179
1 INTRODUCTION
Recently, marine traffic is congested and complex
accordingtotheincreasingofmarinetrafficvolume,
high speed ships, and larger ships. Accordingly,
navigators and captains are stressed more. As the
result, it is supposed to increase accidents such as
collisionsbetweenshipsandsoon.Onceanaccident
happens, not only ship, cargo, and human are lost,
but also it is influenced on the local economy and
environment because of load and oil spillage.
Therefore, evaluating the difficulty of sailing is
necessaryinordertodesignroutes andimprovethe
safetyinmarine.Onthedifficultyindexof
sailingin
marine,somemethodsaresuggested.Inthispaper,a
method using marine traffic simulation system is
used.
For reproducing marine traffic flow, so‐called
macro simulation such as the network simulation is
used,butnowadaysso‐calledmicrosimulationwhere
individual ships are directly controlled, is used. In
most
cases, ships are sailing according to the
predefinedplanedroute,buttherearesomemethods
where ships can avoid collisions according to the
situation. Marine Traffic Simulation System
(abbreviating as MTSS hereafter) (Hasegawa (et al.)
1987,1989,1990,1993,1997,2000,2001,2004a,2004b,
2008,2010,2011,2012a,2012b),
whichisdevelopedin
Osaka University and used in this study, has this
feature.Itappliesfuzzyreasoningtopredictcollision
risk using DCPA and TCPA, and can treat multiple
shipencountersituation.Applyingforseveralmarine
areas, it is proved that MTSS can reproduce the
marinetrafficflowin
themostrealisticwaycompared
totheotherexistingmethods.However,theresultisa
casestudy,andthesailingdifficultyordangerofthe
area cannot be compared quantitatively among
various marine areas. Therefore in this study, the
indices for evaluating the difficulty or danger of
sailing under the different
conditions are proposed
and compared among various marine areas
quantitatively.
Qualitative and Quantitative Analysis of Congested
Marine Traffic Environment – An Application Using
Marine Traffic Simulation System
K.Hasegawa&M.Yamazaki
OsakaUniversity,Osaka,Japan
ABSTRACT:Difficultyofsailingisquitesubjectivematter. Itdepends onvarious factors.UsingMarineTraffic
SimulationSystem(MTSS)developedbyOsakaUniversitythischallengingsubjectisdiscussed.Inthissystem
realistictrafficflowincludingcollisionavoidancemanoeuvrescanbereproducedinagivenarea.Simulationis
doneforsouthwardofTokyoBay,StraitofSingaporeandoff‐Shanghaiareachangingtrafficvolumefrom5or
50to150or200%ofthepresentvolume.Asaresult,strongproportionalrelationbetweennear‐missratioand
trafficdensityperhourpersailedareaisfound,independentontraffic
volume,areasizeandconfiguration.
Thequantitativeevaluationindexofthedifficultyofsailing,herecalledriskrateoftheareaisdefinedusing
thusdefinedtrafficdensityandnear‐missratio.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 7
Number 2
June 2013
DOI:10.12716/1001.07.02.03
180
2 COLLISIONAVOIDANCEALGORYTHM
The feature of MTSS is having automatic collision
avoidance function. In this chapter, automatic
collision avoidance function is briefly explained
(Hasegawa2012a).
2.1 Collisionrisk
There are many collision risk indices proposed by
severalresearchers.Shipdomainconceptisprobably
thefirstconcepttreatingit.In
thisstudyCRisused.
CRisthe collision risk defined by DCPA and TCPA
using fuzzy reasoning. Later the definition of CR is
somewhatmodifiedandnowthefollowingdefinition
is used. For assessing collision risk in normal (WP
modeinFigure4)condition,CRdefinedbyTCPA and
DCPAʹ(eq.(3))isused.
For determining avoiding action, ACR is used to
check the collision risk of the assumed avoiding
action.Inthiscase,followingmodifiedTCPAisused
for calculating ACR considering individual ship
manoeuvrability,especiallyforlargeships.
Figure1.MembershipfunctionforTCPACorTCPAV
Figure2.MembershipfunctionforDCPAʹ
CC
TCPA TCPA C T
(1)
Fordeterminingthetimingtotakereturningtothe
original path, VCR and OCR are used to check the
collisionriskofassumedreturningaction.Inthiscase,
followingmodifiedTCPAisusedforcalculatingVCR
andOCRconsideringrapidturnofsmallships.
TCTCPATCPA
VV
(2)
where C
C and CV are constants and T is the time
constant of Nomotoʹs equation (Nomoto et al. 1957,
Nomoto 1960) of the subject ship. In the simulation,
C
C=2andCV=1000areusedbasedonsomesimulation
results. These modifications are reflecting the
difference of course changing ability roughly
estimatedfromthetimeconstantT.
DCPAis non‐dimensionalisedusing longershipʹs
lengthoftwoshipsencountered.
),max(
TO
LLDCPAADCP
(3)
BothTCPA
C,TCPAVandDCPAʹaredefinedby8
and5linguisticvariablesusingmembershipfunctions
asshown inFigures1 and2respectively,which are
determined by authorsʹ previous researches on
experts knowledge and experience and both
maximum values (360 and 7.2 for open sea
respectively) can be modified based on the
gaming
area, or users can tune them as they like. Collision
risk CR is defined by 8 linguistic variables and
membership functions as shown in Figure 3. The
reasoning fuzzy table to determine CR is provided
usingTCPA
CandDCPAʹasshowninTable 1.CR is
thusdefinedbetween‐1and1anditispositivebefore
passing CPA and negative after passing CPA. The
absolutevalueisproportionaltothecollisionrisk.
Figure3.MembershipfunctionsforCR
Table1.FuzzyreasoningtableforCR
_______________________________________________
TCPA
SAN MEN DAN DAP DMP MEP SMP SAP
_______________________________________________
DA SAN MEN DAN DAP DMP MEP SMP SAP
DM SAN SAN MEN DMP MEP SMP SAP SAP
DCPA’ MESAN SAN SAN MEP SMP SAP SAP SAP
SM SAN SAN SAN SMP SAP SAP SAP SAP
SA SAN SAN SAN SAP SAP SAP SAP SAP
_______________________________________________
Figures4.Procedureofcollisionavoidancemanoeuvre
Table2.Simulationconditions
_______________________________________________
SimulationAreaTrafficVolume(%)
_______________________________________________
SouthwardofTokyoBay50‐200
StraitofSingapore5‐150
OffShanghaiArea5‐150
_______________________________________________
2.2 AVOIDINGACTIONSTRAGETY
TheownshipwillstartavoidingwhenCRisequalor
greaterthanCR
C.CRCisCRg(0.7inthesystem)forthe
181
give‐waysituationandCR
s(0.9inthesystem)forthe
stand‐on situation. After detecting the collision risk
reachestothecriteria,eachshipwill takeacollision
avoidance action. Once avoiding mode started, the
ship will take avoiding action normally by turning
right.Theangleofcoursechangewillbedetermined
by ACR.
ACR is CR assuming the present heading
angle as this angle plus the course changing angle
A
.
A
ischosen30deg.first,butifACRisbigger
thanCR
C,itwillbeincreasedevery
A
 (=5 deg.in
the system) and repeated until ACR becomes lower
thanCR
Cbutitstopsat45deg.inthemaximum.After
A
is fixed, the own ship will change course to
A
.Oncegettingintheavoidingmode,thesystemis
checking VCR continuously until it falls below CR
V1
(0.7inthesystem).If
A
reaches45deg.andACRis
stilllargerthanCR
C,voidcoursechangingandreduce
speedtohalfofthepresentspeed.
3 SIMULATIONCONDITIONS
In order to quantitatively assess and compare the
difficulty of sailing, simulations are done for
southwardofTokyoBay,StraitofSingapore,andoff
Shanghai. Simulation time is 24 hours and the
numberofindividual
simulationsisfivetimes.Traffic
volume is chosen in various percentage of the real
trafficvolumeasshowninTable2.
4 ASSESSMENTUSINGNEAR‐MISS
Inthischapter,quantitativelyassessingthedifficulty
ofsailinginindividualareasisexplained.
4.1 Near‐miss
On evaluating the difficulty ofsailing by
MTSS, the
number of near‐misses is proposed as an index. A
near‐miss is defined that it occurs WHEN CR ≧0.7
ANDothershipexistswithinarectangularareaofFA
heightandSPwidtharoundtheownship,whereFA
andSParedefinedforharbourareaby
Inoue(1994)
as
OT
LLFA )076.20015.0(
(4)
OT
LLSP
)667.0008.0(
(5)
Figure 5 shows this area and the numbers in the
figure is the ratio of the position of the own ship
dividingthisrectangular.
Figure5. The definition of ship domain in harbour area
(Inoue1994)
4.2 Assessmentexamplesusingnear‐missasanindex
The number of near‐misses NM for the simulation
doneforthreeareasfor100%trafficvolumeisshown
in Figure 6. For each area five‐time trial results are
individually shown. The number of near‐misses in
StraitofSingaporeis
about20timesandthatofoff‐
Shanghaiareaisabout70timescomparedwiththatof
southward of Tokyo Bay respectively. Does it mean
the difficulty of the area is also proportional to this
number?
0
100
200
300
400
500
600
700
800
900
1000
Nearmiss(count)
SouthwardofTokyo bay
Strait ofSingapore
off Shanghai
Figure6.Thenumberofnear‐missesbysimulation
5 ASSESSMENTUSINGTRAFFICDENSITYAND
NEARMISSRATEASINDICES
In previous chapter, the difficulty of sailing is
discussed quantitatively using the number of near‐
misses. However, it is difficult to compare, because
thenumberofshipsandtheareasize,configuration
andsoonaredifferent.
5.1 Trafficdensityand
Near‐missrate
Inordertoassessthedifficultyofsailingonthesame
conditionsinanymarinearea,numberofships,and
near‐miss count per the unit time and size of area,
whicharedefinedastrafficdensityTDandnear‐miss
rateNR.Inthisstudy,the
unittimeis1hourandthe
unitsizeofareais1mile
2
.Nextdiscussionishowto
182
evaluatethedefinitionofthesizeoftheareaA.Itis
defined as the number of the unit rectangular areas
whereatleastoncebyashiporshipspass.Inthecase
ofFigure7,thenumberofrectangularareasis13,so
number of ships NS
is 2, A is 13 mile
2
and time of
simulationT
sisnumberofhourstakingbothshipsto
passthisareainhours.
1mile
2
Figure7.Theexamplehowtomeasurethesizeofthearea
Usingthis method,theformula ofTrafficdensity
TDandNear‐missrateNRaredefinedasfollows.
NS
TD
A
(6)
s
NM
NR
TA
(7)
5.2 AssessmentexamplesusingTrafficdensityandNear‐
missrate
UndertheconditionsshowninTable2,theresultsof
near‐missrateNRisplottedversustrafficdensityTD
in logarithm scale (Figure 8). The strait line in the
figure is an approximate line fitting the simulation
results.
Althoughtheareasarequitedifferentintheir
size, configurationandtrafficvolume, the near‐miss
rate NR including the artificial variation of traffic
volume is surprisingly proportional to the traffic
densityTD.
0.00001
0.0001
0.001
0.01
0.1
1
10
0.01 0.1 1
Nearmiss rate
(count/hour・mile
2
)
Traffic density
(count/mile
2
)
Southward of Tokyo bay
Strait of Singapore
off Shanghai
NR=1.24TD
2.39
Figure8. The relation betweentraffic density and Near‐miss
ratebysimulation
6 ASSESMENTUSINGRISKRATEOFTHEAREA
Inpreviouschapter,thestrongrelationbetweennear‐
missrateandtrafficdensityisshown.However,itis
still difficult to evaluate how much dangerous the
areais.Arethereanythresholdvaluesforthetraffic
densityandthenear‐missrate?
6.1
ThedefinitionofRiskrateofthearea
Toanswerthisquestion,anassumptionisconsidered.
Supposeallshipsinthearea feeldangerous(=near‐
miss),every timethey meet other ships.Thismeans
the near‐miss rate is O(NS
2
), where O() is the order
andNSisthenumberofshipinthearea.
This is the maximum near‐miss rate to be
expected. The ratio of the near‐miss rate to this
maximum near‐miss rate defined as MNR will be a
measuretoevaluatetherisk
ofthearea.Thereforethe
riskratiooftheareaRRAcanbedefinedas
2.39
0.39
2
1.24
1.24
NR TD
R
RA TD
MNR TD
 (8)
6.2 AssessmentexamplebyusingRiskrateofthearea
Maximumnear‐missrate MNR is addedinFigure 9
andcomparedwithFigure8.Table3showstherisk
rateof theareaRRAthusestimated foreach area at
100%trafficvolumeusingequation(8),althoughthe
actualsimulationresultsaresomewhatmoreandless
aroundthesevalues.ThedifficultyofsailinginStrait
of Singapore is about 1.7 times, and that of off‐
Shanghai are 2.1 times compared with that of
southward of Tokyo Bay respectively. As MNR is
extreme condition, from the safety point‐of‐view,
RRAhadbettertobekeptaslowaspossibleandthe
value of off‐Shanghai area seems quite close to the
dangerouszone.
0.00001
0.0001
0.001
0.01
0.1
1
10
0.01 0.1 1
Nearmiss rate
(count/hour・mile
2
)
Traffic density
(count/mile
2
)
Southward of Tokyo bay
Strait of Singapore
off Shanghai
NR=1.24TD
2.39
NR=TD
2
Figure9.Thetrafficvolumeallowancedegree
Table3.Riskrateoftheareabysimulationresults
_______________________________________________
SimulationArea(trafficvolume) RiskRateoftheArea
_______________________________________________
SouthwardofTokyoBay(100%)0.35
StraitofSingapore(100%)0.59
Off‐Shanghaiarea(100%)0.75
_______________________________________________
183
7 CONCLUSIONS
Thedifficultyofsailingisdiscussedinthispaper.The
proposed index of the difficulty of sailing is
independent and quantitative for the area.
Conclusionsaresummarizedasfollows.
1 Near‐miss rate is strongly proportional to traffic
density.
2 Risk rate of the area is defined
and expressed the
difficulty of sailing independently from the area
size, configuration and traffic volume and
quantitatively.
3 Todeterminethemaximumallowanceofriskrate
of the area, further discussion should be done
continuously.
8 NOMENCLATURE
[Symbol][Definition][(Unit)]
ACR Collision risk assuming taking
consideredavoidancemanoeuvre(‐)
A Areaswhereshipssailinthesimulation
at least once in a unit (1 mile
2
) area
(mile
2
)(cf.Figure7)
C
C Constant to evaluate TCPAC taking
accountoftimeconstantT(‐)
CPA Closestpointofapproach
CR CollisionriskcalculatedfromTCPAand
DCPAusingfuzzyreasoning(‐)
CR
C CRthresholdforchangingmanoeuvring
mode to avoiding mode from waypoint
mode(‐)
CR
g CRCforgive‐wayship(‐)
CR
O CRthresholdforchangingmanoeuvring
mode to returning mode from parallel
manoeuvringmode(‐)
CR
s CRCforstand‐onship(‐)
CR
V1 CRthresholdforchangingmanoeuvring
mode to parallel manoeuvring mode
fromavoidingmode(‐)
CR
V2 CRthresholdforchangingmanoeuvring
mode to returning mode from parallel
manoeuvringmode(‐)
C
V Constant to evaluate TCPAV taking
accountoftimeconstantT(‐)
DCPA Distancetoclosestpointofapproach(m)
DCPAʹ Non‐dimensionalisedDCPA(‐)
L,L
O,LT Shiplengthingeneral, thatofownship
andthatoftargetship(m)
MNR Maximumnear‐missrate(1/mile
2
hour)
MTSS Marine Traffic Simulation System
developedbyOsakaUniversityasakind
of marine traffic simulation system
taking account of collision avoidance
manoeuvres
NM The number of near‐misses in the
simulationareaandtime(‐)
NR Near‐missrate(1/mile
2
hour)
NS Theaveragenumberofshipsexistingin
thesimulationarea(‐)
OCR Collisionriskassumingtakingreturning
manoeuvre(‐)
RRA Riskratioofaarea(‐)
T Timeconstantofashipformanoeuvring
(sec)
TCPA Timetoclosestpointofapproach(sec)
TCPA
C TCPAforCRevaluation(sec)
TCPA
V TCPAforVCRevaluation(sec)
TD Trafficdensitydefined(1/mile
2
)
T
s Simulationtime(hour)
VCR Collision risk assuming taking parallel
shiftmanoeuvre(‐)
Coursechanging angleinavoidingmode
(deg)
T
A
Relative angle to target ship measured
fromownshipstern(deg)
T
E
Encounterangleoftargetshipmeasured
fromownshipbow(deg)
REFERENCES
Fukuto,J.etal.2011.IntroductionofanAutomaticCollision
Avoidance Function to a Ship Handling Simulator (in
Japanese).JapanInstituteofNavigation(JIN)(125):63‐
71
Fukuto, J. et al. 2012. Ship Handling Simulator for
Assessing On‐board Advanced Navigation Support
SystemsandServices‐‐‐IntroductionofIntelligentShip
HandlingSimulator‐.MARSIM2012
Hasegawa,K.1987.AutomaticCollisionAvoidanceSystem
for Ship Using Fuzzy Control. Eighth Ship Control
SystemsSymposium(SCSS)(2):34‐58.
Hasegawa, K. 1989. Modelling of the Behaviours and
Decision‐Making of Ship Navigators. 3rd International
FuzzySystemsAssociation(IFSA)Congress:663‐666
Hasegawa, K.
et al. 1989. Ship Auto‐navigation Fuzzy
Expert System (SAFES) (in Japanese). Society of Naval
Architects,Japan(SNAJ)(166):445‐452
Hasegawa, K. 1990. Automatic Navigator‐Included
Simulation for Narrow and Congested Waterways.
NinthSCSS(2):110‐134
Hasegawa,K.1990.AnIntelligentMarineTrafficEvaluation
System for Harbour and
Waterway Designs. 4th
International Symposium on Marine Engineering Kobe
ʹ90(ISMEKOBEʹ90):(G‐1‐)7‐14
Hasegawa, K. 1993. Knowledge‐based Automatic
Navigation System for Harbour Manoeuvring. 4 Tenth
SCSS(2):67‐90
Hasegawa, K. et al. 1997. Reconfiguration of Ship Auto‐
navigationFuzzyExpertSystem(SAFES)(inJapanese).
The Kansai Society of Naval Architects of Japan
(KSNAJ)(8):191‐196
Hasegawa, K. et al. 2000. Feasibility Study on Intelligent
Marine Traffic System. 5th IFAC Conference on
Manoeuvring and Control of Marine Craft (MCMC
2000):327‐332
Hasegawa, K. et al. 2001. Intelligent Marine Traffic
Simulator forCongested
Waterways. 7th IEEE
International Conference on Methods and Models in
AutomationandRobotics:632‐636
Hasegawa, K. et al. 2004a. Maritime Traffic Simulation in
Congested Waterways and Its Applications. The 4th
ConferenceforNewShipandMarineTechnology(New‐
STech2004):195‐199
Hasegawa, K. et al. 2004b. Simulation‐based
Master Plan
Design and Its Safety Assessment for Congested
Waterways Management. International Maritime
ConferenceonDesignforSafety:265‐270
Hasegawa,K.etal.2008.TransmissionEvaluationofShip‐
borne Automatic Identification System (AIS) in
CongestedWaterways.The8thInternationalConference
onITST:18‐23
Hasegawa, K. et al.
2010.Marine Traffic Simulation of the
StraitofMalaccaandSingapore(inJapanese).JIN(122):
91‐96
Hasegawa, K. et al. 2010.The effect of the collision
avoidancealgorithminthemarinetrafficsimulation(in
Japanese).JIN(122):8
184
Hasegawa, K. et al. 2011. Safety Assessment of Marine
Traffic by Intelligent Marine Traffic Simulation. JIN
(125):33‐41
Hasegawa, K. et al. 2012a, An Intelligent Ship Handling
SimulatorwithAutomaticCollisionAvoidanceFunction
of Target Ships, International Navigation Simulator
LecturersConference(INSL17),F23‐1‐10
Hasegawa, K. 2012b,
Some Recent Researches on Next
GenerationMarineTrafficModelsandItsApplications,
The International Workshop on Next Generation of
NauticalTrafficModel(IWNTW2012),25‐31.
Inoue,K.1994.ModellingofMarinersʹSensesonMinimum
Passing Distance between Ships in Harbour. JIN (125):
63‐71
Nagasawa, A. 1984. Marine Traffic Simulation
Including
CollisionAvoidance.JIN(80):28‐34
Nomoto,K.etal.1957.OntheSteeringQualitiesofShips(2)
(inJapanese),J.ofsocietyofNavalArchitectsofJapan,
101.
Nomoto,K.1960.AnalysisofKempf’sStandardManoeuvre
Test and Proposed Steering Quality Indices, First
SymposiumonShipManoeuvrability,DTRCReport1461
Okuyama,Y.1984.NetworkSimulation.JIN (80):20‐27
Sugisaki,M.1984.OntheMarineTrafficSimulationwitha
MicroscopicModel.JIN(80):14‐19