489

1 INTRODUCTION

In1985afundamentalstudywaspublished[1]which

for long decades defined the views over the port

development. One of the most prominentresultsof

the study was the employment of the queuering

theory. Under some restrictions (not important at

that time) this tool enabled to achieve the results

beforeconsideredimpossible:thei

ntroductionofthe

berthutilizationcoefficientК

occasa controlparameter

tied together infrastructural and commercial

characteristicsoftheport.Really,portalwaysusedto

be a collision point of ship owners and terminal

operators interests: both would like to see their

expensive assets earning money. The ship owner

likestoseealltheberthsintheportidleandwait

ing

forhisshiptoserve;theportoperatordreamsofall

berthsoccupied,preferablywith the queue of ships

waitingforafirstberth tofree.  Thequeuingtheory

offered a simple and understandable way to set a

desiredbalanceofportandshiplosses.

2 SEAPORTASAQUEUINGSYSTEM

Aportcouldbetrea

tedasaqueueringsystemwith

ships as the jobs (vessels) arriving to the servers

(berths) [4].  The mean arrival rate could be

determinedbythenumberofshipscallingattheport

withinayearNorthemeanintervalbetweenarrivals

int:

Simulation for Service

uality and Berths Occupancy

Assessment

A.L.Kuznetsov&A.V.Kirichenko

dmiralMakarovStateUniversityofMaritimeandInlandShipping,SaintPetersburg,Russia

ABSTRACT:Currentdevelopmentofthemaritimetransportationsystem,namelyfleetandportsspecialization,

growth of vessel sizes, rationalization of routs, trade regionalization etc., has made many traditional

approaches and calculation techniques practiced for many long years in port design procedures to be

inadequat

eandinsufficient.Agenerallyacknowledgedtoolforthistasktodayisthesimulationtechnique.In

thesametime,modernobjectorientedsimulationapproachprovidesusuallyonlyadhocsolutionforaproject.

Itlacksthegeneralitythatwasthemainandnaturalfeatureofitstraditionalanalyticalpredecessors.Veryhigh

meandlaborconsumptionofsimulationcomestoaconflictwithaverynarrowscopeoftheresultingmodel’s

applicationdomain.Thispaperdescribesanewapproachusedtocreateasimulationtoolfortheportdesigners

andplannerscombiningtheuniversalityandgeneralityoftheanalytical(socalled“

static”)methodswiththe

efficiency and accuracy of the object‐oriented simulation. The concept represented in the paper was

implemented in the software product, which enabled to conduct experiments that proved the validity and

adequacyofthemodel.Thesimulationtoolwasusedinseveralseaportdesignprojectandnowisa common

inst

rumentofseveralleadingportdesignandconsultingcompanyinRussianFederation.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 10

Number 3

September 2016

DOI:10.12716/1001.10.03.14

490

int

365 Т







The ship berthing time in this case could be

interpretedasanaverageservingtimeТ

serv.Thejobs

servedand leaving the system are described by the

servingrate

serv





.

Thevalue









 iscalledtherelativedensityof

arrival. This value shows how many vessels would

arrive during the berthing time of one vessels. The

number of ships which should be served

simultaneously defines the number of berths in the

port. Insufficient number would cause the queues

and losses for the ship

owners, redundant number

wouldleadtolossesfortheportownersduetopoor

utilization of expensive capital assets (berths). The

queueringtheoryoffersawaytofindthebalanceof

these losses thus finding the optimal value of n

opt.

Specifically, the theory provides a formula for the

averagelengthofthequeuem

s



































nnk

)(!!



Thisformulaincludesasvariablesthenumberof

servers

 and the relative density



. Since

occ=



/n,forpracticalpurposesitismoreillustrative

toexpressm

sasafunctionofКocc. 

Thisdependencewaspresentedin[1]asatable,

without sufficient explanations and with references

toratherrareliteraturesources.Themissing link in

reasoning put certain obstacles to development of

advanceperceptionandheuristicenhancementofthe

proposed approach. As an additional unpleasant

consequence, the value К

occ started to be generally

treated as a design parameter, while the nature of

thisvaluemakesitjustanintermediateone. 

Itismorelogicaltosetadirectexplicitrelationof

twomainvaluescriticallyimportantforshipowners

and port operators – average waiting ratio and

utilization of

 berths – as functions of the annual

cargoturnoverQandnumberofberthnintheport.

The dependence of К

occ from Q at given berth

number n in this case is trivial:

occ=(N*Тserv)/(n*365)=(Q*Тserv)/(n*365*V),whereVisthe

ship capacity. In more complicated cases treated

below,thisdependenceisnotassimple.Ifwedenote

theberthproductivityasP=V/Т

serv,thentohandlethe

annual cargo turnover Q we would need the time

interval T

work=Q/P would needed.Since the annual

budget of time for n berths is n

*365, eventually we

haveК

occ=Q/(P*n*365)/

Thus we can offer a new structure for the

gueueringsystemmodelasgivenbyFigure1.



Figure1.Newstructureofthegueueringmodel

3 THERESTRICTIONSOFTHEQUEUERING

MODELS

Today, with much wider vessel size range,

complicated rationalization of routes and new port

infrastructuredesign,nearlyallmainassumptionsof

the ship arrival discipline needed to imply  the

queuering system model are not observed. The

arrival flow is never stationary due to commercial



circumstances,withsomeshipsarriverandomlyand

some obey different schedules. Moreover, the most

important is totally different interpretation needed

fortheberthsasservers.

Historically, a berth as construction entity was

equaltoadministrative(management)unit.Sincethe

ship’s sizes were close to the berth length, this fact

did

not cause any inconveniences. The constant

growthoftheshipandberthsizescausedproblems

in interpretation of berth occupancy, since in some

casesseveralshipscouldbeservedatoneberthand

inothercasesoneshipcouldoccupymorethanone

berth.

The definition of К

occ in this case could be

correctedasК

occ=(Σl

ship

i)/L

Тб,butanywayit

wouldruinthebasicassumptionenablingtousethe

queueringtheory.

4 THEDESCRIPTIONOFGENERALMODEL

Let us assume that we would like to estimate the

maximal cargo turnover Q during an interval Т

realizedwiththeshipswithdifferentcapacity,whose

inputs in Q are

 defined by the probability

distributionP(V). An exampleof thisdistribution is

givenbyFigure2.

491



Figure2.Histogramofshipcapacitydistribution

This distribution gives probabilities pi of

appearance among all N ships arriving within a

givenintervalTtheshipswithcapacityv

i,i.e.



Thuswehave



Thisenablesustocalculatetheaveragenumberof

callsoftheshipsofdfferentcapacity:



Foreveryshiptype we canestimatethe average

arrival interval τ

i = T/ni . Naturally, the stochastic

values of every ship type arrival interval fluctuates

around this mean values. If we know the lows of

these fluctuations,possibly different for every type,

we could generate a partial arrival flows for every

shiptype(Figure3).



Figure3.Partialarrivalflowsofdifferentshiptypes

Let us further assume that we have several

different berths, B

k, k=1,…,K , whose characteristics

(permitted ship length and draft, cargo handling

equipment, commercia l terms of the contracts with

shipping lines etc.) permit to accomodate not all

ships at every berth, while different productivity

establish different turnaround time at different

berths.Inageneralcasetheequipmentcouldbuilda

common

pooltobedistributedbysomespecificlows

amongsinglberthsin the group.Therestrictions to

usetheberthscouldalsohavecommercialnature.

Letusintroduceamatrix[tik]IxK,whoseelement

ikshows,atwhattimeashipofcapacityv iishandled

at the bertB

k. If tik=0, the ship cannot be

accommodatedat this particular berth (see Figure

4).



Figure4.Matrixofservingtimeatdifferentberths

The general structure of the model dealing with

the above mentioned assumptions is illustrated by

Figure5.



Figure5.Thestructureoftheproposedmodel

Theproposedmodelenablesustoundertakethe

study of two main parameters – occupation of

different berths and waiting ratio for different ship

types–asfunctionofcargoturnoverQ.Inorderto

do so we will run the model (with a set of fixed

external parameters) increasing

the main variable

(cargoturnover)fromzerotoanygivenvalue (ora

value showing unlimited waiting ratio growth at

least for one berth, giving the maximal terminal

throughput,oritscapacity).

5 IMPLEMENTATIONOFTHEMODEL

The described model is realized on a very

sophisticated and licensed object‐oriented platform.



Formanyapplications,forexamplefortechnological

design of ports and termina ls, when the number of

berths and number of STS is under optimization,

therewouldbeenoughtouseasimplifiedversions, 

since the use of the advanced software would be

connected with the barrier of learning. For this

purposes a dedicated MS EXCEL version of the

model was developed, where the well‐known

spreadsheets are used as a common or easily

studying interface. The sophisticated software

“engine”ishidden“underthehood”ofthisproduct,

makingthelatterlooksverysimpleandinnocent.

Thedataarekeyedinthe

screenformsshownon

figures6‐8.

492

Description

Unit Denomination Value

TotalQuayLength

[m]

L 3500

Turnoverbysimulationinterval

[teu/interval]

Q 10000

STSproducivity

[move/hour]

TEUfactor

[teu /b ox]

teu

1,00

Shipcapacityutilization

shp

1,00



Mooringgap

0,10

ProductivitydecreasebytheNoofSTS

lin

1,00

Simulationinterval

[hou r] T

8760

Annualcargoturnover

[teu/year]

Qyear 10000

RTGproducivity(Sea‐>CY)

[move/hour]

P1 8

RTGproducivity(CY‐>Land)

[move/hour]

P2 8

RTGproducivity(Land‐>CY)

[move/hour]

P3 8

RTGproducivity(CY‐>Sea)

[move/hour]

P4 8

Cargoturnoversimulationrange Begining End Step Noofsteps

Annualcargoturnover 1600000 2800000 100000 12



Figure6.Generaldataontheproject

Shiptypes v1 v2 v3 v4 v5 v6 v7 v8 v9 v10

Capacity

[te u]

1000 882 1890 2178 2430 2836 2926 1828 9000 10000

Importparty

[te u]

Imv

1000 441 945 1089 1215 1418 1463 1645,2 8100 9000

Exportparty

[te u]

Exv

0 441 945 1089 1215 1418 1463 1645,2 8100 9000

Shareofcargoturnover α

1000000 000

Numberofcalls N

10000000 000

STSrequired n

4222445 566

LOA

[m]

180 180 180 180 300 350 400 400 400 400

Auxilliaryoperationtime

[ho ur]

0444223 333

Cargooperationtime

[ho ur]

10,0 17,6 37, 8 43,6 24, 3 28,4 23, 4 26,3 108, 0 120,0

unl oading

[ho ur]

Imt

10 8, 82 18,9 21,78 12,15 14,18 11,704 13,1616 54 60

[ho ur]

Ext

0 8, 82 18,9 21,78 12,15 14,18 11,704 13, 1616 54 60

Totalhandlingtime

[ho ur]

10,0 21,6 41, 8 47,6 26, 3 30,4 26, 4 29,3 111, 0 123,0

Callintervaldistribution

code

 равномерно эрланг эрланг эрланг эрланг эрланг эрланг эрланг эрланг эрланг

Parameter1 2222222 222

Parameter2



Figure7.Shipsdescription

Ships v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 Berthlength NoofSTS

STSal ocate d 4222445566

BERTHS [m] [unit]

B1 1111111 200 2

B2 1111111 200 2

B3 1111111 200 3

B4 1111111 380 3

B5 380 4

B6 380 4

B7 440 5

B8 440 5

B9 440 6

B10 440 6



Figure8.Berthsdescriptionandship/berthcompatibility

Figures 9‐10 display the screenshots of the

model’s serial run over some interval where the

cargo turnover reaches maximally accepted values

for a given ship capacity distribution and specified

berth’scharacteristics.



Figure9.Waitingratiogrowthwithcargoturnover



Figure10.Bertutilizationgrowthwithcargoturnover

6 CONCLUSIONS

1 Theapproachisdescribedwhichcouldbetreated

asalogicalextensionofthequeueringtheoryfor

modernberthsandcargohandlingequipmentin

portdesignprocedures.

2 The adequacy of the approach is proven by the

comparison with the queuering theory results

whenapplicable.

3 The approach is implemented both in a highly

specificproduct(builtinthefull‐scalesimulation

model used for the task of global resource

optimizationsoftwareunderdevelopment)anda

stand‐aloneversionusingMSEXCELasafriendly

interface.

4 TheMS EXCELversion proved to beuseful and

efficientatthestage ofport and terminal design

fortheoptimizationofberthnumberandSTSfleet

justification.

5 The product could be recommended for any

persons engaged in the optimization of the

number of berths, berth productivity, number of

cranes on the berths, the influence on the port

capacityofthedifferentshipcallsdistribution. 

6 Especiallyusefullythisinstrumentcouldbewhen

design and planning of port operations for non‐

interchangeableberths. 

7 Any interested specialists could apply for an

advancedsimulationtoolswithmuchwidescope

andenhancedresearchfeatures.

LITERATURE

[1]Port development. A handbook for planners in

developing countries. Second edition. UNCTAD, NY,

1985,ISBN92‐1‐112160‐4.

[2]KuznetsovA.L.etal.(2010)Simulationasanintegrated

platform for container terminal developmentlife‐cycle

The proceedings of the 13th Internationalconference

on Harbor Maritime Multimodal Logistics Modeling

and

Simulation,Fez,October2010,ISBN2‐9524747‐4‐5,

p159‐162

[3]Kirichenko A.V.,  Kuznetsov A.L., Izotov O.A. (2013)

Methodology decisions in transport logistics. Final

Report on the scientific work. Admiral  Makarov State

University of Maritime and Inland Shipping, Saint

Petersburg.№reg.01201172251.

[4]KuznetsovA.L.,EglitJ.J.,KirichenkoA.V.

(2013)Onthe

issue of organizing the operation of a transport hub.

TransportoftheTransportofRussianFederation.№1

(44).С.30–33.

[5]Kuznetsov A. L. (2009) The Methodology of modern

container terminal’s technological design.Academy of

TransportoftheRussianFederation,SaintPetersburg.



