International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 6
Number 3
September 2012
317
1 INTRODUCTION
For two decades, many of changes have arisen in
sizes and shapes of a ship in maritime traffic. Since
many ships are navigating inside of narrow fairway
in a harbor area specially, the navigational difficulty
by traffic congestion is also increasing. In order to
correspond to such a change and to secure the safety
of navigation, it is required to presume the relation
between a width of route in fairway and allowable
traffic volume.
Generally, a fairway can be explained to be a
maritime passage where ships cruise and maneuver.
It can classify into ocean route and coastal route as
like narrow water service as like Incheon entrance
located westly in Korea. The base elements which
constitute a route in fairway are a width, a length,
and a depth. As usual, because the length of a route
changes according to each geographical condition,
there is no standard uniform in a fairway or route.
However, a width and a depth are closely concerned
with the safe navigation of a ship.
The existing method of route design which calcu-
lates a width is common concept that the movement
of a maximum size ship in the route has taken into
consideration for designing a route, but taken into
consideration for another ships passing around. On
other hand, in case of road design in land transport,
numbers and widths of a lane are decided in consid-
eration for designed traffic volume.
This research aims at approaching the design in
consideration of traffic flow on a route width from
such a view point, concurrently on the assumption
that the design of route which took the movement of
the one maximum model of a ship into considera-
tion. In addition as the first approach, this research
examines for one-way route in comparatively large
water area which is not influenced by an island and a
shoal, which has sufficient margin depth of water
too.
2 NECESSITY FOR APPROPRIATE WIDTH TO
CORRESPOND TRAFFIC FLOW
As a conventional method determining route width,
"Approach Channels A Guide for Design" (It calls to
PIANC-Rule below) is internationally proposed by
PIANC and IAPH in 1997.
PIANC Rule considers a wind, a current and nav-
igational aids such as a beacon for calculated ele-
ments in design of the width. The required width of
route is needed to the multiple numbers of maximum
size ship’s beam (B) and a curvature radius is ex-
pressed with the multiple numbers of lengths (L) of
the ship. Contrarily when it is calculated for move-
ment of the one maximum model of ship which
cruises a route, it has considered neither passing nor
the existence of another ships which carries out sim-
ultaneously is taken into consideration.
The Relation with Width of Fairway and
Marine Traffic Flow
Y. C. Seong, J. S. Jeong & G.K. Park
Faculty of division of maritime transport system, Mokpo Maritime University
ABSTRACT: Nowadays, many of changes have arisen in maritime traffic due to the enlargement of ship’s
size and improvement of ship’s speed. It is common that the risks of handling a ship in narrow water area is
increasing according to increase traffic volume. In order to correspond to these changes and risks, it should be
necessary to make sure the relation between proper width of route in fairway and allowable traffic volume.
The conventional method of designing a fairway takes into consideration of movement by one ship of maxi-
mum size. But the congestion by traffic volume is not taken in the concept. In a while, a case of road design is
generally considered about a traffic volume. From such a view point, this research proposes the method of de-
termining fairway-width in consideration of traffic flow. To evaluate traffic congestion in a route, the Envi-
ronmental Stress model is adopted as the index of standard, using traffic simulation with avoiding a collision
for reproducing traffic flow.
318
In actual, various ships exist in the route in which
route’s state is very crowded with traffic rushes de-
pending on time zone.
The method such as PIANC rule designs a route
only depending on the basis of maneuvering maxi-
mum size model. Therefore it cannot be guaranteed
of the navigational safety in such a situation.
This research will examine required width of a
route from a viewpoint of navigational safety. For
this examination, it is necessary to clarity two
points. First is that one ship of the maximum model
can guarantee safety up to how much traffic conges-
tions become. Second point is how much width of
route is needed to the capable degree of traffic vol-
ume.
3 SIMULATION OF MARINE TRAFFIC
3.1 Algorithm of Collision Avoiding
In order to calculate the width of a route in consider-
ation of a congestion of traffic flow, it is required to
reproduce a traffic congestion state under the condi-
tions of certain given width of route, to evaluate the
navigation difficulty. Here, the simulation technique
based on desirability of collision avoiding was used
in this research.
As an evaluation index showing the navigation
difficulty under traffic congestion, the environmen-
tal stress value by an ES(Environmental Stress)
model was adopted. The method of a judgment and a
rule of collision avoiding in the simulation model
used here is explained below.
3.1.1 Judgment of collision avoiding>
A start domain of collision avoiding is a standard
area which sets up the start of collision avoiding ac-
cording to approach a collision distance by another
(target) ship, just when there is a possibility of col-
liding with ownship.
Fig.1 Concept of Collision Avoidance
In the model used in this paper, it also sets to the
relative speed of an ownship and target ships accord-
ing to average lengths among the ships, as shown in
Fig.1.
3.1.2 Process of collision avoiding
As shown in a formula (1), the efficiency of colli-
sion avoiding and the safety of ownship are calculat-
ed by all navigational means including change a
course and a speed. The optimal area finally is cho-
sen by an evaluation.
)}({)()(
,
,1
,, jik
mK
jiji
XRMaxaXPbXu
=
×−=
(1)
)(
, ji
Xu
: Evaluation Function to choose optimal
navigation
)(
, ji
XPb
: Probability changing all courses and
speeds to avoid
)(
, jik
XR
: Risk colliding with ships or obstacles
ji
X
,
: Area to avoid collision with other ships or
obstacles
pi ~1=
: Preference group to change a course
qj ~1=
: Preference group to change a speed
a
: Weight factor,
m
: Ship’s numbers of encounter-
ing
Probability changing a course to avoid:
)exp()(
00,
CaXPb
ci
∆⋅−=
Probability changing a speed to avoid:
)exp()(
,0
VaXPb
vj
∆⋅−=
Probability changing a courses and a speed to avoid:
)()()(
,00,, jiji
XPbXPbXPb ⋅=
0
C∆
： An angle of course change (deg）
V∆
： A ratio of speed change (%）
c
a
= 0.0190(Left change of course), 0.0260(Light
change of course),
v
a
=0.0456
3.2 Condition of simulation
A simulation area is considered to one-way passage,
which the length is 10000m. The evaluation section
is 4000m off the center of this area. This water area
is not influenced by an island, a shoal, etc, which has
also sufficient depth of water.
About a condition of a simulation, three compo-
nents were set up parametrically; a width of route,
319
composition of ship’s appearance and traffic volume
as shown in Fig.2 Process simulation.
The width of a route was considered as three pat-
terns (300m, 500m, and 700m) by referring to main
ports of Korea. The compositions of ship which
form a traffic flow set up for small size, medium size
and large size patterned to be a percentage of 7:2:1
and 4:5:1. Traffic volumes could be 10, 20 and 30
ships per an hour.
The size of a ship was classified into the small
ship (48.26m±20m), middle ship (104.08m±20m)
and the large ship (240.00m±50m) based on the ac-
tual data of an entrance to Mokpo in Korea. The
ship’s speed was used as the small ship
(9.7kts±2.2kts) and middle ship (14.5kts±3.2kts) and
the large ship (15.4kts±3.0kts).
Simulation time is recommended that the time be
longer in order to obtain a reliable evaluation result.
However, a simulation by increasing time recklessly
will be wasted. So this simulation could be up to 100
hours.
In addition, the interval time generating ships
(making traffic volume) asks for the average time in-
terval according to the number of target ships. The
ships were generated using exponential distribution
with such an average value.
Fig.2 Process of Simulation.
4 ANALYSIS ON SIMULATION’S RESULTS
4.1 Index of evaluation
In this research, the environmental stress value by an
ES model was adopted as an evaluation index show-
ing the navigation difficulty under traffic congestion.
A description is simply added to below about the ES
model.
4.1.1 Environmental Stress model, ES model
The elements of the environmental conditions
that can be taken into account in the model are as
follows;
1 Topographical conditions such as land, shoals,
shore protection, breakwaters, buoys, fishing nets,
moored ships and other fixed or floating obsta-
cles.
2 Traffic conditions such as the density of other
ships and traffic flow.
3 External disturbances such as winds and currents.
The proposed model, which expresses in quantita-
tive terms the degree of stress imposed by topo-
graphical and traffic environments on the mariner, is
called the Environmental Stress Model (ES-model).
The ES-model is composed of the following three
parts:
1 Evaluation of ship-handling difficulty arising
from restrictions to the water area available for
maneuvering. A quantitative index expressing the
degree of stress forced on the mariner by topo-
graphical restrictions (ESL value) is calculated on
the basis of the time to collision (TTC) with any
obstacles.
2 Evaluation of ship-handling difficulty arising
from restrictions on the freedom to make colli-
sion-avoidance maneuvers. A quantitative index
expressing the degree of stress forced on the mar-
iner by traffic congestion (ESs value) is calculated
on the basis of the time to collision (TTC) with
other ships.
3 Aggregate evaluation of ship-handling difficulty
forced by both the topographical and traffic envi-
ronments, in which the stress value(ESA value) is
derived by superimposing the value ESL and the
value ESs.
The model is a practical method for evaluating
the ship-handling difficulty of navigation in topo-
graphically restricted and congested waterways, and
in ports and harbors. The strength of the model lays
in its ability to evaluate simultaneously or individu-
ally the difficulties of ship-handling arising from
topographical restrictions and encounters with other
ships and because it includes acceptance criteria
based on a mariner’s perception of safety.
Star t, Simulation T ime
Occur r ence of Shi p
1. Ship speed : 6 kts ± 3kts
2. Length : S M L = 70% 20% 10%
3. Volume traffic = 10 ~ 20
T raffic of Ship
1. Manuever ing : K T model
2. Cour se : N or t hbound, V ar iabl e 1
3. Avoidance collision : V ariable 2
Invasion Domain_j udgement
by T ar get_ship and N eed of
Collision_judgement ?
K eep up Cour se & Speed
Pr int, Depiction of Flow
Yes
Change 2,3
No
Star t, Simulation T ime
Occur r ence of Shi p
1. Ship speed : 6 kts ± 3kts
2. Length : S M L = 70% 20% 10%
3. Volume traffic = 10 ~ 20
T raffic of Ship
1. Manuever ing : K T model
2. Cour se : N or t hbound, V ar iabl e 1
3. Avoidance collision : V ariable 2
Invasion Domain_j udgement
by T ar get_ship and N eed of
Collision_judgement ?
K eep up Cour se & Speed
Pr int, Depiction of Flow
Yes
Change 2,3
No
320
4.2 The standard of allowance judgment
The marine traffic simulation with collision avoiding
was carried out. The environmental stress model was
applied to all the ships which form a traffic flow in a
simulation. The difficulty which a ship operator felt
in combinative conditions was calculated by this
model.
In evaluation, it adopted as an index of a judg-
ment of the appearance ratio [P (ESA>=890)] of the
environmental stress value 890 equivalent to the
state where 80 percent of ship operator groups are
nonpermissible.
In addition to the judgment of the limit of permis-
sible traffic volume, P (ESA>=890) of the ship for
evaluation was made into less than 5% of the per-
missible judging standard, from the meaning in con-
sideration of existence of the uncertain factor which
cannot be specified.
4.3 Result of simulation
4.3.1 Calculation of allowable traffic on route
width
In evaluation of ship traffic, it could not consider
that a small ship and a large ship were the same traf-
fic of 1 vessel, but traffic was normalized using L
conversion traffic by using a 70m [ in full length ]
ship as a standard ship.
Fig.3 compares route width with the appearance
ratio of load nonpermissible for every combination
of an ownship model. In simulation, it has a plot
which case route width is from 300m to 700m.
In these figures, ship’s percentages are <4:5:1>
and <7:2:1> is united and plotted. Since these ships
were expected that they could normalize using L
conversion traffic, there were some variations. But
the graphs performed linear regressions for the
group of six points respectively.
Fig. 3 Rate of appearance of P (ESA>=890) by width of route
in 500m
(◆:Large ownship, ■:Middle ownship)
Fig. 4. Required route-width according to traffic volume
(In case ownship is middle-sized)
Although an ownship is extrapolated as a part, the
amount of allowable traffic to each width of route
and each case of ownship’s size can be obtained if
an approximation straight line reads L conversion
traffic in case the value of a vertical axis [P
(ESA>=890)] used as 5% based on these figures.
Thus, the amount of allowable traffic to each
route width can be presumed from Fig.4 when an
ownship are each a large size and a middle size ship.
4.3.2 Presumption of allowable traffic on route
width
Fig.4 shows plotted graphs presumed result of the
amount of allowable traffic to each route width
when taking from the case in a middle size of own-
ship.
From this figure, the required route width to the
allowable limit of the traffic can be read to the given
route width conditions or the traffic conditions.
If it becomes route to 500m for a large ship, 10
ships per an hour will become as for the amount of
allowable traffic of which L conversion was done. If
700m, 15 ships per an hour will become.
When it comes from a middle size ship, it turns
out that permissible traffic volume increases respec-
tively by every 5 ships per an hour.
4.4 Relation to existing rule of route design
The existing route design method is a common
method of designing in consideration of movement
of one maximum ship in a route.
However on an actual route, the states that ships
navigate to compete with other ships would be a
normal state. In this research, the design of the route
width in consideration of traffic was approached, es-
caped from the conventional route width design
method which is width in consideration of move-
ment of the one maximum model of a ship.
0
10
20
30
40
50
60
0 5 10 15 20 25 30 35 40 45
Traffic volume by L-conversion
P(ES
A
≧890)
0
5
10
15
20
25
30
0 100 200 300 400 500 600 700 800 900
Required width (m)
Allowable traffic (ship)
321
Fig.5 is a mimetic diagram shows the mutual rela-
tion of the design method in consideration of the ex-
isting route width design method and the congestion
of traffic based on Fig.4.
If the route width designed by the existing meth-
od cannot allows a certain traffic to exceed, it can
explain the need of increment of fairway which the
concept of shifting to the view based on the route
width in consideration of traffic volume designed by
this research.
Fig. 5, Idea of required route-width over traffic volume
5 CONCLUSION
As many changes in maritime conditions have arisen
in narrow waterway including the enlargement of
ships, so navigational difficulty by traffic confusion
is increasing. In order to secure the safety of naviga-
tion to such a change, it is needed the concept based
on ship’s traffic, which concept considers ship’s
traffic in congested situation and the maneuvering
movement of maximum size ship in the traffic.
From such a viewpoint, the route design method
in consideration of traffic congestion was ap-
proached by presuming the relation between route
width and permissible traffic amount.
This paper examined for one-way route in com-
paratively large water area which is not influenced
by ships and any obstacles as the first approach,
which has sufficient margin depth of water. Asked
for appropriate width of simulated route in consider-
ation of congested traffic, the traffic congestion state
was reproduced by marine traffic simulation. The
navigation difficulty under traffic confusion was
evaluated with the application of Environmental
Stress model.
As a result, it could clarity that how much of
width in a route be able to guarantee a state of traffic
congestion to navigational safety in the simulation.
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R.G. Garthune et al. (1948) : The Performance of Model Ships
in Restricted Channels in relation to the Design of a ship
Canal, DTMB report 601.
J. Siebol and J.H.G. Wright (1974) : Application of Ship Be-
havior Research in Port Approach, Proceedings of Ship Be-
havior in Confined Water, Symposium held in London.
PIANC PTCⅡ(1997) : Approach Channels A Guide for De-
sign. Report of Working Group Ⅱ－30. Supplement to
Bulletin No.95.
Kinzo Inoue et al. (1998) : Modeling of Mariner’s Perception
of Safety, The journal of navigation, No.98, pp. 235-245.
(in Japanese)
Kinzo Inoue (2001) : Evaluation Method of Ship-handling Dif-
ficulties for Navigation in Restricted and Congested Wa-
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