1195

1 INTRODUCTION

Efficient vessel traffic management on constrained

inland waterways requires robust modeling tools to

support both infrastructure planning and operational

decision-making. The Świnoujście–Szczecin waterway,

a vital maritime corridor in Poland, is under increasing

pressure due to the expansion of port operations and

the expected deployment of larger vessels following

the implementation of the "12.5m Project."

To mitigate these challenges, a new passing lane has

been proposed in the Policki Canal to reduce

bottlenecks and enhance navigational efficiency. This

paper evaluates the potential impacts of this

improvement using a custom-built microscopic

simulation model (Figure 1).

Conventional analytical models for capacity

estimation, based on ship domain theory, are

inherently static and fail to reflect the stochastic nature

of ship traffic processes. To address this, stochastic

simulation models are increasingly used [Groenveld,

2006; Almaz and Altiok, 2012; Olba et al., 2018]. Several

approaches incorporate alternative transitions

[Bačkalić and Škiljaica, 1998; Ugurlu et al., 2014],

discrete optimization [Mohring et al., 2005], queueing

theory [Mou et al., 2005], and cellular automata [Feng,

2013]. Typically, domain-based models [Zhou et al.,

2013] are employed, where the ship's domain defines a

safety area around each vessel.

Marine traffic system performance is generally

evaluated using two primary indicators:

− Delay time of ships and its distribution.

− Average queue length of waiting ships and its

distribution.

Gucma and Sokołowska [2012] validated a

stochastic model of vessel traffic on the Świnoujście–

Szczecin waterway using empirical delay data. Further

validation with real-world observations (Gucma et al.,

2016) confirmed the model’s reliability.

In this study, we assess the effectiveness of

introducing a new passing lane in the Policki Canal

(Figure 1).

Waterway Capacity Enhancement through Traffic Flow

Simulation: A Case Study of the Policki Canal Passing

Lane

L. Gucma

, R. Gralak

& B. Kundakçi

Maritime University of Szczecin, Szczecin, Poland

Iskenderun Technical University, İskenderun, Turkey

ABSTRACT: This paper presents a simulation study of marine traffic optimization along the Świnoujście-Szczecin

waterway, with a particular focus on the proposed implementation of an additional passing lane in the Policki

Canal. Using a microscopic simulation model based on the Monte Carlo method, the study evaluates three traffic

scenarios for 2022 and beyond 2025 under different infrastructure development conditions. The results highlight

the operational and economic benefits of the proposed lane, including reduced vessel delays and associated

congestion costs. The results offer strategic insight into future maritime infrastructure planning in the region.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 19

Number 4

December 2025

DOI: 10.12716/1001.19.04.17

1196

Figure 1. Location of the proposed deep-water passing lane

in the Policki Canal (marked in red) and the existing 12.5 m

deep-water fairway (marked in green).

2 STUDY ASSUMPTIONS

A study of the parameters of ship traffic streams for the

modernized Świnoujście-Szczecin waterway is

presented, taking into account the new passing lane on

the Police Canal. It will allow 2-way traffic of all vessels

passing through the Świnoujście-Szczecin waterway.

The model excludes inland and recreational vessels

operating outside the main fairway.

In the context of ship traffic streams, particularly

passing and overtaking maneuvers, vessels were

categorized into four main size groups (Table 1) and

two ballast-related subgroups, resulting in six distinct

traffic categories. Based on these classifications, the

permissible passing combinations for vessels across

different sections of the waterway were determined

and are summarized in Table 2. This division, while

conventional, provides a practical framework for

analyzing ship traffic patterns. A graphical

representation of the traffic regulation zones along the

Świnoujście–Szczecin waterway is provided in Figure

2. In the simulation model, a detailed table specifying

allowable passing widths and draught limits was used

to support the analysis of ship traffic streams.

Table 1. Adopted division of ships in terms of traffic streams

Group of ships

Dimensions

Group name (designation)

1 & 2

L < 100m

Small

3 & 4

L >= 100m and L < 150m

Medium

L >= 150m L <200m

Large

L >= 200m

Maks

Vessel speeds were assumed according to the speed

table (Table 3).

Table 3. Permissible ship speeds [knots] in groups on

individual sections of the Świnoujście-Szczecin waterway

No.

Fairway section

[km]

Container ship (cB <

0.65)

Bulk carrier (c(B) ≥

0.75)

T > 10 m

T ≤ 10 m

T > 10 m

T ≤ 10 m

5.7 ÷ 17.0

17.0 ÷ 48.5

48.5 ÷ 54.4

54.4 ÷ 63.5

64km

0km

Zalew Passing area

2 directions

klasy 1, 2, 3, 4

Police Passing + Policki Canal

2 directions

class 1, 2, 3

2 directions

1/1, 1b/1, 1b/2, 2b/2b

2 directions

class 1/1, 1b/1

Świnoujście

Szczecin

2 directions

1/1, 1b/1, 1b/2, 2b/2b

Figure 2. Basic principles of traffic regulation on the

approach of the Świnoujście-Szczecin waterway.

The adoption of arbitrary groups of ships was

preceded by an analysis of ship size and a table of

width and length ratios of passing ships for the

planned Świnoujście-Szczecin waterway dredged to

12.5 meters.

Table 2. Basic principles of traffic regulation on the Świnoujście-Szczecin waterway

No.

Episode

Kilometer of track "from"

[km]

Kilometer of track "to"

[km]

Type

Slope

Ability to pass in accepted size

classes

Port of Świnoujście

5.3

Bend/straight

1:3

1/1, 1/2, 1/4, 2/2, 2/4

Paprotno/Mielin

5.3

11.4

Bend

1:3

1/1, 1/2, 1/4, 2/2, 2/4

Piastowski Canal

11.4

17.0

Straight

1:3

1/1, 1/2, 1/4, 2/2, 2/4

Szczecin Lagoon N

17.0

23.8

Straight

1:4

1/1, 1/2, 1/4, 2/2, 2/3, 2/4, 2/5, 4/4

Pass Lagoon BT II-III

23.8

28.8

Passing area

1:4

1/2/3/4/5/6

Szczecin Lagoon S

28.8

41.0

Straight

1:4

1/1, 1/2, 1/4, 2/2, 2/3, 2/4, 2/5, 4/4

Mixed N

41.0

49.5

Bend/straight

1:3

1/1, 1/2, 1/4, 2/2, 2/4

Pass Police (Scenario A and B)

49.5

51.5

Passing area

1:3

1/2/3/4/5

Police Pass and Police Canal

(Scenario C)

43.6

51.5

Passing area

1:3

1/2/3/4/5/6

Mixed S

51.5

64.0

Bend/straight

1:2

1/2, 2/2

Legend: example designations: 1/2 - group 1 can pass with group 2. 1/2/3/4/5/6 - can pass in all groups, 1/2/3/4/5 - can pass in all groups

except 6 (Max).

1197

2.1 Analysis and forecast of traffic volumes

Both the Port of Szczecin and Police show no

significant growth in ship traffic, which fluctuates at

the level of 3,000 and 300 ship entries per year for

Szczecin and Police, respectively. Świnoujście shows

some change in ship traffic between 2014 and 2021, as

it increased by a value of about 3-5% per year. This

increase is mainly due to ferry traffic. The ship

intensity yearly data presented in Figure 3 show the

entrances of vessels to the Szczecin-Świnoujście port

complex in 2009-2021.

Figure 3. Dynamics of vessel traffic entering Szczecin, Police

and Świnoujście in 2009-2021.

In order to determine the intensity of vessel traffic

in ship classes on the approach to Świnoujście, data

from the government database of vessels entering

Polish ports were analyzed. Accurate data from

01.2008 to 08.2021 were analyzed, and the frequencies

of vessel lengths entering Szczecin and Police were

determined (Fig.4).

Figure 4. Frequencies of vessel lengths entering Szczecin and

Police between 2009 and 2021.

The group of medium-sized vessels, i.e. from 100m

to 150m in length, is made up of vessels with a draught

not exceeding the draught allowed in the previous

fairway of 10.5m (i.e. T<9.15m), i.e. these are vessels

that were not limited by their draught (a typical vessel

with L=150m has B=20m and T=9m). The dynamics of

change in this group for the period 2008-2020 was

analyzed and is shown in Fig. 4. From this figure it can

be seen that although there has been some upward

trend in such units in recent years, but in general they

maintain a fairly stable level of inputs, which may

indicate the dynamics of future increases in maximum

vessels for the 12.5m track. However, the changes

between 2018 and 2020 are not large and amount to 1%

per year.

The analysis and traffic forecasts, accounting for the

enlargement of the fairway parameters under the so-

called "12.5m Project," were primarily based on

planned developments aimed at accommodating

larger vessels in the ports of Szczecin and Police. The

key wharf modernization projects following the

implementation of the "12.5m Project," along with the

anticipated vessel traffic intensities, are summarized in

Table 4. It was optimistically assumed that all

infrastructure upgrades enabling the operation of

maximum-size vessels on the 12.5m fairway would be

completed by 2025. For several projects where no

specific traffic forecasts were available, it was

conservatively assumed that each terminal would

handle two vessel calls per month, corresponding to an

estimated cargo throughput of approximately 120,000

tons per month.

Table 4. Projected numbers of entries Group 4 (Max) vessels

over 200 m in the port of Szczecin and Police after 2025

No.

Name

Expected annual

number of entries of

units over 200m

Vessel type, data

origin notes

PDH Police

Terminal

Gas carrier.

Navigational

analysis

Skolwin Terminal

Tanker. Navigational

analysis

CPN Terminal

Szczecin

Tanker. Estimated -

no data available

Słowackie and

Zbożowe quay

Bulk carriers.

Fińskie, Czeskie

and Norweskie

quay

Container ships.

Gryfia dock

Renovation.

Estimated - no data.

Katowickie &

Chorzowskie quay

Bulk Carriers.

Estimated - no data

available

Huk quay

Bulk Carriers.

Estimated - no data

available

Alfa Terminal

Tankers. Estimated -

no data available

Skolwin

Tankers. Estimated -

no data available

Total

325

The main criterion for estimating future ship traffic

is the assumption that the average intensity of entering

ships to Szczecin and Police is 3000 and 300

entries/year, respectively, which corresponds roughly

to a ten-year average. Attached to these intensities was

the number of estimated maximum ships according to

the projects' assumptions, that is, the value of 325 ships

per year. The approach track to Świnoujście and

Świnoujście itself were not taken into account.

Three traffic scenarios, labeled A, B, and C, were

analyzed:

− Scenario A: Baseline conditions for 2022, assuming

the upgrading of the main waterway to a 12.5 m

depth, but without corresponding modernization of

individual wharves and without the construction of

a passing facility in the Policki Canal.

− Scenario B: Projected conditions after 2025,

assuming a target increase in large vessel traffic to

325 calls per year on the 12.5 m fairway, but without

the construction of a passing facility in the Policki

Canal.

1198

− Scenario C: Projected conditions after 2025,

assuming both the increase in large vessel traffic to

325 calls per year on the 12.5 m fairway and the

construction of a new passing facility in the Policki

Canal.

The initial parameters for traffic estimation are

shown in Table 5.

Table 5. The assumed growth dynamics of the number of

entries of each size group of ships in Szczecin and Police

(combined) and the traffic forecast for scenarios A, B and C

Group

Dimensions

Baseline

frequency

for 2022

[%].

Scenario

A. 2022

without

quays for

12.5m

Scenario B.

2025

completion

of all quays

12.5m

Scenario C.

2025 Traffic

as in

Scenario B

and the

passing of

the Police

Canal

L < 100m

59.4

1960

L >= 100m L

< 150m

32.5

1073

L >= 150m L

< 200m

7.2

238

L >= 200m

0.9

355

Total

100

3300

3625

For the target projected number of ship entrances to

Szczecin and Police for each scenario, group traffic

intensities were determined for both one-way and two-

way traffic (Tables x.9 and x.10). These intensities

served as input data for the simulation model.

3 SIMULATION MODEL FOR PORTSYM SHIP

TRAFFIC FLOW STUDY

A dedicated simulator was developed to model vessel

movements along the waterway. The simulation

approach is microscopic, meaning that each vessel is

treated individually as a discrete object. The model

operates based on stochastic principles, utilizing a

Monte Carlo simulation framework (Figure 5).

The simulation logic is organized into three core

modules:

− Ship generation and input: Randomized creation of

vessels based on defined traffic parameters.

− Movement and queue handling: Vessel progression

along the waterway, including queuing when

passage is restricted.

− Decision logic for entry and exit: Rules governing

when vessels are permitted to enter or leave the

simulated waterway sections.

The basic features of PortSym are:

1. Ship Characteristics

− Vessel arrival times are generated according to a

Poisson distribution.

− Ship lengths and dimensions are sampled from

uniform distributions, constrained within

group-specific bounds.

− Vessel speeds are drawn from a truncated

normal distribution, with regulatory limits

applied as upper bounds.

− It is assumed that 50% of vessels are outbound

(seaward) and 50% are inbound (toward port).

− Night-time traffic operations are excluded from

the simulation.

2. Waterway Representation

− The fairway is divided into discrete sections,

each characterized by specific passing

capabilities and speed restrictions.

− Passing rules between vessel groups are

implemented through pre-defined matrices that

govern allowable encounters.

3. Movement Logic

− The model verifies whether a vessel can enter the

waterway based on the real-time positions of

other ships and the applicable passing rules.

− If passage is not possible, the vessel queues until

conditions permit safe entry.

− Vessel movement is modeled at constant,

section-specific speeds without dynamic speed

adjustments.

4. Output and Data Handling

− The simulation logs detailed data for each vessel,

including delays, passing events, and queuing

statistics.

− Simulation dynamics are driven by three

synchronized loops operating at a 1-minute time

resolution:

− Ship generation and system status logging.

− Vessel position updates and verification of

passing conditions.

− Decision-making for vessel entry

permissions.

The simulation model operates through three

primary loops, each with a time step of 1 minute, as

specified in the program input parameters:

1. Ship Generation and System Logging Loop:

Responsible for generating new vessels according

to traffic intensity profiles and recording the key

operational parameters of the system.

2. Ship Position Update and Passing Event Loop:

Updates vessel positions along the fairway and logs

passing or overtaking events between ships.

3. Entry Decision Loop: Verifies whether conditions

permit a new vessel to enter the waterway, based on

real-time traffic states and predefined passing rules.

The core algorithm of the simulation model

operates according to the following sequence:

1. Generate ship groups: Ships are generated

according to predefined group characteristics and

traffic intensities.

2. Create ship objects: For each generated ship, an

individual object is created with assigned attributes

such as length, speed, and direction of movement.

3. Register ship objects: Each ship object is added to

the active list of vessels present within the

simulation environment.

4. Evaluate passing possibilities: For every new ship,

the model checks existing vessels on the waterway

to determine whether safe passing is possible

according to the passing rules matrix.

5. Decision on entry or waiting: If passing conditions

are satisfied, the ship enters the track; otherwise, it

queues and its waiting time is calculated.

6. Update ship positions: Ships already on the track

move forward by a distance corresponding to their

assigned speed and the elapsed simulation time

step.

7. Record passing events: When vessels pass or

overtake, the events are logged along with

associated positional data.

1199

8. Record queuing data: Waiting times and queuing

statistics for delayed vessels are recorded for

further analysis.

The model was verified for algorithmic errors using

simple, properly selected test input data at the outset.

Generate ships

in groups

Generate ships data

Input ship to object list

Wait to permission

Wait in queue

Record gueue

Is passing

possible on all sections

of the waterway?

Record waiting

time

Move the ship along

the waterway

Passing or

overtaking?

Record position

End of simulation

for given ship

End

of waterway?

Iterate

Record start time

Figure 5. PortSym model operation diagram for a single

vessel

The data provided by the model makes it possible

to analyze the basic parameters of the waterway

system's traffic stream, including:

1. Queue distribution at the entrance in classrooms.

2. The distribution of the exit queue in the classrooms.

3. Track transition time without delays (ideal).

4. Total delay time in classes and types.

5. Totals of ships generated in classes and types.

6. Average delays per ship in classes and types.

Model verification was carried out on simple

examples for which analytical solutions existed. At a

further stage, the model was verified with real track

delays [Gucma et al. 2016]. A high convergence of the

resulting values was obtained (differences of 10%). For

the first time, the model was used during the design of

a passing pass at the Szczecin Lagoon for the so-called

"12.5m" project (deepening of the Świnoujście-Szczecin

track to 12.5m).

The program was written in Python using the

PyCharm interpreter and relevant modules. The model

was verified for algorithm errors using simple

appropriately selected test input data at the beginning.

The hourly intensities for the model are shown in Table

Table 6. Hourly ship intensities [st./h] in one direction (to

sea / to port) for each year adopted into the model for the

traffic scenarios studied

Group/year

2022

2025

2035

0.1119

0.0612

0.0136

0.0017

0.0202

Total 1 direction of traffic

0.3615

0.3800

3.1 Dynamic approach - the domain of the ship

The dimensions of a ship's domain in such very narrow

waterways, when port regulations play a major role,

depend on the cross-section of the waterway (x). The

domain length DL(x) can be defined as (Figure 3):

( ) ( ) ( )

L F A L

D x L D x D x



= + + +

where:

L - length of the ship,

DF(x) - the length of the domain from the bow (from

zero to the minimum tracking distance)

DA(x) - length of the domain from the stern (assumed

as 0)



L - domain variability

A similar formula can be applied to the width DB(x)

of the ships' domain:

( ) ( ) ( )

B S P B

D x B D x D x



= + + +

where:

B- width of the ship

Ds(x) - right side domain width

Dp(x) - width of the left side domain



B - domain variability

Figure 6. Definition of a ship's domain in a restricted

waterway.

In the one-dimensional domain model used, DB(x)

can be defined as two state variables:

( ) { ( ) (1,0); ( ) (0,1)}

D x o x p x= = =

where o(x) and p(x) are

logical variables that determine whether passing or

overtaking of the vessels in question is allowed on a

given section of the waterway (0 - passing/overtaking

possible, 1 - passing/overtaking prohibited).

The navigator has very limited influence on

adjusting the length of the domain aft (DA), and

subsequent ships adjust the size of this domain

according to ship dimensions, port regulations and

intentions, so it is set to zero. The dependence of the

domain dimensions x is due to the variability of the

waterway sections and regulations within the sections,

and the variability of ship speeds in the sections. The

1200

variability of the domain (error) changes according to

the behavior of navigators.

The most important domain dimension in this

study is DF i.e. the length in front of the ship that the

navigator intends to keep free when one ship is

following another due to the prohibition of overtaking.

This distance is determined by regulations or by the

navigator himself, taking into account the possibility of

accidentally stopping his own ship. Accidental

stopping on a narrow waterway is usually performed

by means of a so-called stage maneuver, which

depends on the maneuvering characteristics of the

ship. The stage maneuver is usually performed in steps

that change the set to the engine in order to prevent the

ship from running aground. Usually, in the first phase

of the stage maneuver, "Full Astern" is set on the

engine, and then, when the ship begins to change

course significantly (usually to starboard), the speed

telegraph is set to "Stop" and the rudder is set to

starboard (right or left depending on the

maneuverability of the ship). The procedure is then

repeated. In the last step, an anchor is usually thrown,

if possible.

4 RESULTS OF SIMULATION STUDIES OF

TRAFFIC PERFORMANCE ON THE UPGRADED

TRACK FOR SELECTED

4.1 Cost of ship downtime

Based on the publication [Pocuca 2006], the daily total

cost of ships was determined for three different groups:

bulk carriers, container ships and tankers. It was

assumed that in 2020 the cost increased compared to

2006 (about 3% per year - average inflation). Based on

these, the daily average cost of operating units in size

groups was determined (Table 7). It does not take into

account the cost of LNG or LPG units, which, due to

the specific cargo, is much higher than analyzed.

Table 7. Averaged daily demurrage costs of ships in groups

Group

Cost [USD/day]

1 and 2

15000

3 and 4

20000

25000

30000

4.2 Conduct surveys and analyze their results

The study was conducted for the assumed size groups,

their intensities and the adopted traffic stream layout.

A simulation time of 365 days (1 year), a simulation

step time of 1min and a simulation parameter

recording time of 3h were assumed. Simulations of a

single scenario take about 1 minute.

The data was analyzed in terms of the basic

parameters of the waterway system's traffic stream,

including:

1. Distribution and probability of entry/entry queue in

classrooms,

2. Classroom lag time,

3. Sums of ships generated in classes,

4. Downtime costs.

Table 8 shows the results of the annual simulation

for the projected traffic data in the 3 scenarios

considered.

Table 8. Annual downtime in entry and exit groups

[days/year]

Group/year

Total

169

205

171

The simulation results (without active traffic

control) indicate that annual vessel downtime under

current traffic conditions is approximately 170 ship-

days per year. However, following the introduction of

Group 6 (maximum-sized) vessels, which exert the

greatest load on the waterway, this figure is projected

to increase to around 205 ship-days per year. With the

implementation of a passing lane in the Policki Canal,

the annual downtime is expected to return to

approximately 170 ship-days.

The probability of a group queue increases

significantly with the traffic load of large vessels is

particularly high for the group of maximum and

medium (L=150m) loaded vessels (Table 9).

Table 9. Probability of queuing in groups

Group/year

3.3%

2.5%

5.5%

1.9%

2.7%

3.6%

12.3%

14.2%

15.1%

3.6%

4.4%

2.2%

1.6%

3.6%

0.3%

3.6%

1.1%

The annual cost of vessel downtime, without the

introduction of maximum-sized vessels, is estimated at

approximately USD 2.5 million (Table 10). Following

the introduction of Group 6 vessels, this cost is

projected to increase to around USD 3.1 million per

year. However, the implementation of a passing lane in

the Policki Canal would reduce the annual downtime

cost to approximately USD 2.6 million, representing a

16% reduction.

The net annual savings resulting from the

construction of the passing lane are estimated at USD

0.5 million (i.e., USD 3.1 million minus USD 2.6

million). Assuming a service life of 25 years for the

facility, the cumulative financial benefit would amount

to approximately USD 12.5 million, equivalent to over

50 million PLN.

Table 10. Annual cost of downtime [million USD]

Group/year

1 and 2

0.6

0.8

0.7

3 and 4

1.6

1.3

0.3

0.2

0.0

0.4

Total

2.5

3.1

2.6

5 RESULTS AND CONCLUSIONS

Three simulation-based study offers a clear view of

how projected traffic growth and infrastructure

investments will shape navigation efficiency along the

Świnoujście–Szczecin waterway. Based on the model

outcomes, the following conclusions can be drawn:

1. The developed microscopic traffic flow model,

based on the Monte Carlo method, demonstrated

1201

high consistency with empirical data from the

Świnoujście–Szczecin waterway. Deviations did

not exceed 10%, confirming the model's adequacy

for practical applications.

2. Under present (2022) traffic conditions, annual

vessel downtime is approximately 169 ship-days.

The existing infrastructure, without additional

improvements, will not sustain future traffic

demands, particularly with the introduction of

larger vessel classes (Group 6).

3. Without the implementation of a new passing lane,

projected traffic growth after 2025 would raise

vessel downtime to 205 ship-days per year,

significantly deteriorating the operational efficiency

of the waterway.

4. The construction of a passing lane in the Policki

Canal is projected to reduce vessel downtime to

approximately 171 ship-days per year, representing

a 17% reduction compared to the no-intervention

scenario. This confirms the functional necessity of

the investment.

5. The passing lane would yield annual savings of

approximately 0.5 million USD in reduced

downtime costs. Over a projected 25-year

operational lifetime, this translates to cumulative

savings exceeding 12.5 million USD, justifying the

investment economically.

6. Delays and queuing probabilities are most

pronounced for medium-sized (Group 3) and

maximum-sized (Group 6) vessels. Infrastructure

planning should prioritize enhancements that

accommodate these groups to ensure optimal

system performance.

7. While the model realistically captures the stochastic

nature of vessel traffic, it does not include active

traffic control mechanisms such as dynamic VTS

interventions or pilot scheduling optimization.

Incorporating these elements could further improve

system performance and should be considered in

future studies.

8. The proposed passing lane in the Policki Canal

should be considered a critical element of the long-

term development strategy for the Świnoujście–

Szczecin waterway. Its implementation is essential

for maintaining competitiveness, reducing

congestion, and supporting the expected growth in

cargo throughput.

REFERENCES

[1] Almaz, O.A., Altiok, T., (2012). Simulation modeling of

the vessel trafﬁc in Delaware River: impact of deepening

on port performance. Simulation modelling practice and

Theory vol. 22.

[2] Bačkalić T. & Škiljaica V. (1998). Modelling of Vessel

Traffic Process in One-Way Straits at Alternating

Passing, Proceedings of the "MARIND '98" Bulgaria.

[3] Feng H. (2013). Cellular Automata Ship Traffic Flow

Model Considering Integrated Bridge System.

International Journal of Service, Science and Technology

Vol.6.

[4] Groenveld, R. (2006). Ship trafﬁc ﬂow simulation study

for port extensions, with case extension Port of

Rotterdam. In: 31st PIANC Congress, Estoril, 2006.

[5] Gucma L. & Sokolowska S. (2012) The ships entering to

Szczecin port dimensions analysis with over-normative

vessels consideration. EXPLO-SHIP 2012.

[6] Gucma L., Sokolowska S. & Bak A. (2016). Stochastic

Model of Ships Traffic Capacity and Congestion -

Validation by Real Ships Traffic Data on Świnoujście -

Szczecin Waterway. Annual of Navigation. Vol. 24.

[7] Mohring R. et all. (2005). Conﬂict-free real-time AGV

routing. Operations Research Proceedings 2004, Berlin,

Springer-Verlag.

[8] Mou. J.M. et all (2005). Research on application of queuing

theory in communication engineering, Journal of Wuhan

Institute of Shipbuilding Technology.

[9] Olba X.B., Daamen W., Vellinga T., Hoogendoorn S.P.

(2018). State-of-the-art of port simulation models for risk

and capacity assessment based on the vessel navigational

behavior through the nautical infrastructure. Journal of

Traffic and Transportation Engineering. Vol.5.

[10] Pocuca M. (2006) Methodology of day-to-day ship cost

assessment. Transport Economics Review vol.18 2006.

[11] Ugurlu, O.; Yuksekyildiz, E.; Kose E. (2014) Simulation

model on determining of port capacity and queue size: a

case study for BOTAS Ceyhan Marine Terminal.

TransNav International Journal on Marine Navigation

and Safety of Sea Transportation 2014, 8, 143-150.

[12] Zhou H. et all (2013). Nanjing Yangtze River Bridge

Transit Capacity Based on Queuing Theory 13th COTA

International Conference of Transportation Professionals.