495
1 INTRODUCTION
Channel‐through capacity is described as the
maximum number of vessels passing a particular
channel per unit time. It is not only an important
parameter to measure port workload and port
throughputcapacity,butalsoareferenceindicatorfor
vessel traffic management and port channel design.
Besides, channel‐through capacity is of great
significance to channel and port operating condit
ion
assessment(Yeoetal.2007,Yangetal.2016),channel
efficiency optimization (Davis et al. 1980) and ship
navigation risk evaluation. In recent years, people
have been paying more attention to water
transportation and the demand for navigational risk
reduction and waterway operation efficiency
improvementhasbeenincreasing.Thus,theresearch
forchannel‐throughcapacitybecomesmoreandmore
realist
icallysignificant.
Currently,therearemainlythreetypesofmethods
tocarryouttheresearchonchannel‐throughcapacity:
Static Calculation Method (SCM), Dynamic
Evaluation Method (DEM) and Model Simulation
Method (MSM). SCM, ba
sed on ship domain model
theory (Fujii & Tanaka 1971, Elisabeth & Goodwin
1975),isageometricanalysismethodinwhichsome
correction coefficients can be selected according to
previous experiences and then an empirical formula
can be set up to calculate the channel‐through
capacity at different water condit
ions. With the
research becoming in‐depth, ship‐following theory
(Zhu&Zhang2009)
andotherresearchmethodshave
gradually been infiltrated into this calculation
method.Somescholars,withconsiderationofthereal
condition of channels, have also explored the
calculation method by expanding the channel‐
through capacity measurement not only for specific
waters like channel and port (Wang et al. 2015),
but
A Novel Through Capacity Model for One-way Channel
Based on Characteristics of the Vessel Traffic Flow
Y. Nie, K. Liu, X. Xin & Q. Yu
School of Navigation, Wuhan University of Technology, Wuhan, China
H
ubei Key Laboratory of Inland Shipping Technology, Wuhan, China
N
ational Engineering Research Center for Water Transport Safety, Wuhan, China
ABSTRACT:Vesseltrafficflowisakeyparameterforchannel‐throughcapacityandisofgreatsignificanceto
vesseltrafficmanagement, channel andportdesign andnavigationalrisk evaluation.Basedonthe study of
parametersofcharacteristicsofvesseltrafficflowrelatedtochannel‐throughcapacity,thispaperputsforward
a bra
nd‐new mathematical model for one‐way channel‐through capacity in which parameters of channel
length,vesselarrivalrateandvelocitydifferenceindifferentvesselsareinvolvedandatheoreticalcalculating
mechanismforthechannel‐throughcapacityisprovided.Inordertoverifyavailabilityandreliabilityofthe
model,extensivesimulationstudieshavebeencarriedoutandba
sedonthehistoricalAISdata,ananalytical
casestudyontheXiazhimenChannelvalidatingtheproposedmodelispresented.Bothsimulationstudiesand
the case study show that the proposed model is valid and all relative parameters can be readjusted and
optimized to furt
her improve the channel‐through capacity. Thus, all studies demonstrate that the model is
valuableforchanneldesignandvesselmanagement.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 3
September 2017
DOI:10.12716/1001.11.03.16
496
alsoforanyapplicableplaceofnavigation(Liuetal.
2016). SCM is a quantitative analysis method; the
advantageofSCMisthattheoutputisvisual,anditis
especially good for analyzing the result of simple
channelconditions.
DEM,basedonanalysisofdynamiccharacteristics
ofchanneloperation,
helpsestablishaqueuingmodel
applicabletoacertainchannelwiththestatisticsand
studiesofvesselarrival& servicetimeandevaluate
channel‐through capacity dynamically by such
parameters as stand‐by time, stand‐by queue length
and stand‐by probability (Mavrakis & Kontinakis
2008, Zhou et al. 2013).
Typically, this method can
reflect stochastic characteristics of vessel traffic and
together with vessel traffic simulations can also be
usedtoassesschannelcongestion(Gucmaetal.2015)
andtocheckthestabilityofportservicesystemwhich
determines whether the port channel capacity meets
the requirement of port operation, thus
helping put
forwardasystemoptimizationschemebasedonthe
aboveestimation.
SMM,basedonanalysisofcharacteristicsofvessel
traffic flow and channel system, is a method
conducive to build some sub‐models such as vessel
model and channel model so that the whole vessel
navigation process can be
simulated in a certain
simulationenvironmentandthenasimulationmodel
forchannel‐throughcapacitycanbeestablishedafter
taking multiple rounds of simulation tests
(OʹHalloran et al. 2005, Qu & Meng 2012). Some
relative studies have also further explored dynamic
linkages between certain influencing factors and
channel‐through capacity. For example, Almaz &
Altiok(2012)analyzedthechangeofchannel‐through
capacitywithnavigablechanneldepth,vesselarrival
rate, vessel’s scale and other
factors through the
established simulation model. SMM can reflect the
actualoperationconditionofthechannel, describing
rather accurately the influence of those dynamic
changes when vessels are navigating in the channel
onchannel‐throughcapacity.Inaddition,themethod
isoftenusedtodecideandselecttheoptimalchannel
route
(Gucmaetal.2015).
At present, in the research of channel‐through
capacity, SCM aims to calculate the maximum
numberofvesselspassingthroughacertainchannel
section within a certain time. Channel length is not
concernedandcorrectioncoefficientsaremostlyused.
But the data collection of SCM is
subjective and
randomandtheinfluenceofeachfactoronchannel‐
through capacity cannot be accurately reflected just
by using correction coefficients to correct the
calculation formula of channel‐through capacity.
DEM generally focuses on channel‐through capacity
of port system which is actually about whether the
numberofportberths
isenough.One‐wayChannel‐
throughcapacitychannelisrarelymentionedandthe
method is mainly about qualitative analysis. SMM
providesneitherdueconsiderationoftheinteraction
amongvesselsnoreasyaccesstodiscoveringfactors
and the impact mechanism influencing channel‐
throughcapacity,thusfailingtounveilessentiallaws.
Due
to limitations of above traditional research
methods,thispaperintendstoestablishabrand‐new
mathematicalmodelforchannel‐throughcapacity.In
this model, a one‐way channel is taken as the main
studyobjectand such parameters aschannellength,
vessel safety distance, vessel velocity and velocity
differenceindifferent
vesselswhichareallrelatedto
vesseltrafficflowareconcerned.Basedonthismodel,
a theoretical calculating mechanism of channel‐
through capacity for one‐way channel can be
discovered.
2 VESSELTRAFFICANALYSIS
Topresentthecircumstancesofchanneltrafficflow,a
series of indexes are employed for analysis.
In this
part, with the concept of vessel traffic flow (VTF)
beingfirstlyproposed,avesseltrafficflowmodeland
theories of mutual interference between vessels are
both explored to illustrate the issue of one way
channel‐throughcapacity.
2.1 VesselTrafficFlowModel
Vessel traffic flow (VTF) has been defined
as the
overalldynamiccharacteristicsofcontinuousvessels
that navigate in the same direction along a channel
(Wu & Zhu 2004). Main parameters of vessel traffic
flow are vessel arrival rate, vessel velocity, and so
forth.
Vesselarrivalrate(VAR)refersto the number of
vesselsarrivingattheentranceofthechannelperunit
time. VAR is closely related to the total number of
passing vessels and
the degree of congestion of the
channel.Vesselvelocity(VV)considerstwoissuesof
vesseltrafficflow,thevelocitydistributionrangeand
theaveragevelocity.Anychangeof twofactorswill
instantaneouslyinfluencethe VTFstateand analysis
of these two parameters helps guide the
implementation of vessel traffic management.
Some
researches before this one have proved that typical
parameters of vessel traffic flow obey certain
distributions. In general, VAR complies with the
Poisson distribution, and vessel velocity (VV) obeys
theNormaldistribution.
Besidestheabovetwoindexes,shipdomain(SD)
isanotherimportantparameterrelatedtoVTF.SDis
presented
fortheeffectofvesselsontheenvironment.
Here the concept of environment includes other
vessels, channel situation and other options that
directly or indirectly influence the safety of vessels.
Hence, SD should be noted at all time to keep the
minimumsafetydistancebetweentwovesselsandto
improve
channelpassingefficiency.Vesselinterval,a
sub‐concept of ship domain (SD), refers to the area
whereothervesselsareavoidedfromenteringforthe
reason of safety (Fujii & Tanaka 1971, Elisabeth &
Goodwin 1975). The size of ship domain (SD) is
closely related to such aspects as traffic density,
visibility,vesselvelocity,vesseltypeetc.Forinstance,
highseasusuallytake2milesasastandardreference
forvesselcollisionavoidance.
Having described the main parameters, the next
stepisto discuss the distributionregulationofVAR
andVV.Inordertosolvetheproblem,acasestudyof
Xiazhimen Channel is conducted in this paper to
analyze characteristic s of vessel traffic flow. As
shown in Figure 1, Xiazhimen Channel, located
497
between Taohua Island and Xiazhimen Island, is a
typical one‐way channel with high traffic density.
With an overall length of about 7 miles, the
navigation condition of the channel is quite
restrictive. The hydrological conditions of this
channelaresuperiorowingtotheremarkabletarget
for vessel location, enough
water depth, clear
navigationsignalandsmallwaves.
Figure1.XiazhimenChannel
By using the Matlab software, this case study
analyzes, fits and tests the AIS data for the vessel
trafficinXiazhimenChannelcollectedfromMarch24
to 29, 2015. According to the data statistics and
distribution test, the VAR at the entrance of the
channel follows the Poisson distribution with an
average of two vessels per hour and the VV of the
vesseltrafficflowfollowstheNormaldistributionin
which the average velocity is 10 knot and the
standarddeviationis1.8,asshowninTable1.
Table1. Typical parameters of vessel traffic flow in
XiazhimenChannel
_______________________________________________
TypicalDistribution expressionunit
parameters typesmodel
_______________________________________________
Vesselarrive PoissonPOISS(2)ship/h
ratedistribution
VesselnormalNORM(10,1.8)kn/h
velocitydistribution
_______________________________________________
2.2 MutualInterferencebetweenVessels
Vessel‐vesselinterferencemeansthatonevesselasa
give‐way vessel or a following vessel in a one‐way
channel(orstraightchannel)needstomakenecessary
adjustmentstoitsvelocity toensuresufficientsafety
clearance for avoiding collision situations when its
velocity is
greater than that of the consecutive front
vesselandwhentheintervaldistancebetweenthemis
closetotheminimumsafetydistance.
Viabriefanalysisoftheinteractionmechanismof
vessels,vessel‐vesselinterferencecanbedividedinto
twoforms:directinteractionandindirectinteraction.
Figure 2 demonstrates the interference
analysis
between two consecutive vessels. The velocity of
vesselS
iandSjissettoV1andV2respectively.Aftera
periodoftimerepresentedast
1whenthefrontvessel
S
i has sailed for a known distance marked as Dij, it
beginstoenterthechannel.Accordingtoshipdomain
theory,D
ij,theintervaldistancebetweentwovessels
shouldbegreater than the minimum safetydistance
d
0sothattherewillbenocollisionriskbetweenthese
two vessels. Otherwise, vessel interaction will exist
and when it becomes effective, some preventive
measureshouldbetaken.
Thevelocitydifference canbeconcludedasthree
situations, stable，negligible and intolerable. At the
stable situation when V
1 equals V2, the distance
between two vessels remains unchanged. The
negligible situation means that V
1, the front vessel
velocity, is higher than V
2, the following vessel
velocity.Therefore,thedistancebetweentwovessels
willgraduallyincrease.
Figure2.Interferencebetweentwoconsecutivevessels.
Intheabovetwosituations,thereisnointeraction
between two vessels, hence no measures need to be
taken to avoid collision. But at the intolerable
situationwhenthefrontvesselvelocityV
1issmaller
than V
2, the velocity of the following vessel, if the
following vessel continues catching up the front
vessel,theintervaldistancebetweentwovesselswill
approachtotheminimumsafetydistance,whichwill
threat vessels’ safety. Assuming that the interval
distance between two vessels reaches the minimum
safety distance at a certain time
t2 when the front
vesselexitsthechannel,vessel‐vesselinterferencewill
reach the maximum. According to the collision
regulation, deceleration should be taken by the
followingvesseltoavoidcollision.Theprocessabove
explainsdirectinterferencebetweentwovessels.
Based on the direct interaction analysis, another
interference mechanism, the interaction
between a
series of vessels sailing in the channel is studied to
exploreindirectinteraction.Thereisanimpactchain
among these vessels which passes on from one to
anotherandstopsonlywhenthechainisbroken.This
impactchainillustratesindirectinteraction.InFigure
3,thereareaseries
ofvesselsS1,S2,S3inthechannel,
andthelevelofvesselvelocitiesare V
1<V2<V3. At
the time shown in Figure 3, the interval distance
betweenvesselS
1andvesselS2reachestheminimum
safetydistanceduetothevelocitydifference.Inorder
to ensure navigational safety, S
2 will decelerate and
this operation will continually impact later vessels,
accelerating the process of shortening the interval
betweenS
2andS3.ThenS3willreduceitsvelocityto
avoid collision risk. Hence, S
1 has an indirect
interferenceonS
3throughthetransitionfromS2.This
interaction chain not only reduces the number of
vessels through the channel per unit time but also
raisesthechannelcongestionapparently.
498
Figure3.Achainreactionofmultiplevesselsinterference.
To confirm the influence of vessel‐vessel
interference on the vessel traffic, an experiment for
vessel‐vessel interaction in a one‐way channel is
implementedintheMatlabsoftware.Obviously,this
procedurehassome limitations,asitisbasedsolely
oninstantaneousdecelerationcriteriaand,aboveall,
it neither includes other
parameters except for
channellength,vesselnumberandvesselvelocitynor
considers the difference between vessels except for
vessel velocities and time when vessels enter the
channel. The experiment explores only the relation
between vessel‐vessel interaction and vessel traffic
flow.
According to the difference of velocity, the
experiment is
conducted under three circumstances:
1)Four vesselsenterthechannelinaccordancewith
the velocity changing from small to large; 2) Four
vessels enter the channel with randomly distributed
velocity; 3) Four vessels enter the channel in
accordance with the velocity changing from large to
small. The simulation results of the
three cases are
showninTable2.
Table2.Datacomparisonofthevessel‐vesselinterference.
_______________________________________________
Vesselinitial VesselfinalTimeofallvessels
velocityvelocitythroughthechannel
_______________________________________________
V1=10,V2=9.5 V1=10,V2=9.52533
V
3=9,V4=8.5V3=9,V4=8.5
V
1=9.5,V2=10 V1=V2=9.52607
V
3=8.5,V4=9V3=V4=8.5
V
1=8.5,V2=9 V1=V2=V3=V4=8.52656
V
3=9.5,V4=10
_______________________________________________
WithreferencetotheresultsshowninTable2,the
followingobservationscanbemade:inthefirstcase,
thereisnoneedforanyvesseltoslowdown,andthe
time required for four vessels to pass through the
channelistheshortest.Inthelastcase,S
2,S3,S4need
to take a proper decelerating reaction, and the time
requiredforallvesselstopassthroughthechannelis
the longest. It can be observed that vessel‐vessel
interference has hindered the smoothness of the
traffic flow and increased the time required for the
samenumberofvesselstoleave
thewaterway,which
indirectlyeffectsthechannel‐throughcapacity.
3 CHANNEL‐THROUGHCAPACITYMODEL
In this part, to simplify vessel traffic system some
assumptions for a calculation model of channel‐
throughcapacityareputforward.Afterthat,basedon
ideal channel‐through capacity, a brand‐new
mathematical model is established,
which can
manifesttherelationshipbetweensomeparametersof
vesseltrafficandchannel‐throughcapacity.
3.1 ModelAssumptions
The operation process of vessel traffic system in the
channel mainly includes two parts: the channel
environment model and vessel traffic flow model,
working together to show a real environment of
vessel traffic
system. Here in order to describe and
analyze the relevant problem conveniently, some
optimizations and assumptions are made for the
calculationmodel,whichisdescribedfullyasfollows.
Channelenvironmentdesigningisonefoundation
process for vessel traffic system analysis. It includes
manysubfactorssuchaschannellength,width,
water
depth, bending radius, tide and etc. This paper
focuses on one‐way channels, hence the channel
modelissimplifiedbyregardingchannellengthLas
the main parameter. Channel length will not restrict
vessels’ normal operation. In the design process, a
straightchannelwherethereisnoturnorintersection
interference is chosen. Meanwhile, channel depth
ensuresthenormalnavigationforallvesselsandthe
effect of tide is eliminated in this model. Lastly,
vesselsareallowedtosailonlyatthesamedirection
andovertakingisforbiddeninthechannel.
With a reasonable channel environment model
beingdesigned,vessel
trafficflowcanbeintroduced
as a main object to be considered later. The main
parameters of vessel traffic flow include velocity,
density, vessel arrival rate, vessel interval and etc.
Generallyspeaking,theevaluationandcalculationof
traffic flow can intuitively reflect the vessel
navigation state and the navigation environment of
the channel. Here, considering all characteristics of
one‐way channel, ship domain needs to be
highlighted. In this research, a navigational
environment with neither overtaking vessels nor
restrictions on the width of the channel is built. All
vessels at trailing condition form a queue in the
channelandthereis
noapproachingdangerfromport
side and starboard side. Therefore, according to the
general situation of traffic flow and the actual
demandofthemodel,thetrafficflowmodelprovides
thefollowingassumptions:
1 All vessels at stand‐by condition are allowed to
enterthechannelimmediately.
2 Vessels shall enter
the channel according to the
FCFS(Firstcome,firstserve)mode,whichmeans
thatvesselsareorderedtoenterwaterwaysmerely
bytheirarrivaltime.
3 Thevesselvelocitywillremainsteadyduringthe
wholevoyageifthereisnointerferencefromother
vessels.
4 Overtakingandhead‐onsituation
areforbiddenin
the channel, and safety interval, the distance
between the front vessel’s stern to the second
vessel’s fore is harnessed as the index of
navigationsafety.
3.2 Establishment ofaComputationalModel
Accordingtotheconceptofchannel‐throughcapacity,
themaximumnumberofvesselspassingthroughthe
channel
during a period of time, defined as C,
togetherwithchannellength,navigationvelocityand
safety distance between the front and second vessel
forms a relationship which can be described via the
following function: C=f (L, V, d
0). This part of the
499
study analyzes the microscopic characteristics of
vessel traffic flow, and then finds the final function
based on the geometrical relationship between
vessels.
3.2.1 Idealchannel‐throughcapacity
Ideal channel‐through capacity studies the
maximum number of vessels that can pass through
the section of channel in unit time under a
certain
conditioninwhichbothchannelconditionsandtraffic
conditionsareinidealstate,andvesselsareakindof
standard ones with same technical performance and
navigation parameters. In addition, vessels need to
enter the channel consecutively with the distance
between two adjacent vessels larger than the
minimum safety
distance (Dong et al. 2007). In this
case,whennavigatinginthechannel,vesselshaveno
opportunity to overtake, but only to follow the trail
until exiting the channel. Based on the theoretical
channel‐through capacity, the channel‐through
capacityinanidealconditionisanalyzed.
Figure4.The analysisschematicdiagramofidealchannel‐
throughcapacity.
InFigure4,twovesselsconstituteabasicunit.Itis
assumedthatarrivingvesselsnavigatewiththesame
velocity and enter the channel in a continuous
manner. In order to ensure the safety of navigation,
the distance between the front vessel S
i and the
second vessel S
j should be clarified. When the front
vesselisnavigatinginthechannel,thesecondvessel
isallowedtoenterthechannelonlywhenthepathof
the front vessel is bigger than the minimum safe
distance d
0. According to the above procedure, a
traffic flow queue is created. It is an orderly
management in which each vessel keeps the
minimum safety distance to enter the channel. The
time interval T
ij can be easily concluded as the
followingformula:
0
/
ij
TdV
(1)
In this formula, the vessel velocity is a constant
number.Thevesselentersthe waterwayatacertain
timeintervalT
ij,sothenumberofvesselsenteringthe
channelperhourisshownasfollows:
0
3600 /CVd
(2)
Informula(2),unitsofd
0andVareexpressedby
meterandmeterpersecondrespectively.
3.2.2 Channel‐throughcapacityanalysismodel
Objectively, there is a velocity difference for two
adjacent vessels when they reach the channel. The
velocity difference between two vessels exerts direct
influenceonchannel‐throughcapacity.Ifthevelocity
ofthe
secondvesselis smallerthanthatofthe front
one, the distance between two vessels increases
gradually, which guarantees that two vessels can
alwaysmeettherequirementoftheminimumsafety
distance in the navigational state. Conversely, if the
secondvesselvelocityisgreaterthanthatofthefront
one, the
distance between two vessels decreases
graduallyuntilcollisiondangerarises.
Figure5. Analysis of vessels’ distance variation under
differentvelocity.
As shown in Figure 5, when the front vessel
velocityissmallerthanthesecondvesselvelocity,in
order to ensure that the distance between S
i and Sj
meets the minimum safety distance requirement
marked as d
0 during the whole period when two
vessels are navigating in the channel, the initial
distance d
1 between two vessels needs to be
recalculated. Under the circumstance when the
minimumsafedistancebetweenthefrontandsecond
vessel can be guaranteed, each vessel is capable of
maintainingaconstantvelocityinthenavigation.The
size of d
1 can be deduced from vessel velocity and
channellength,asshowninthefollowingformula:
10
()/
ji j
dVVLVd
(3)
When the front vessel velocity is greater than or
equal to that of the second one, the minimum safe
distance d
0 can be chosen as the initial distance
betweentwovessels.
In consideration of the above two situations, for
the first situation when the front vessel velocity is
greaterthanthatofthesecondone,theprobabilityof
thissituationoccurringis P
1.Inthe second situation
when the velocity of the first vessel is smaller than
thatofthesecondone,theprobabilityisindicatedas
P
2. In order to find out the distribution rule of the
initial distance, the concept of initial interval
expectation is proposed. The calculation formula is
shownasfollows:
10 21
()
E
dPdPd
(4)
Figure6. Analysis of channel through capacity based on
vesselvelocitydifference.
500
The average initial distance of successive vessels
entering the channel is replaced as initial interval
expectationE(d)inFigure6.Obviously,ifthedistance
between the front vessel and the channel entry
terminalisE(d),thesecondvesselhasnorestrictionto
enter,andthenthisstep
isrepeatedgradually.With
combination of equations (2) ~ (4), the channel‐
throughcapacitycanbeexpressedasfollows:
02
3600 3600
() ( ) /
ji j
VV
C
Ed d P V V L V
(5)
Under the realistic navigational environment, the
initial velocity of different vessels entering the
channel distributes in a certain value yet within a
nominatedrange,thedistributionofvesselvelocityis
similar to that of a Normal distribution. Here the
assumed certain value is indicated as μ and the
standard deviation
is as σ, therefore, the initial
velocity V can be replaced as N(μ,σ
2
). With the
increaseofσ,thepossibilityofthevelocitydifference
getting greater will increase, which means that P
2 ×
(V
j−Vi)willincrease.Similarly,withthedecreaseofσ,
the possibility of the velocity difference getting
greater will decrease and so will the value of P
2 ×
(V
j−Vi). Obviously, there is a kind of certain
correlationbetweenP
2×(Vj−Vi)andσ,which canbe
simplifiedas(V
j−Vi)∝σ.Inaddition, Vj ispositively
correlatedwithV,whichcanbeformulatedasV
j∝V.
With simplification, the formula of channel‐
throughcapacitycanbeconcludedas:
2
03
3600 V
C
dVk L
(6)
In formula (6), channel‐through capacity C is
effectedbyaveragevelocityV,standarddeviationσ,
channellengthL,andsafedistanced
0.k3representsa
constant and can be obtained by simulation
afterwards. In order to intuitively reflect the
relationship among channel‐through capacity,
standard deviationσ and channel length L, the
formulaisfurthersimplifiedbytakingd
0andVasthe
fixedvalue:
1
23
k
C
kk L
(7)
Informula(7),bothk
1andk2representaconstant
andcanbeobtainedbynumericalinput.
4 SIMULATIONEXPERIMENTANALYSIS
In this part, a simulation scene is firstly designed.
Thensomesimulationexperimentsare conducted to
further explore the proposed calculation model and
verify the reliability of the model. Finally by
analyzingsimulationresults,itcan
befoundthatthe
calculationmodelisreasonabletosomeextent.
4.1 SimulationSceneDesign
The invented simulation model contains two parts:
thevesselmodelandthechannelenvironmentmodel.
The vessel model contains three sub‐modules which
are the vessel generation module, the vessel motion
module and the vessel decision
‐making module. In
thevesselgenerationmodule,someparameterssuch
as vessel arrival regularity and vessel interval are
necessary. These input data for vessel generation
model have been concluded from the statistical
analysis of the vessel traffic flow at Xiazhimen
Channel.Thevesselmotionmoduleismainlyusedto
show
navigational performance of vessels in the
channel. Lastly, the working mechanism for vessel
decision‐making model is employed to compare the
real‐time interval and the minimum safety distance.
The channel model is designed to limit vessels’
navigation by primarily setting up external
parameters such as the channel situation and
hydrological
conditions, all of which are taken from
the statistics provided in the study of Xiazhimen
Channel.
Apart from some of conditions having been put
forwardinchapter3.1,morelimitationsofthevessel
traffic flow model for future analysis are given as
follows:
1 Eachvessel is considered separately as
an object.
No interference except vessel interval
requirementsisinvolved.
2 In the channel, the movement of the vessel is
modeled in one dimension only. Besides, vessels
movelinearlyalongthedirectionoftrafficflow.
3 Once vessel velocity changes, the change is
completedflashily.Afterdeceleration,thevelocity
ofthe
followingvesselwillbethesameasthatof
thefrontone.
During the simulation of the vessel navigating
process, to set up the simulation scenario, the
following five parameters are concerned: channel
lengthL,vesselminimumsafetydistanced
0,average
velocity V, velocity standard deviation σ and vessel
arrivalrateλ.Inthedesignofchannelenvironment,
theaveragevelocityVandthevesselminimumsafety
distance are considered as two significant constants
whiletherestoftheparametersarevariables.Ineach
simulation experiment, Mont Carlo simulation
methodisadoptedtoobtainanevaluationparameter
for channel‐through capacity with reference to the
numberorquantityproportionofallthedeceleration
vessels achieved by changing vessel arrival rate.
Based on the statistical analysis of the vessel traffic
situationatXiazhimenChannel,itisassumedthatthe
minimumvessel
safetydistanceisaround1000m,the
average velocity is about 10 knots and the standard
deviationisspearedwithintherangefrom1knotto
3.7knot.Besides,whenthevalueofλismorethan25,
theproportionofthenumber ofdecelerationvessels
ismorethan95%,which
meanstheλmorethan25is
insignificant. Therefore, in the experiment, λ varies
from 1 to 25. Consequently, four research programs
canbedesigned,aslistedintable3.
501
Table3.Experimentprogramdesign.
_______________________________________________
Parameters L(nm) σ V(kn) d0(m) λ
_______________________________________________
Example1 6 1.5 10 1000 variable(1~25)
Example2 6 2 10 1000 variable(1~25)
Example3 10 1.5 10 1000 variable(1~25)
Example4 10 2 10 1000 variable(1~25)
_______________________________________________
When the proportion of the number of
deceleration vessels reaches 80% in one day, the
stand‐by time for each vessel will significantly
increaseandthechannelwillbeovercrowded.Inthis
situation, 80% of the number of deceleration vessels
per day can be regarded as a reasonable number
representingthe
channel‐throughcapacity.
4.2 SimulationResultsAnalysis
Basedontheabovementionedexperimentalscenario,
the large data of statistical averages in the same
experimentalscenarioistakenastheeffectiveoutput
oftheexperimentbyMontCarloprinciple.Thispart
of the paper focuses on the change of some
parameters
accompaniedwiththecontinuouschange
ofvesselarrivalrate.
Referring to the channel‐through capacity
equation having been mentioned in chapter 3.2,
parameters k
1and k2, related to the average velocity
andtheminimumsafetydistance,canbeobtainedby
calculation.However,theconstantnumberk
3needsto
befurtherstudiedbythesimulationanalysis.Specific
vessel arrival rate will be gained to calculate
parameter k
3 in the calculation model and then by
comparing and analyzing k
3 within multiple
experimentalscenarios,reliabilityandstabilityofthe
calculationmodelforchannel‐throughcapacitycanbe
verified. Figure 7 shows the relationship between
vesseldecelerationproportionandvesselarrivalrate
underdifferentexperimentalscenarios.Inthefigure,
the channel‐through capacity for each experimental
scenarioispointedoutwith
marks.
It can be observed from Figure 7 that the
simulation experiment has verified the relation of
channel‐through capacity and the velocity standard
deviation, the channel length. When channel length
remains constant, the velocity standard deviation is
larger,whilethechannel‐throughcapacityissmaller.
When standard deviation is constant,
the channel
length is longer, while channel‐through capacity is
smaller.Thevariationtrendofthesimulatedchannel‐
throughcapacitywiththevariationofchannellength
andthevelocitystandarddeviationisconsistentwith
the calculation model of channel‐through capacity,
which indicates that the calculation model has a
certain
degreeofcredibility.Consideringresultsofall
the analyses above, the following measures can be
taken to improve channel‐through capacity. On the
onehand,ifchannellengthisreducedtodecreasethe
possibility of interference between vessels, channel‐
throughcapacitywillincrease.Ontheotherhand,if
vesselvelocityentering
thechanneliscontrolledina
relatively concentrated range, that is, when the
velocitydifferenceissmall,channel‐throughcapacity
canalsobeimproved.
Figure7. Simulation analysis of the channel through
capacity.
Thevalueofk3forthefourgroupsofexperimental
conditions can be obtained by applying channel‐
through capacity in simulation to the calculation
model, which is 0.223, 0.3076, 0.2461 and 0.2855
respectively.Itcanbeseenthatthefluctuationrange
ofk
3isnotlargeandthemeanvariance is 0.001089.
Therefore, it can be predicted that the value of k
3
tends to be a stable interval in the case that the
channellengthorthestandarddeviationofthevessel
velocity is different, which indicates that the
rationality of the model derivation is in a relatively
acceptablerange.
5 CONCLUSIONS
Basedonthecharacteristicsofvesseltrafficflowand
vessel‐
vesselinterferenceanalysis,thispaperpresents
a calculation model of channel‐through capacity. A
setofsimulation experiments are designed to verify
the rationality of the calculation model. The results
showthatthedataofthecalculationmodelcanmatch
up with the simulation data to a certain extent.
Meanwhile, the
calculation model clearly
characterizestherelationofchannel‐throughcapacity
and vessel velocity, channel length. For a particular
one‐waychannel,characteristicsofvesselvelocitycan
be analyzed by means of data acquisition and
probabilitystatistics.Basedonthat,thevalueofk
3of
thecalculationmodel canbeobtained by simulation
fitting. With further experiences, it will be of great
theoretical significance to guide the calculation of
channel‐throughcapacity.Inaddition,themodelcan
502
provide certain scientific basis and decision‐making
support for relevant departments to determine the
velocity limit standard and to improve its
managementlevel.
However,theresearchresultsofthispaperarejust
rudimentalandpreliminary,andtherearestillmany
places worthy of further study. In the process of
model
derivation,inordertosimplifythecalculation
and to facilitate the analysis, the velocity difference
betweentwoadjacentvesselsisassumedtobelinear
withthevelocitystandarddeviation,whichresultsin
the fluctuation of k
3 to some extent. The follow‐up
workwillmainlydiscussthescientificissuesofk
3in
the calculation model, and continue to modify and
optimizethederivationprocessofthemodel.Further
studies on the problem of k
3 under complex
conditions such as the intersection of vessels, tide
navigationandsoonwillalsobeexpected.
ACKNOWLEDGEMENTS
The authors would like to acknowledge National
Natural Science Foundation of China (NSFC) under
GrantNo.51479157forsupportingthisresearch.
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