothnia. We developed novel algorithms upgrading our decision-support

tool to model the dynamics of the icebreaker resource availability, optimize icebreaker allocation in the Bay of

Bothnia, and study how changing the directed pathways affects the efficiency of the winter navigation system.

We demonstrated the capabilities of the developed algorithms in the case studies.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 19

Number 4

December 2025

DOI: 10.12716/1001.19.04.10

1132

longer be relevant, e.g., they change the dynamics of

ice development and break and redirect the moving ice

[8, 9].

The size of a typical ship seems to grow in the

future, and the new strict environmental regulations

will decrease the engine power installed on ships. The

International Maritime Organization (IMO) adopted

Energy Efficiency Design Index (EEDI) regulations in

2011 to reduce the amount of greenhouse gases (GHGs)

emitted by ships [10]. These regulations promote

energy-efficient solutions [11] but may prioritise

underpowering of fossil-fuelled ships and their

optimization for open water conditions. This will

decrease the ice-going capabilities of these ships

dramatically and possibly will result in higher demand

for icebreaker assistance. Therefore, developing

system-level simulation tools that study such factors is

essential to understand and reliably predict future

trends.

Over the last decades, a number of studies have

contributed to the topic at hand by modeling the

system-level performance of winter navigation. They

aim to develop [4, 12-14], upgrade, and apply [15-16]

software that can be used to simulate the need for

icebreakers in the future when ice conditions, maritime

traffic, and characteristics of ice-strengthened ships are

under dynamic change.

The present paper upgrades the method by

Kulkarni et al. [4] to account for the new WNS features.

This allows for a more realistic simulation of the WNS

operation by considering additional practical

navigation aspects not presented in [4]. Specifically, we

developed the novel algorithms and prepared the

input data to model the dynamics of the icebreaker

resource availability, optimize icebreaker allocation in

the Bay of Bothnia, and study how changing the

directed pathways affects WNS efficiency. The

remainder of this paper is structured as follows.

Section II analyses existing approaches and models for

the simulation of winter navigation in the Baltic Sea

and their applications. Section III describes newly

developed algorithms and input data for the case

studies and demonstrates the results of thirty-six

simulation experiments, followed by a discussion of

the results and conclusions.

2 DEVELOPMENT OF SIMULATION

FRAMEWORKS FOR WINTER NAVIGATION IN

THE BALTIC SEA

2.1 Existing approaches for simulation of the winter

navigation in the Baltic Sea

One of the early models of winter navigation in the

Baltic Sea [12] considered navigation in the Bay of

Bothnia, estimating the performance of independent

and icebreaker-assisted ships in the ice. However, the

outlook of the framework is not systemic, which limits

the number of factors that can be analyzed. Lindeberg

et al. [13] proposed a new systemic simulation

approach, individually modeling ships and icebreakers

to address this problem. The approach considered

vessel performance in ice for different regimes, e.g.,

independent navigation in level and brash ice,

icebreaker-assisted navigation in convoy, and towed

mode [15]. Transport ships and icebreakers follow the

network of fairways (see Fig. 1) that consist of linear

and y-shaped segments whose location may change

over time. The limitations of the approach are long

running time and limited visualizing capabilities.

Figure 1. The fairway network implemented in the

simulation approach by Lindeberg et al. [13]. It consists of the

building blocks – sections (black) and junctions (yellow). The

red stripes show an example of one operational area.

Bergström and Kujala [14] developed a stochastic

discrete-event approach in the Simulink modeling

environment for the FSWNS simulation, which can

change the environment parameters with a specific

time step inside the event. The discrete-event

simulation allows the creation of the model from the

standard building blocks – predefined templates of

different events like delay, queue, service by resource,

or moving. The stochastic ice parameters are defined

individually for each segment of the route. The

approach considered the possibility of convoy

formation, with an icebreaker assisting up to two

transport vessels. It allows for estimating the total

waiting time of transport ships for icebreaking

assistance and the transport capacity of the FSWNS for

a specific period.

Figure 2. The flowchart of the stochastic discrete-event model

of the FSWNS by Bergström and Kujala [14].

Fig. 2 shows an example of the event diagram

provided in the study, where a ship is modeled as a

passive entity, and an icebreaker is modeled as a

limited resource. The behavior of ships and icebreakers

is assigned collectively based on a specific general

pattern. In other words, ordering a particular ship to

1133

move to a specific point would require changing the

structure of the model, which would affect all vessels

and icebreakers. The approach has high computational

efficiency of the simulation, making it faster. It benefits

from using stochastic parameters, as it allows the

capture of complexities of nature and conducting

reliability studies by assigning the confidence level to

a specific conclusion.

Kulkarni et al. [4] proposed an agent-based

approach developed in the AnyLogic modeling

environment for the simulation of the WNS in the

Baltic Sea. The approach stands out from the previous

state of the art by individually modeling the behavior

of the WNS elements called agents (i.e., transport

vessels, icebreakers, ports, routes, ice). Thus, transport

vessels and icebreakers may behave differently

depending on the dynamic circumstances (i.e.,

environment and other agents) they encounter. This

feature allows for significant modularity of the model,

resulting in some benefits. Firstly, it provided great

potential for analysis of how different factors of winter

navigation affect system performance indicators.

Secondly, modularity made the model easy to upgrade

for new functionality, as the changes will only

influence the corresponding modules of the model. The

model has advanced capabilities for visualizing the

simulation process, allowing for more accessible

verification and interpretation of the results. The

approach has favorable computational efficiency. An

average run of a simulation model for one winter

month takes from thirty minutes to one hour for the

average office laptop. Considering the benefits of the

approach by Kulkarni et al. [4], different studies

extended the approach to account for new features and

regions of application [15-16]. The present study

upgrades the method by Kulkarni et al. [4] to account

for the dynamics of the icebreaker resource availability

and optimization of icebreaker allocation in the Bay of

Bothnia and to analyze how changing the directed

pathways affects the WNS efficiency.

2.2 System-level simulation model for sustainable winter

navigation in the Baltic Sea

Fig. 3 shows the principle organizational scheme of the

approach by Kulkarni et al. [4]. It is based on two

primary model layers: Traffic flows and Environment.

Traffic flows include necessary data on transport ships,

icebreakers, and their operation. The definition of

Traffic flows starts from processing raw Automatic

Identification System (AIS) data, i.e., automatic regular

reports of coordinates of the vessels with specific time

intervals. The data are processed for a specific area and

period into the unified information on voyages of

transport vessels. The voyage data includes the

Maritime Mobile Service Identity (MMSI) number of

the vessel, starting and destination ports, and the time

when the voyage commences and finishes. The finish

time of the voyage is used to verify the estimated

voyage duration by comparing it with the actual

practical data. Alongside vessel location, the input

traffic data include the basic vessel parameters

corresponding to a specific MMSI number, i.e., vessel

type (e.g., tanker, bulker, containership, Ro-Ro), ice

class, the total engine power, deadweight, maximum

speed in open water, and breadth. Considering that the

number of merchant vessels in the traffic may include

hundreds of vessels, it is often time-consuming to

specify the individual technical information for every

ship. For that purpose, about fifty default ship

descriptions – further called ship types – are entered

into the model, which includes detailed technical

information on the most typical merchant vessels in the

Baltic region.

The technical information includes the necessary

data to model the performance of ships in ice and open

water (i.e., to estimate attained speed at specific power

output). For every merchant vessel, the closest default

ship is selected using the basic parameters from the

input data, as shown in Fig. 4. Later, in calculations, the

merchant ship is assumed to be identical to the selected

default ship.

The attained ship speed v in specific ice conditions

is calculated based on the cubic polynomial h-v curves

(see Fig. 5), where h stands for the equivalent ice

thickness. The h-v curves are defined for independent

operation and moving behind an icebreaker, assuming

100% power output. The h-v curves for the default ship

types were developed in Project Winmos II [17-19] by

Aker Arctic. When a ship is moving at a partial engine

load (i.e., the power output is less than 100%), the h-v

curve is recalculated assuming the speed in the limit ice

proportional to power output to the 4/9 power, and the

speed in open water proportional to the 1/3 power as

described in Kulkarni et al. [4]. The limit level ice

thickness of a ship is typically defined by conditions

when it cannot move faster than from 1.5 to 2 knots.

Independent navigation in thicker ice is considered

unsafe and is not allowed.

Figure 3. The organizational scheme of the simulation

approach by Kulkarni et al. [4].

All icebreakers are divided into three types (A, B,

and C) with specified h-v curves, where A has the most

advanced icebreaking characteristics. The model

allows for up to two vessels in an icebreaker convoy.

The speed of the convoy is calculated as the minimum

of values of attained speed for an icebreaker and

assisted vessels considering their h-v curves. Convoys

are moving along the directed pathways, similar to the

fairway network shown in Fig. 1. In practice,

authorities issue the directed pathways as

recommended routes for merchant vessels, considering

ice conditions, available icebreaker resources, and their

allocation. The directed pathways consist of waypoints

connected by linear paths. Since the voyage data are

limited by starting and destination ports, the

information on reaching from one port to another is

stored separately for all possible combinations as a

sequence of waypoints a ship passes along the way.

1134

Figure 4. Mapping the merchant ship to the closest prototype

ship [4].

Figure 5. Estimating the ship transit speed in specific ice

conditions [4].

The second model layer is the Environment, which

includes a Geographical Information System (GIS) map

of the studied region (see Fig. 6) with directed

pathways, ports, waypoints, and ice conditions

presented corresponding to their geographical

coordinates. Considering that h-v curves for vessels

and icebreakers are specified for level ice thickness,

complex ice conditions are modeled using the concept

of the equivalent ice thickness. As per this concept, the

complex ice conditions with many properties (e.g.,

thickness, ridging, concentration, size of the ice floe)

may be replaced in the model by only one characteristic

– equivalent level ice thickness, assuming

corresponding ship speed is the same in both complex

and level-ice conditions [4].

The quality of ice data significantly affects the

accuracy of simulation results. The ice information is

available through ice forecast data published by the

Finnish Meteorological Institute (FMI). The

Environment layer is divided into cells with a

geographical area of a square mile. The ice data in the

model are specified for each cell with a time resolution

of one day, allowing for the trade-off between

calculation time and accuracy. The equivalent ice

thickness is calculated as a function of concentration

and thickness [4]. Besides ice data, each cell has

information to which icebreaker assistance zone it

belongs. The GIS map is divided into icebreaker

assistance zones, allowing for allocating icebreakers

based on ice conditions. One or more icebreaker zones

are identified, through which the vessel will navigate

to its destination. At least one icebreaker is available in

each zone [20].

Figure 6. The GIS map of the simulation model [4]. Ice

conditions are shown by different grades of blue color, where

darker shades indicate thicker ice.

When the data from the Traffic flows and

Environment layers are read, the voyages are

simulated chronologically. The individual flow charts

of agents guide the simulation. Every vessel aims to

finish the voyage from the start port to the end port

using the directed pathways. The speed of the vessel is

recalculated every time the ice parameters change. If

the vessel speed drops below a certain threshold, it

requests assistance from the ice-breakers available for

the relevant icebreaker assistance zone. The

icebreaking assistance threshold may not be less than

the limit level ice thickness of a ship specified for the h-

v curve. Each icebreaker serves first the vessel that

waited the longest for assistance according to the first

in, first out principle. The same icebreakers may assist

multiple vessels through convoys if they are headed in

the same direction. The simulation ends when all

vessels in the considered period have completed their

schedules.

Vessels often need assistance across multiple

icebreaker zones. Typically, each icebreaker guides a

vessel through its operating zone, leaving it at a

boundary waypoint unless the port is in the zone [20].

The next icebreaker takes over the assistance mission at

the waypoint, guiding the vessel further along its

navigational journey. However, icebreakers can

operate outside their operating zones to ease traffic

build-up or help larger vessels that need two

icebreakers. A list of requests for each icebreaker is

maintained and updated as the vessel moves from one

zone to another. The vessel is removed from all lists

once it reaches a port [20].

The model can change the directed pathways

during the model run, which allows for adjusting the

shipping routes for more favorable ice conditions.

Respectively, there is a need for an algorithm for

transition between the directed pathways. The ongoing

journeys are completed on the old directed pathways,

and the new journeys are scheduled on the new

directed pathways [20]. Icebreakers need to coordinate

between both sets of directed pathways until all traffic

flows smoothly on new directed pathways. Lu et al.

[16] applied the model to a new region – the Gulf of

Finland and the Gulf of Riga – considering Estonian

and Finnish traffic and a new set of icebreakers. This

did not require modifying the core modules of the

model and demonstrated its significant flexibility.

1135

2.3 Key performance indicators for assessing the efficiency

of the winter navigation system

The assessment criterion has a critical role in estimating

the efficiency of the winter navigation system. The

winter navigation system is a complex entity with

many qualities. Most of them are naturally

contradicting, resulting in the need to find a trade-off

between different KPIs. Kulkarni et al. [4] proposed

measuring the efficiency of the FSWNS using the total

waiting time (TWT) of merchant ships for icebreaking

assistance as per (1). The total waiting time is often

used in the FSWNS shipping practice.

v max

TWT W



(1)

where nv is the number of a simulated merchant ship,

T is the simulation time (days), Wnv is the accumulated

waiting time of the vessel number nv in minutes.

The total waiting time is the most straightforward

KPI. Advancing the framework [4], Kondratenko et al.

[15] demonstrated that although the total waiting time

is an important KPI, it may prioritize less sustainable

solutions. Minimizing the total waiting time of the

WNS corresponds to more intensive use of the

resources, e.g., leads to faster speeds of merchant ships

and icebreakers with a higher total running time of the

icebreakers, resulting in increased fuel consumption.

Kondratenko et al. [15] proposed using the total CO2

emissions (2) and the total cost of the WNS operation

(3) as additional KPIs for more sustainable and

informed decision-making. The total CO2 emissions

(ECO2) and cost are estimated for all merchant ships and

icebreakers.

max max

d hl

CO f

tr hl

P SFC P SFC

E t C





=  +







(2)

where n is the number of simulated vessels, including

icebreakers, t is the number of the simulation period,

and Δt' is the duration of the simulation period. The

simulation period ends if external circumstances affect

the speed or the propulsion power in use Pd (kW). Cf is

the conversion factor between fuel consumption and

CO2 emissions [21-26]. Phl is the hotel load – the power

required for non-propulsion power consumers of a

ship, estimated as a function of vessel type, size, and

capacity using the statistical method by the Central

Marine Research & Design Institute [27]. SFC1 and SFC2

are the specific fuel consumptions (t/kWh) for the main

engine and the electric generator. The specific fuel

consumption is calculated using quadratic polynomial

approximations [15] depending on the engine load in

% of the total maximum continuous rating (MCR).

Approximations are provided for low-speed engines

and medium-speed engines. ηtr and ηhl are the power

transmission efficiencies for propulsion and the hotel

load.

max max

d hl

n fuel

tr hl

P SFC P SFC

Cost t R C





=  + +







(3)

where Rn is the time charter rate (USD/hour) of a

transport vessel or an icebreaker, and Cfuel is the fuel

price (USD/t).

Using several discussed KPIs together results in a

more systemic overview of the WNS system efficiency.

Kondratenko et al. [15] demonstrated that their

approach may provide the WNS with about a 7%

decarbonizing effect or up to 14.2% cost reduction,

depending on the priorities. They also show that the

hotel loads are responsible for from 13.4% (moving at

the max speed) to 100% (waiting for icebreaker

assistance) of CO2 emissions of a merchant ship on

different modes of operation, and correspondingly

must be considered in sustainable decision-making.

3 STUDYING NEW OPPORTUNITIES TO

ENHANCE THE EFFICIENCY OF WINTER

NAVIGATION SYSTEMS

Lu et al. [16] demonstrated that different ice conditions

associated with different winters significantly affect

the total waiting time, the need for icebreakers, and

CO2 emissions. Lu et al. [16] and Kondratenko et al. [15]

also concluded that providing a more capable

icebreaker fleet (in terms of their number and ice class)

with fixed ice conditions improves the efficiency of the

WNS till a specific point when further strengthening of

the icebreaking fleet results in high additional cost with

insignificant effect.

The present study provides further analysis of how

the icebreaker assistance parameters and ice conditions

affect the efficiency of the FSWNS. In the original

approach by Kulkarni et al. [4], all the modeled

icebreakers are available for the entire simulation time.

However, in the shipping practice, the number of

icebreakers is adjusted considering the dynamics of ice

conditions, starting from a few icebreakers in the early

winter and gradually adding more icebreakers later. In

the present research, we implement the algorithm to

account for the dynamics of the icebreaker resource

availability and provide the corresponding simulation

experiments. We also study the influence of the

icebreaker allocation in different icebreaking zones on

the efficiency of the FSWNS. Finally, we analyze how

the location of the directed pathways influences the

WNS efficiency and provide insights into the

importance of ice routing of ships in the FSWNS.

3.1 Preparing new algorithms and input data for

modeling more WNS features

The new features to be modeled are dynamics of the

icebreaker availability, optimization of icebreaker

allocation, and dynamics of the directed pathways. The

basic scenario (Scenario 1) is discussed with the Finnish

Transport Infrastructure Agency specialists and

represents the existing practice. The selected AIS traffic

data corresponds to one month of winter 2018 (15 Jan –

15 Feb) – an average winter from traffic and ice

perspectives. The AIS data includes 485 voyages of 181

merchant vessels. Icebreaker data is provided in Table

I, where all icebreakers have medium-speed engines.

Fig. 7 shows on the map the icebreaking assistance

zones applied in the simulation, and Fig. 8 shows the

relevant zones for icebreakers and their operating

schedule. According to the schedule, the number of

operating icebreakers grows from four at the beginning

of the simulation to nine at the end. Technically, this is

achieved by blocking the ability of a merchant ship to

1136

select the icebreaker for assistance before its starting

date of operation.

Figure 7. Icebreaking assistance zones in the Bay of Bothnia

assumed in the simulation.

Table 1. Parameters of the icebreakers for the case study,

where home port identification numbers are as follows: 25 is

Quarken, 3 is Oulu, and 56 is Lulea.

Name

Type

Home

port

Engine

power,

Propulsion,

Transmission

Engine

SFC

(100%

power),

g/kWh

Polaris

21000

19000

Diesel-

electric

Medium-

speed

185

Otso

21840

15000

Diesel-

electric

Medium-

speed

185

Kontio

21840

15000

Diesel-

electric

Medium-

speed

185

Urho

17100

16200

Diesel-

electric

Medium-

speed

175

Frej

17100

16200

Diesel-

electric

Medium-

speed

175

Oden

18000

Shaft

Medium-

speed

185

Ymer

17100

16200

Diesel-

electric

Medium-

speed

175

Thetis

3500

Shaft

Medium-

speed

180

Ale

3500

Shaft

Medium-

speed

180

In the original model by Kulkarni et al. [4], the

maximum number of icebreakers per zone is assumed

to be two. The ID number of the last used icebreaker in

a specific zone is stored in a variable, and the vessel

selects another icebreaker to assist vessels in this zone.

According to the icebreaker schedule assumed in the

present study (see Fig. 8), the available icebreaker

resources are dynamic, and the maximum number of

icebreakers per zone is up to four. This is achieved

through the vessel selecting the icebreaker (see Fig. 9)

according to the uniform distribution by drawing the

random number from 0 to the maximum number of

icebreakers in the zone. The random number is drawn

again if the number belongs to an icebreaker whose

schedule has not started.

Figure 8. Operation schedule for icebreakers in the Bay of

Bothnia with the starting dates.

Figure 9. The algorithm for a vessel to select an icebreaker for

assistance during the simulation.

Figure 10. The directed pathways in the Bay of Bothnia for

the considered case studies.

We consider two options for directed pathways (see

Figure 10) to study the effect of their change on the

WNS efficiency. Directed pathway (Dirway) 1 is closer

to the Eastern coast of the Bay of Bothnia, and Dirway

2 is near its center. Because of spatial ice variation, ice

conditions are different for different directed

pathways. This allows us to analyze the importance of

providing accurate recommendations on directed

pathways, i.e., whether it is worth carefully selecting

the most beneficial directed pathways or whether it

could be deemed insignificant for the chosen type of

winter. In the case studies, we considered three

different options for using directed pathways: vessels

moving along Dirway 1, Dirway 2, and stochastically

migrating between them. For example, in the basic

scenario (Scenario 1), directed pathways are randomly

changed one time per day.

The case studies include seven different scenarios

(see Table II). Considering that the model is stochastic,

several simulation rounds were performed for every

scenario, resulting in 36 simulation runs in total, with

an accumulated simulation time of about 21 hours for

the average office laptop. The simulation assumes that

the icebreaking assistance threshold is 5 knots and that

every merchant vessel is assisted individually.

1137

3.2 Simulation results for the case studies

Simulation results for different scenarios are presented

in Table III and Figure 11. Most simulations (16 rounds)

are performed for the basic Scenario 1. It is noted that

the number of simulation rounds is different for some

scenarios, which may cause a selection bias of

unequally represented statistics. Figure 11 shows

significant variations in KPIs for Scenario 1, e.g., about

a 45% difference in the total waiting time and a 7.5%

difference in CO2 emissions. This difference is caused

by the stochasticity associated with the icebreaking

decision-making and changes of the directed

pathways. Finding the reasons behind those

fluctuations may unlock significant potential for

optimization of the FSWNS. Scenario 2 differs from

Scenario 1 by deterministic directed pathways: the

vessels navigate using only Dirway 1. Variations for

Scenario 2 (5 rounds) account for about a 24%

difference in the total waiting time and a 3.7%

difference in CO2 emissions. The average CO2

emissions for Scenario 2 are only about 1% lower than

for Scenario 1, but the corresponding average total

waiting time is almost 17% higher. This means that for

the considered conditions, ice routing of ships (i.e., the

directed pathways optimization) may be beneficial to

significantly reduce the total waiting time of the

FSWNS if the icebreaker resource is limited (e.g., by the

limited number of available icebreakers and their

schedule) and their location is not optimized.

Scenario 3 (3 rounds) is compared with Scenario 1

to analyze how the availability of all icebreakers during

the simulation period affects the KPIs. The results

show that the difference in KPIs is insignificant, which

means that the schedule (see Figure 8) proposed by the

Finnish Transport Infrastructure Agency experts is

nearly optimal for the proposed allocation of the

icebreakers.

Table 2. Values of the WNS parameters in the case studies.

Icebreakers are abbreviated as IB.

Case

Dirway

Schedule

IB Location

Scenario 1

Stochastic

Dynamic

Basic

Scenario 2

Dirway 1

Dynamic

Basic

Scenario 3

Stochastic

All IB available

Basic

Scenario 4

Stochastic

Dynamic

Optimized

Scenario 5

Stochastic

All IB available

Optimized

Scenario 6

Dirway 1

All IB available

Optimized

Scenario 7

Dirway 2

All IB available

Optimized

Figure 11. The values of KPIs for different scenarios of the

case study.

Simulations for Scenarios 1 – 3 showed that they

have shared problems – starting from the beginning of

February, many ships are stuck in Zone 3, but Zones 1

and 2 are free from the ship traffic (see Figure 12). This

problem can be mitigated by optimizing the allocation

of the icebreakers (Scenario 4), using the rest of the

parameters as in Scenario 1. Figure 13 shows the

improved schedule, where the icebreakers are

redistributed to provide more assistance in Zone 3, and

their operation time is kept unchanged.

The simulation results for Scenario 4 (see Figure 11

and Table III) demonstrate a 35% reduction in the

average total waiting time of the FSWNS compared to

Scenario 1, when the average CO2 emissions stay

almost the same. This means that optimized allocation

of icebreakers without changing their operation time

may be a very efficient method to improve the

performance and cost-efficiency of the FSWNS.

Previously, Scenario 3 demonstrated that the

availability of icebreakers during the entire simulation

period insignificantly affects the KPIs for the basic

allocation of the icebreakers. Scenario 5 is designed to

check if this conclusion is still relevant for their

optimized allocation. The corresponding simulation

results demonstrate a 42% average reduction in the

total waiting time of the FSWNS and the same CO2

emissions compared to Scenario 1. This demonstrates

an additional 7% reduction in the total waiting time of

the FSWNS compared to Scenario 4 due to extended

icebreaker re-sources assuming the optimized

allocation of icebreakers. Figure 14 shows that unlike

Scenario 3 (Figure 12), the vessels are evenly

distributed between the icebreaker assistance zones for

the same virtual date, resulting in enhanced

performance of the FSWNS, especially at the final

stages of the simulation when the ice is the thickest.

Scenarios 6 and 7 show that using deterministic

directed pathways may result in about a 6% additional

reduction of the total waiting time, associated with no

need for transition between the directed pathways.

Table 3. Simulation results for different scenarios.

Number of the

round

The average

waiting time,

minutes

The total fuel

consumption,

tonnes

CO2 emissions,

tonnes

Scenario 1

746

6853

21587

633

7191

22652

517

6987

22009

728

6962

21930

409

6662

20985

662

6932

21836

661

6932

21836

547

7081

22305

538

6743

21240

521

7049

22204

751

6767

21316

718

7154

22535

723

7033

22154

596

6902

21741

567

6808

21445

535

6778

21351

Scenario 2

622

6862

21615

656

6720

21168

816

6897

21726

779

6981

21990

726

6906

21754

Scenario 3

676

6866

21628

570

6816

21470

630

6825

21499

1138

Scenario 4

415

6886

21691

388

6921

21801

405

6966

21943

Scenario 5

359

6988

22012

333

6815

21467

377

6839

21543

Scenario 6

291

6772

21332

309

7012

22088

362

6870

21641

Scenario 7

331

6886

21691

338

6866

21628

370

6993

22028

4 DISCUSSION

The developed simulation tool aims to capture all the

main elements of the winter navigation system: ice-

going ships, icebreakers, varying ice conditions, and

varying situations for independent navigation and

assisting ships in ice. These elements are challenging to

simulate. Firstly, the ice-going performance of vessels

and icebreakers depends on many specific technical

parameters of a ship and may vary for different ice

conditions. For example, an icebreaker designed for

navigation in a lake may not necessarily show the best

performance for navigation in sea ice. Secondly,

modeling ice conditions is challenging. Ice is very

dynamic – it changes fast, even for one day. Moreover,

it is usually necessary to reflect all the complexities of

ice conditions and reliably simulate the average speed

of a ship using only one value of the equivalent ice

thickness. That is why the evaluation of the equivalent

ice thickness needs accurate physics-based models to

simulate the ship performance in varying ice

conditions.

A critical aspect of the WNS simulation studied in

the present research is how to model the decision-

making process of icebreaker captains coordinating all

maritime operations during wintertime. This has a

significant effect on the efficiency of the winter

navigation system. This decision-making process

should include knowledge of the allocation of

icebreakers in the studied region and how their

availability changes in time, a summary of the ships

being in or approaching the studied area and their ice-

going performance, recommended routes for ships to

follow and receive icebreaker assistance, and the most

probable development of ice conditions in the near

future.

Figure 12. Scenario 3, vessels are congested in Zone 3, but

Zones 1 and 2 are free from the ship traffic.

Figure 13. Optimized operation schedule for icebreakers in

the Bay of Bothnia. The icebreakers are redistributed to

provide more assistance in Zone 3.

Figure 14. Scenario 5, awaiting vessels are equally distributed

per zones.

The newly developed functionality allowed us to

analyze how some of these parameters affect the WNS

performance. We studied the isolated and combined

influence of changing the dynamics of the icebreaker

resource availability, optimizing ice-breaker allocation

in the Bay of Bothnia, and varying the directed

pathways on the WNS efficiency. The results of the case

studies revealed the complex, non-trivial effects of the

studied factors, especially when different measures are

applied simultaneously. We conclude that the total

waiting time is susceptible to the examined factors and

recommend considering them if the total waiting time

is essential for decision-making. However, unlike some

WNS parameters considered in the study by

Kondratenko et al. [15], the examined factors affect

CO2 emissions insignificantly under the studied

conditions and assumptions.

The calculations indicated that optimizing

icebreaker allocation in the Bay of Bothnia is the most

effective isolated measure to reduce the total waiting

time by up to 35%. Based on the case studies, we

concluded that solely extending the availability of all

icebreakers for the entire simulation period does not

improve the performance of the WNS. The latter,

however, may indicate that the icebreaker availability

schedule used in the basic scenario is already near-

optimal for the basic allocation of the icebreakers.

Complementing the optimized icebreaker allocation

with the extended availability of the icebreakers

provides an additional 7% reduction in the total

waiting time, resulting in a 42% reduction compared to

the basic scenario. Further enhancing the WNS through

the improved directed pathways gives 6% less total

waiting time, resulting in a 48% total reduction

compared to the basic scenario.

The case studies, therefore, demonstrate that more

intelligent usage of the existing resources (through

optimizing icebreaker allocation and directed

pathways) may be much more efficient than the

expensive usage of more resources (through the charter

1139

of icebreakers for a more extended period). We may

conclude that the development of the WNS simulation

tools has significant prospects for uncovering the full

potential of the ice-going fleet.

The demonstrated simulation tool has the following

limitations. Firstly, in the present form, the tool mainly

uses the maximum waiting time for ice-going ships as

the main decision-making criteria, which is naturally

too simple. Secondly, the methods used to evaluate the

equivalent ice thickness for these ice conditions need

further re-search on how to link the equivalent ice

thickness calculation methods to the main particulars

of the ice-going ships so that the performance-

equivalence, rather than volume-equivalence, ice

thickness can be achieved. Historically, ship

performance in level ice has been the dominating

research area for developing analytical formulations

for ship resistance. The other ice conditions, such as

ridges, dynamic moving ice, and ice floes with varying

concentrations, have obtained less attention. Although

some randomness has been included in this paper,

significant uncertainties are still associated with

information about ice conditions and ship performance

evaluation. Quantification of such uncertainties can be

an important direction for future work.

However, the results of applying the system-level

simulation tool are promising despite the existing

challenges. This is a unique tool worldwide simulating

all the main elements of the winter navigation system.

5 CONCLUSIONS

The ice presence complicates maritime navigation in

northern regions, which requires better ice-going

qualities of ships and icebreaking assistance.

Developing a simulation tool to study the performance

of winter navigation activities in the Baltic Sea region

at the maritime system level may significantly improve

the quality of decision-making, resulting in more

efficient and sustainable shipping. In the present

paper, we demonstrated newly developed algorithms

and case studies for the simulation of the Finnish-

Swedish Winter Navigation System to predict the need

for icebreakers and to plan their operation policies in

the future. Specifically, extending the methods [4] and

[15] with the newly developed functionality allowed us

to analyze the influence of changing the dynamics of

the icebreaker resource availability, optimizing ice-

breaker allocation in the Bay of Bothnia, and varying

the directed pathways on the WNS efficiency. The

results of the case studies demonstrated that the total

waiting time is significantly sensitive to the studied

factors.

We concluded that optimizing icebreaker allocation

in the Bay of Bothnia is the most effective isolated

measure to reduce the total waiting time and that solely

extending the availability of all icebreakers for the

entire simulation period is not always effective.

Complementing the optimized icebreaker allocation

with the extended availability of the icebreakers and

the improved directed pathways may result in a 48%

total re-duction of the total waiting time compared to

the basic scenario. The case studies demonstrated that

more intelligent usage of the existing icebreaker

resources may be much more efficient than the

expensive usage of more resources.

The tool has significant potential to provide

recommendations to reduce the total waiting time of

the transport ships for icebreaking assistance.

However, it is necessary to advance the methodology

for estimating the equivalent ice thickness [28-30] and

calculating h-v curves for different ships and ice

conditions for more reliable modeling of the ship

performance in ice, e.g., by means of ice tank

experiments [31-35].

STATEMENTS AND DECLARATIONS

The paper reuses the vector map of Europe distributed under

the Creative Commons Attribution-Share Alike 4.0

International license

(https://commons.wikimedia.org/wiki/File:Blank_map_of_E

urope_cropped_%28blue%29.svg). In addition, the authors

would like to thank Aker Arctic Technology Inc for providing

the sample ship database containing established h-v curves.

FUNDING STATEMENT

This work has been realized with financial support by the

European Regional Development Fund within the

Operational Programme “Bulgarian national recovery and

resilience plan”, Procedure for direct provision of grants

“Establishing of a network of research higher education

institutions in Bulgaria”, under the Project BG-RRP-2.004-

0005 “Improving the research capacity and quality to achieve

international recognition and resilience of TU-Sofia.

Author 1 is also supported by the POTENT-X project funded

under the Clean Energy Technology Partnership (CETP) with

funding from the Swedish Energy Agency, Innovation Fund

Denmark, Agencia Estatal de Investigación (AEI), Spain, and

the European Commission (GA N°101069750).

Author 2 was supported by the Academy of Finland project:

Towards human-centered intelligent ships for winter

navigation (Decision number: 351491). Author 5 received

funding from the Science and Technology Commission of

Shanghai Municipality (Project No. 23YF1419900).

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