275
1 INTRODUCTION
The maritime transport is the most effective and
relatively inexpensive transportation mode.
Mandatory elements of this complex system are:
ports, ships and ICT supporting and management
systems. It is well‐known fact, that ports are the
connectors between the seas, oceans, and land, and
specificallybetweenwatertransport and land.Thus,
logist
icsanddistributionofgoodsareoneofthemain
tasksoftheportcentres.Thus,atthemacroeconomic
level, the ports provide contacts with distant
countries, continents, through easier access to them.
Inthecaseofthemicroeconomicscale,itisdoingthe
business activities, services by the operators at the
portarea.Theseeconomica
ctivitiescanincludecargo
handlingand stowage,repair, parts production, and
many other services performed for the port or the
ships being in the port. The connections between
particularportsarecarriedoutusingtheships,which
are very important components of the ma
ritime
transportationsystem.Theirtechnicalcondition,crew
training, traffic safety are influential factors for the
whole safety of transportation system. Complement
of these elements of maritime transport are: vessel
traffic and monitoring systems, telecommunication
systems and port management and information
systems.Theyareveryimportantfactorforsafetyof
portsandshipping.TheyaresubjectedtotheEUlaw
regulations and implementations to Member States
law[26].Theirtechnological development alsogives
the opportunity to improve safety of navigation,
commercia
l efficiency and security which is
manifestedinthee‐Navigationconcept[31],[36].
According to [30], [35], the national airspace,
ma
ritime and land transportation systems, and the
vessels operating thereon, pipelines and other
deliveryservicesarethephysicaldistributionsystems
critical to supporting the national security and
economicwell‐beingofthisnation.
Thus, the European Commission defines the
Critical Infrastructure (CI) as an asset or system
whichisessentialforthemaintenanceofvita
lsocietal
Modelling Operation Process of Baltic Port, Shipping
and Ship Traffic and Operation Information Critical
Infrastructure Network
S.Guze&K.Kołowrocki
GdyniaMaritimeUniversity,Gdynia,Poland
ABSTRACT:ThemainaimofthearticleismodellingtheoperationprocessoftheBalticPort,ShippingandShip
TrafficandPortOperationInformationCriticalInfrastructureNetwork.Toachievethisgoalitisnecessaryto
definethreecriticalinfrastructurenetworksforaBalticSeaRegionandtheiroperationprocesses:portcrit
ical
infrastructurenetwork,shippingcriticalinfrastructurenetworkandshiptrafficandportoperationinformation
criticalinfrastructurenetwork.Thus,theconceptofnetworks ofthreenetworks, calledBalticPort,Shipping
andShipTrafficandPortOperationInformationCriticalInfrastructureNetwork,isintroduced.Thisway,the
operationprocessofnetworkofnetworksisproposed.Tounderstandthi
sapproach,thebasicclassificationand
descriptionofinterdependenciesandinterconnectionsinthisnetworkarepresented.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 10
Number 2
June 2016
DOI:10.12716/1001.10.02.10
276
functions. The damagetoa critical infrastructure, its
destructionordisruptionbynaturaldisastersorother
threats (terrorism, criminal activity or malicious
behaviour),mayhaveasignificantnegativeimpacton
the security of the EU and the well‐being of its
citizens [9]. Nowadays, the main goal of the EU
is
reducing the vulnerabilities of critical infrastructure
and increasing their resilience [19], [25], particularly
for the weather‐climate changes [18]. Thus, the
European Programme for Critical Infrastructure
Protection (EPCIP) has been started [5], [10]. The
EPCIP has proposed a list of European critical
infrastructures based upon inputs by its Member
States. According to the European Commission’s
“Green Paper“ on the EPCIP the following 8 main
criticalinfrastructurenetworks operatingintheBaltic
SeaRegionaredistinguished([1],[5]):
portcriticalinfra structurenetwork;
shippingcriticalinfrastructurenetwork;
oilrigcriticalinfrastructurenetwork;
windfarmcriticalinfrastructurenetwork;
electriccablecriticalinfrastructurenetwork;
gaspipelinecriticalinfrastructurenetwork;
oilpipelinecriticalinfrastructurenetwork;
shiptrafficandportoperationinformationcritical
infrastructurenetwork.
Allofthesenetworksshouldbeconsideredasthe
complex system that is defined as aset or groupof
interacting, interrelated or
interdependent elements
orparts,thatareorganizedandintegratedtoforma
collective unity or an unified whole, to achieve a
commonobjective[1].Accordingtoabove,thecritical
infrastructure is defined as a complex system in its
operating environment that significant features are
inside‐system dependencies and outside‐system
dependencies,
thatinthecaseofitsdegradationhave
significantdestructiveinfluenceonthehealth,safety
andsecurity,economicsandsocialconditionsoflarge
human communities and territory areas [1].
According to this definition, the key features of CIs
are internal dependencies and connections between
theircomponents.
To answer for the
globalization of life and
economy,itshouldbeconsideringnotasingleCIbut
thenetworksofCIs.Thus,thecriticalinfrastructure
network,asthemoregeneralnotion,isintroducedin
literature([1]–[3],[15]–[17]).Itisdefinedasasetof
interconnected and interdependent critical
infrastructures interacting directly
and indirectly at
various levels of their complexity and operating
activity[1].Thiswayofdefiningallowustousethe
well‐known methods for reliability and safety
analysisoflargecomplexsystems[7],[20],[24]–[25].
Furthermore, the approach to modelling operation
processcanbedonebymethods
describedin[7],[21]
– [23]. It also takes into account the environmental
and infrastructural influence on reliability and
operationprocess[21].
Thepaperisdevotedmodellingoperationprocess
ofthe Baltic Port, Shipping and Ship Traffic and
Port Operation Critical Infrastructure Network
(BPSSTPOCIN) and presenting the main
interdependenciesandinterconnections
[27].
2 DEFINITIONOFTHEBALTICPORT,SHIPPING
ANDSHIPTRAFFICANDPORTOPERATION
INFORMATIONCRITICALINFRASTRUCTURE
NETWORK
Accordingtothecurrentapproach,theportsandtheir
supported infra structure (i.e. roads, railways, piers,
breakwaters, power lines, ICT networks, etc.) are
consideredasthemaritimecriticalinfrastructure[25],
[35]. The aspects
of maritime critical infra structures
protection take into account only the ensuring the
security and defence of ports. But the complexity of
theportactivitiescausesthatsuchadescriptionisno
longer sufficient. Thus, the concept of Baltic Port,
Shipping and Ship Traffic and Port Operation
InformationCINetworkisintroduced
asthenetwork
of three networks in [16]. It consists of port critical
infrastructure network [2], shipping critical
infrastructure network [3] and ship traffic and port
operation information critical infrastructure network
[17]. As we know, there are strong inner and outer
dependenciesbetweenthesethreenetworks.
Thedescriptionofthe
abovenetworksiscontained
inSubsections2.1–2.3.
2.1 BalticPortCriticalInfrastructureNetwork
Inthepaper[2],theBalticPortCriticalInfrastructure
Network (BPCIN) is defined and composed of 18
followingcoreportsplacedattheBalticseaside:
1 ThePortofAarhus(
1
P
);
2 TheCopenhagen–MalmöPort(
2
P
);
3 TheLübeckerHafen‐Gesellschaft(
3
P
);
4 ThePortofRostock(
4
P
);
5 ThePortofTallinn(
5
P );
6 TheFreeportofRiga(
6
P
);
7 TheFreeportofVentspils(
7
P
);
8 TheKlaipedaStateSeaport(
8
P
);
9 ThePortofGdańsk(
9
P
);
10
ThePortofGdynia(
10
P );
11 TheSzczecin‐SwinoujściePort(
11
P
);
12 ThePortofHelsinki(
12
P
);
13 ThePortofTurku(
13
P
);
14 ThePortofHamina‐Kotka(
14
P
);
15 ThePortofGothenburg(
15
P );
16 ThePortofLuleå(
16
P
);
17 ThePortofStockholm(
17
P
);
18 ThePortofTrelleborg(
18
P
).
The distribution of ports form the BPCIN is
presentedinFigure1.
277
Figure1.TheBalticcoreportsformingBPCIN[2]
Moredetailsareprovidedinpaper[2].
2.2 BalticShippingCriticalInfrastructureNetwork
Accordingtothepaper[3]thesetofshipsoperating
attheBalticSea waters atthefixed moment of time
(or at the fixed time interval) is called the dynamic
Baltic Shipping Critical Infrastructure Network
(BSCIN).
2.3
BalticShipTrafficandPortOperationInformation
CriticalInfrastructureNetwork
Thepaper[17]definestheBalticShipTrafficandPort
Operation Information Critical Infrastructure
Network (BSTPOICIN) composed of 121 AIS base
stations and 25 DGPS stations and 21 port/terminal
operationsystemslistedin[17].
ThedistributionofAISbasestation
ispresentedon
Figure2.
Figure2. The map of Baltic Sea Region area – the yellow
pointsrepresentstheAISbasestations[3]
Besides, the Baltic Marine DGPS network is
presentedonFigure3.
Figure3.BalticMarineDGPSStations[17]
The detailed information about this critical
infrastructurenetworkispresentedin[15]‐[17].
3 INTERDEPENDENCIESAND
INTERCONNECTIONS
InearlierSectionsthestronginternalconnectionsand
dependenciesbetweentheelementsofCInetworkare
distinguished.Therefore,thissectionisdevotedtothe
classification and description of these internal
relationships([27],[30],[32]).
According to the [32] we take into account four
typesofinterdependency:
Physical – the state of one is dependent on the
materialoutputoftheother;
Systems – the state of the one depends on the
properties of the system transmitted through
anotherasset;
Geographic–
anincident in anasset may impact
thestateofassetsinadefinedspatialproximity;
Logical–amechanismthatdoesnotfall intoany
oftheabove.
As itis presented in Figure 4, infrastructures are
interconnected not only across national and
continental boundaries. There exist the
interconnections
and interdependencies between
infrastructuresectors(seeFig.4).
278
Figure4.Criticalinfrastructureinterdependencies[32]
In thisway, the chain dependencies is created. It
providestotheunforeseencascadingeffectordomino
effects.ThismeansthatdisruptionofoneCInetwork
or one CI in this network may become a source of
disturbance to other CI or CI networks [4]. It seems
the big problem, because
interconnectedness and
interdependence make these infrastructures more
vulnerable to disruption or destruction ([19]).
Moreover,intheeraoftheadvancedICTtechnologies
CI networks have become more dependent on
common information technologies, including the
internet and space‐based radio‐navigation and
communication[4].
A clear understanding of the extent of
the
interdependence is crucially important for dealing
with such cascading effects, along with the
application of effective emergency preparedness
measures[4].
3.1 PortCInetwork’sinterconnectionsand
interdependencies
Theportsare theplace,wheretheinteraction
between the private sector (which owns and
operates most infrastructures) and the public
sectoroccurs.Thus,seaportscannotbeanalysed
as infrastructures that merely handle ships. A
modern port interconnects and offers a choice
betweenvariousmodesoftransport.Goodscan
be transferred from sea to rail, road or inland
navigation. They constitute a vital
interconnectioninthe world logistics, including
several trade activities. This interconnection
allows citizens to buy cheap products from all
overtheworld.
Ontheothersidearetheinterdependence of
maritimeactivitiesandpolicies.Thesejustifythe
need
for a comprehensive system of spatial
planning. Such system would prevent
unintended and contradictory effects of
legislation,developedaccordingtotheneedsand
objectives of policy, on other maritime goals in
the context of sustainable development. The
example of this approach is the TEN‐T
infrastructure.
Theanotherwayofthe
interconnectionisa trade
(direct connections) between the ports from
BPCIN. It represents the country’s
interconnection and interdependence with the
maritimeelement andwiththe exterior(port to
port).Inthisway,wealsotakeintoaccount,the
geographic interconnections and independence
port to port and port to the city, where it is
located. Mainly, it corresponds to the trade
market and workplaces. Besides, the important
thing is transportation environment of ports,
what are constituted the connections and
dependencies with other types of transport (i.e.
railwayandroad).
As it was mentioned before, the set of ships
operating in the Baltic
Sea waters at the fixed
momentoftime(oratthefixedtimeinterval)we
call the Baltic Shipping Critical Infrastructure
Network (BSCIN) that is particularly described
in[1]and[3].Theoperationprocessandsafetyof
the shipping critical infrastructure network
depends strongly on the individual ships it is
composedofoperatingareawithintheBalticSea
region[3].
Becauseofthehighdensityoftheshiptraffic
in the Baltic Sea Region, there are strong
interconnections between the different types of
vessels.Theserelationshipsareespeciallyvisible
at the transhipment type ship ‐to‐ship or ship‐
port‐ship (combined
route using, at least, two
ships).
As with the traditional aspects of the
transportation network, interdependencies also
existbetweentheassets,people,andthefacilities
in which they reside. The frequency of
departures mostly depends on the port of ship
destination.
3.2 ShiptrafficandportoperationinformationCI
network’sinterconnectionsandinterdependencies
Modernlifeisincreasinglydependentonamultitude
ofinterconnectedandinterdependentinfra s tructures.
While sectors such as food, water, health and
transportation and the inf r astructure that supports
themhavealwaysbeencritical,theirabilitytodeliver
is increasingly enmeshed with the ICT technologies
that havebecome essential components of daily life.
The maritime transportation system operates using
information and communication systems. They play
an important role in each of these links as a core
platformforaninformationexchangeandsupporting
the safety monitoring of people, vessels, equipment
andcargoinportsandduringtheshippassageonthe
waterways. We
can distinguish two types of ICT
systems:
shiptrafficinformationsystems;
shipportoperationinformationsystems.
Thefirstgroupconsistsof thefollowingsystems:
AIS, LRIT, DGPS, GNSS. They are used by MSSiS,
SafeSeaNet, THETIS. In the second group, we can
highlight the Electronic Data Interchange (EDI)
279
systems and Port Management Information Systems
(PMIS).
TheaboveICTsystems areforming themaritime
information system represented by the maritime
informationnetwork.Thusthemaritimeinformation
system consists of the LRIT, the AIS and VHF ship
equipment,basestationsanddatacenters,vesseland
overland computer systems and other
computing
hardware devices (in ports, terminals, Maritime
Offices, etc.) that are linked together through
communicationandinformationchannelstofacilitate
communication, information and resource‐sharing
among a wide range of users. It is represented by
interconnected and interdependent maritime
information network. The maritime information
networkconsistsofthemaritimeinformation
system
withitsstructureandflow.Thenodesofthisnetwork
can be base stations, satellites, VTS Centres, ports,
terminals, Maritime Offices, data centres, vessels,
goodsstoragesand destination places. Theroutes of
thisnetworkaresinglelinksbetweenthenodes.
Thus, the sum these components create the
cyberspace. It is
sometimes categorized asa discrete
sector, in practice it is so deeply embedded into
sectorssuchasenergyandtransportastomakeany
separationmeaningless.Cyberspacecanbevisualized
instead as a thin layer or nervous system running
through all other sectors, enabling them to
communicateandfunction.
3.3
Port,shippingandshiptrafficandportoperation
informationCInetwork’sinterconnectionsand
interdependencies
Wecantakeintoaccountmoregeneral approach.The
set of assets consists of the ports, ships and ICT
systems described as the large, complex systems.
Besides,asitwasmentionedinSections2‐3,theport,
shipping and ship traffic and port operation critical
infrastructure network represents the system
interconnection and interdependency. It is the fact,
because,the state ofthe one componentdependson
the properties of the system transmitted through
anotherasset.Exemplary,theport,andtheshipsare
connected, first of all, by
ICT systems: VTS, LRIT,
DGPS, and PMIS. It seems that the ICT systems are
needed for safe and secure ship traffic and port
operationsineveryareaofBalticSeaRegion.
4 BPSSTPOICINOPERATIONPROCESS
AnapproachtotheBPSSTPOICINoperationprocess
has been introduced in [15]. This paper extends
results
to the complete elements necessary to
modellingtheoperationprocess.
AsitwasmentionedinSection2,weconsiderthe
network composed of the following three critical
infrastructure networks which operates in Baltic Sea
Regionarea:
)1(
CIN
‐the Baltic Port Critical Infrastructure
Network(BPCIN),
)2(
CIN
‐theBalticShippingCriticalInfrastructure
Network(BSCIN),
)3(
CIN
‐theBalticShipTrafficandPortOperation
Information Critical Infrastructure Network
(BSTPOICIN).
This network of networks is characterized by
strong interacting, interconnections and
interdependencies,whichare presentedin Section 3.
Moreover,wesupposethattheoperationprocessesof
these critical infrastructure networks have an
influence on their safety and depend
on their
operatingareawithintheBalticSeaRegion.
Asitismentionedin[15],wecandividetheBaltic
Sea area
D
into a grid of rectangles
ab
D
, i.e.
m
a
n
b
ab
DD
11
, where
,,...,2,1 ma
,,...,2,1 nb
Nnm
,
. The grid dimension (
nm
) depends on
the assumed accuracy of geographical coordinates
(seeFig.5).
Figure5. An exemplary grid of the Baltic Sea region
accordingtothegeographicalcoordinates[15]
We assume that the critical infrastructure
networks
3,2,1,
)(
iCIN
i
during its operation
process are taking numbers of different operation
states,describedinSections4.1–4.3.
4.1 OperationProcessofPortCriticalInfrastructure
Network
We assume that the critical infrastructure network
CIN
(1)
duringitsoperationprocessaretakingnumbers
ofdifferentoperationstatesdefinedasfollows([15])
2
2
2222
12
1
, ,..., ,
v
v
Zzzz
(1)
where
)2(
a
z
are the numbers of ships in the port
,
a
P
,,,...,2,1
)2(
a
,
)2(
N
is the number of ports
undertheconsiderationinthetheBalticSeaRegionD
(
18
)2(
forwholeBalticSeaRegion);
280
Further, we define the critical infrastructure
networks
3,2,1,
)(
iCIN
i
, operation processes
)(
)(
tZ
i
, ),,0 t asfollows([15]):
(2) (2)
(2) (2) (2) (2) (2)
12
1
( ) [ ( )] [ ( ), ( ),..., ( )]
Z
tZt ztzt zt
x
(2)
withdiscreteoperationstatesfromthesetdefinedby
(1),wheretheoperationsubprocesses
)(
)2(
tz
a
assume
thevaluesequaltothenumbers
)2(
a
z
ofshipsinthe
ports
,
a
P
,,,...,2,1
)2(
a
atthemoment );,0
t
In detailed definitions of the states and the
operation process
)(
)2(
tZ
of the Baltic Port Critical
InfrastructureNetwork
,
)2(
CIN
consistedofallports
with their facilities, where the operation states are
defined by the numbers of vessels in ports
,
a
P
,,,...,2,1
)2(
a
either waiting for port services or
being under port services, the impacts of those
numbers of ships and their port operations
interactionsshouldbeinclude.
Taking into account the above assumption to
describe the operation process of the port critical
infrastructure network we consider the
18
p
n
main Southern Baltic Sea ports. In the port we
considerthenumberofships(15]):
enteringtotheport,
outgoing intotheport,
waiting,
handled(loaded/unloaded).
According to (1) – (2), we assume that the
operationprocessforasingleport
,
a
P
,18,,...,2,1a
is given by the following vector with dimension
4
([15]):
)](),(),(),([)]([
)1(
4
)1(
3
)1(
2
)1(
11
)1(
tztztztztZ
x4
)](),(),(),([
)1(
4
)1(
3
)1(
2
)1(
1
tntntntn
, (3)
where
)(
)2(
1
tn
‐numberoftheenteringshipsintheport
,
a
P
,18,,...,2,1a
atthemoment ),0
t ,
)(
)2(
2
tn
‐number of the outgoing ships in the port
,
a
P
,18,,...,2,1a
atthemoment ),0 t ,
)(
)2(
3
tn
‐numberofthewaitingshipsintheport ,
a
P
,18,,...,2,1a
atthemoment ),0
t ,
)(
)2(
4
tn
‐number of the handled(loaded/unloaded)
ships in the port
,
a
P
,18,,...,2,1a
at the moment
),0 t .
Thus, the operation states are defined as
follows([15]):
(2)
0
[0,0,0,0]z
,
(2)
1
[1,0,0,0]z
,...,
]0,0,0,[
1
)2(
1
nz
n
,
]0,0,1,0[
)2(
1
1
n
z
,
]0,0,2,0[
)2(
2
1
n
z
,...,
]0,0,,0[
2
)2(
21
nz
nn
,...,
]0,0,,[
21
)2(
21
nnz
nn
,
]0,1,0,0[
)2(
1
21
nn
z
,
]0,2,0,0[
)2(
2
21
nn
z
,...,
]0,,0,0[
3
)2(
321
nz
nnn
,...,
]0,,,[
321
)2(
321
nnnz
nnn
,
]1,0,0,0[
)2(
1
321
nnn
z
,
]2,0,0,0[
)2(
2
321
nnn
z
,
],0,0,0[
4
)2(
4321
nz
nnnn
,...,
],,,[
4321
)2(
4321
nnnnz
nnnn
.
Itmeans,weconsiderthe
4321
nnnn
operation
statesforeveryports
,
a
P
18,,...,2,1a
.
4.2 OperationProcessofShippingCriticalInfrastructure
Network
Critical infrastructure network CIN
(2)
during its
operation process are taking numbers of different
operationstatesdefinedasfollows([15])
(2) (2) (2)
11 12 1
(2) (2) (2)
(2)
21 22 2
(2) (2) (2)
12
[] ,
n
n
n
mm mn
zz z
zz z
Z
zz z
m
(4)
where
)1(
ab
z
are the numbers of ships in the regions
,
ab
D
,,...,2,1 ma
,,...,2,1 nb
;, Nnm
Further, we define the critical infrastructure
networks
3,2,1,
)(
iCIN
i
, operation processes
)(
)(
tZ
i
, ),,0
t asfollows([15]):
(2) (2) (2)
11 12 1
(2) (2) (2)
(2) (2)
21 22 2
(2) (2) (2)
12
() () ()
() () ()
() [ ()] ,
() () ()
n
n
mn
mm mn
zt zt zt
zt zt zt
Zt Zt
zt zt zt
(5)
withdiscreteoperationstatesfromthesetdefinedby
(4) wherethe operation subprocesses
)(
)1(
tz
ab
is
assumedasequaltothenumbers
)1(
ab
z
ofshipsinthe
rectangles
ab
D
,,...,2,1 ma
,,...,2,1 nb
,, Nnm
atthemoment ),0
t ;
Considering interactions between ships creating
the Baltic Shipping Critical Infrastructure Network
,
)1(
CIN
we assume that there are strong inner and
outerdependencies betweentheshipsoperatingina
single fixed rectangle
,
ab
D
,,...,2,1 ma
,,...,2,1 nb
,, Nnm
and that ships in each two
adjacentrectanglesinfluenceeachotheraswell.These
influences that should be included in detailed
definitionsofthisnetworkoperationprocess
)(
)1(
tZ
anditsstatesstronglydependontheoperationstates
of this network defined by the numbers of ships in
theserectanglesandthoseshipstechnicaloperations.
Todescribetheoperationprocessoftheshipping
critical infrastructure network we exemplary divide
theSouthernBalticSeaareaonthesquarematrixwith
dimensionm=5,n=14. (seeFig.6).
281
Figure6. The division of the Southern Baltic Sea region
accordingtothegeographicalcoordinates
Further, we assume that the operation process is
givenbytherectangularmatrixwithaccordanceto(4)
–(5),[15],
(2) (2) (2)
11 12 1,14
(2) (2) (2)
21 22 2,14
(2)
(2) (2) (2)
51 52 5,14
() () ()
() () ()
[()]
() () ()
zt zt zt
zt zt z t
Zt
zt zt z t
514
, (6)
wherethe operation subprocesses
)(
)2(
tz
ab
is
assumedasequaltothenumbers
)2(
ab
z
ofshipsinthe
rectangles
ab
D
,5,...,2,1a
,14,...,2,1b
at the
moment
),0 t ;
Theoperationstatesaredefinedasfollows([15]):
145
][
)1(
0
z
000
000
000
,...,
145
][
)1(
)1(
11
n
z
000
000
00
)1(
11
n
,...,
145
][
)1(
1
)1(
11
n
z
000
000
010
,...,
145
][
)1(
)1(
12
)1(
11
nn
z
000
000
00
)1(
12
n
,...,
145
][
)1(
1...
)1(
13,1
)1(
12
)1(
11
nnn
z
000
000
100
,...,
145
][
)1(
...
)1(
14,1
)1(
13
)1(
12
)1(
11
nnnn
z
000
000
00
)1(
14,1
n
,...,
145
][
)1(
...
)1(
14,1
)1(
13
)1(
12
)1(
11
nnnn
z
000
000
)1(
14,1
)1(
12
)1(
11
nnn
,…,
145
][
)1(
1...
)1(
14,1
)1(
13
)1(
12
)1(
11
nnnn
z
000
001
)1(
14,1
)1(
12
)1(
11
nnn
,...,
145
][
)1(
...
)1(
21
)1(
14,1
)1(
13
)1(
12
)1(
11
nnnnn
z
000
00
)1(
21
)1(
14,1
)1(
12
)1(
11
n
nnn
,…,
145
][
)1(
......
)1(
14,2
)1(
21
)1(
14,1
)1(
11
nnnn
z
000
)1(
14,2
)1(
22
)1(
21
)1(
14,1
)1(
12
)1(
11
nnn
nnn
,...,
145
][
)1(
...............
)1(
14,5
)1(
51
)1(
14,4
)1(
41
)1(
14,3
)1(
31
)1(
14,2
)1(
21
)1(
14,1
)1(
11
nnnnnnnnnn
z
)1(
14,5
)1(
52
)1(
51
)1(
14,2
)1(
22
)1(
21
)1(
14,1
)1(
12
)1(
11
nnn
nnn
nnn
.
Thus,weconsiderthe
)(
,
)()(
,
)(
n...nn...n
1
142
1
21
1
141
1
11
)(
,
)(
n...n
1
143
1
31
)(
,
)()(
,
)(
n...nn...n
1
145
1
51
1
144
1
41
operation
states.
4.3 OperationProcessofShipTrafficandPortOperation
InformationCriticalInfrastructureNetwork
We assume that the critical infrastructure network
CIN
(3)
duringitsoperationstatesprocessaretaking
numbers of different operation states defined as
follows([15])
(3) (3)
12
(3) (3) (3) (3)
[ ] [ , , ..., ],Zzzz
1
(7)
where
)3(
a
z
arethenumbersofshipsintherangeof
the information systems
,
a
I
,,,...,2,1
)3(
a
,
)3(
N
is the number of information systems
under the consideration in the Baltic Sea Region D
(forgeneralcase
146
)3(
).
Further, we define the critical infrastructure
networks
3,2,1,
)(
iCIN
i
, operation processes
)(
)(
tZ
i
, ),,0
t asfollows([15]):
(3) (3)
(3) (3) (3) (3) (3)
12
1
( ) [ ( )] [ ( ), ( ),..., ( )].
Z
tZt ztzt zt
x
(8)
282
withdiscreteoperationstatesfromthesetdefinedby
(7),wheretheoperationsubprocesses
)(
)3(
tz
a
assume
thevaluesequaltothenumbers
)3(
a
z
ofshipsinthe
rangeoftheinformationsystems
,
a
I
,,,...,2,1
)3(
a
atthemoment
).,0 t
The Shipping, Ship Traffic and Operation
Information Critical Infrastructure Network
)3(
CIN
isaplatformtoexchangetheinformationaboutships’
operations and their cargo. Due to the fact that all
informationaregivenmainlyinelectronicform,this
network is very sensitive for any disruption,
especially cyber‐attacks [8], but also for natural
hazards[18].Thus,indetaileddefiningthisnetwork
operationprocessanditsstatesthosefeaturesshould
betakenintoaccount.
AccordingtoSection4.3andformulae(7)– (8),the
operation process of BSTPOICIN is given by the
vector([15])
)](),...,(),([)]([
)3(
146
)3(
2
)3(
11
)3(
tztztztZ
x146
, (9)
wheretheoperationsubprocesses
)(
)3(
tz
a
assumethe
values equal to the numbers
)3(
a
z
of ships in the
range of the information systems
,
a
TPOIS
,146,,...,2,1a
atthemoment ).,0 t
Thefollowingoperationstatesaredefined([15]):
]0,...,0,0,0[
)2(
0
z
,
]0,...,0,0,1[
)2(
1
z
,...,
]0,...,0,0,[
1
)2(
1
nz
n
,
]0,...,0,1,0[
)2(
1
1
n
z
,
]0,...,0,2,0[
)2(
2
1
n
z
,...,
]0,...,0,,0[
2
)2(
21
nz
nn
,
]0,...,1,0,0[
)2(
1
21
nn
z
,
]0,...,2,0,0[
)2(
2
21
nn
z
,...,
]0,...,,0,0[
3
)2(
321
nz
nnn
,...,
],...,0,0,0[
146
)2(
...
1461
nz
nn
,
]0,...,1,1[
)2(
1...
1461
nn
z
,
]0,...,2,1[
)2(
2...
1461
nn
z
,...,
]0,...,,1[
2
)2(
146...2
21
nz
nn
,...,
]0,...,,[
21
)2(
21
nnz
nn
,...,
],...,,[
14621
)2(
4321
nnnz
nnnn
.
Itmeans,weconsiderthe
14621
... nnn
operation
states for Baltic Ship Traffic and Port Operation
InformationCriticalInfrastructureNetwork.
4.4 Semi‐Markovapproachtooperationprocessofthe
BPSSTPOICIN
We assume that the critical infrastructure operation
processes
)(
)(
tZ
i
,
3,2,1i
, is a semi‐Markov
process [11] – [15], [20]‐[25], [28] – [29] with the
conditionalsojourntimes
)(i
bl
attheoperationstates
)(i
b
z
when its next operation state is
,
)(i
l
z
,,...,2,1,
)(i
vlb
,3,2,1i
.lb
Under these
assumptions, the critical i nfrastructure network
operationprocessmaybedescribedby:
the vector of the initial probabilities
),)0(()0(
)()()( i
b
ii
b
zZPp
,,...,2,1
)(i
vb
3,2,1
i
, of the critical infrastructure networks
3,.2,1,
)(
iCIN
i
operation processes
)(
)(
tZ
i
stayingatparticularoperationstatesatthe
moment
0
t
() ()
() () () ()
12
1
[ (0)] [ (0), (0),..., (0)]
ii
iiii
b
pppp
x
, (10)
the matrix of probabilities
,
)(i
bl
p
,,...,2,1,
)(i
vlb
,lb
3,2,1
i
, of the critical infrastructure
networks
3,.2,1,
)(
iCIN
i
,operation processes
)(
)(
tZ
i
transitions between the operation states
)(i
b
z
and
)(i
l
z
()
()
() ()
() () () ()
() () ()
11 12
1
() () ()
21 22
()
2
() () ()
12
() () ()
() () ()
[()]
() () ()
i
i
ii
ii ii
ii i
ii i
i
bl
ii i
pt pt p t
pt pt p t
pt
ptpt p t
x
,(11)
where by formal agreement
()
0
i
bb
p
for
;,...,2,1
)(i
vb
the matrix of conditional distribution functions
)()(
)()(
tPtH
i
bl
i
bl
, ,,...,2,1,
)(i
vlb
,lb
3,2,1
i
, of the critical infrastructure networks
3,.2,1,
)(
iCIN
i
, operation processes
)(
)(
tZ
i
conditional sojourn times
)(i
bl
at the
operationstates
()
()
() ()
() () () ()
() () ()
11 12
1
() () ()
21 22
()
2
() () ()
12
() () ()
() () ()
[()]
() () ()
i
i
ii
ii ii
ii i
ii i
i
bl
ii i
H
tHt Ht
H
tHt Ht
Ht
H
tH t H t
x
, (12)
where by formal agreement
0)(
)(
tH
i
bb
for
;,...,2,1
)(i
vb
Weintroducethematrixoftheconditionaldensity
functions of the critical infrastructure networks
3,.2,1,
)(
iCIN
i
, operation processes
)(
)(
tZ
i
conditional sojourn times
bl
at the
operation states corresponding to the conditional
distributionfunctions
)(
)(
tH
i
bl
()
()
() ()
() () () ()
() () ()
11 12
1
() () ()
21 22
()
2
() () ()
12
() () ()
() () ()
[()]
() () ()
i
i
ii
ii ii
ii i
ii i
i
bl
ii i
ht ht h t
ht ht h t
ht
htht h t
x
, (13)
where
)]([)(
)()(
tH
dt
d
th
i
bl
i
bl
for
,,...,2,1,
)(i
vlb
,lb
andbyformalagreement
0)(
)(
th
i
bb
for
.,...,2,1
)(i
vb
283
The next steps in modelling the BNPSSTPOICIN
operation process, considering taking into account
just defined processes
),(
)1(
tZ
)(
)2(
tZ
and
)(
)3(
tZ
interactionsandinterdependences,thejointoperation
process of this network of critical infrastructure
networks can be defined in the form of the vector
([15])
(1) (2) (3)
() [ (), (), ()],
Z
t Z tZ tZ t (14)
where
).,0 t
Under above definition, the critical infrastructure
networkjointoperationprocessmaybedescribedby:
the vector of the vectors of the initial
probabilities
),)0(()0(
)()()( i
b
ii
b
zZPp
,,...,2,1
)(i
vb
3,2,1i
, of the joint critical
infrastructure network operation processes
)(tZ
staying at particular operation states at the
moment
0t
(1) (2) (3)
(1) (2) (3)
13
111
[ (0)] [ (0)] ,[ (0)] ,[ (0)]
bbb b
ppp p
x
xxx
(15)
where
)(
1
)(
)]0([
i
i
b
p
x
isgivenby(10);
the vector of the matrices of probabilities
)(i
bl
p
,
,,...,2,1,
)(i
vlb
,lb
3,2,1i
, of the joint
critical infrastructure network operation process
)(tZ
transitionsbetweentheoperationstates
)(i
b
z
and
)(i
l
z
(1)(1) (2)(2) (3)(3)
(1) (2) (3)
13
[] [ ] ,[ ] ,[ ]
bl bl bl bl
pp p p
x
xxx
, (16)
where
)()(
][
)(
ii
i
bl
p
x
is given by (11) and by formal
agreement
0
)(
i
bb
p
for
;,...,2,1
)(i
vb
the vector of the matrices of conditional
distribution functions
)()(
)()(
tPtH
i
bl
i
bl
,
,,...,2,1,
)(i
vlb
,lb
3,2,1i
, of the joint
critical infrastructure network operation process
)(tZ
conditional sojourn times
)(i
bl
at the
operationstates
(1)(1) (2)(2) (3)(3)
(1) ( 2) (3)
1
[ ( )] [ ( )] ,[ ( )] ,[ ( )]
bl bl bl bl
Ht H t H t H t
x3
xxx
(17)
where
)()(
)]([
)(
ii
tH
i
bl
x
isdescribedby(12)andby
formalagreement
0)(
)(
tH
i
bb
for
.,...,2,1
)(i
vb
We introduce the vector of the matrices of the
conditional density functions of the joint critical
infrastructure network operation process
)(tZ
conditionalsojourntimes
bl
attheoperationstates
corresponding to the conditional distribution
functions
)(
)(
tH
i
bl
(1)(1) (2)(2) (3)(3)
(1) (2) (3)
13
[ ( )] [ ( )] ,[ ( )] ,[ ( )]
bl bl bl bl
ht h t h t h t
x
xxx
,(18)
where
)()(
)]([
)(
ii
th
i
bl
x
isdescribedby(13)and
)]([)(
)()(
tH
dt
d
th
i
bl
i
bl
for
,,...,2,1,
)(i
vlb
,lb
andbyformalagreement
0)(
)(
th
i
bb
for
)(
,...,2,1
i
vb
.
5 CONCLUSIONS
The definitions of the Critical Infras tructure and
CriticalInfrastructureNetwork hasbeenintroduced.
Based on these, the three critical infrastructure
networks are defined: the Baltic Shipping Critical
Infrastructure Network (BSCIN), the Baltic Port
Critical Infrastructure Network (BPCIN) and the
BalticShipTrafficandOperationInformationCritical
Infrastructure Network
(BSTPOICIN). Furthermore,
the Baltic Port, Shipping and Ship Traffic and Port
Operation Information Critical Infrastructure
Network has been defined as the network of three
networks.
The basic description of the interconnections and
interdependencies for CI networks in Baltic Sea
Regionhavebeenintroduced.
The semi‐Markov approach to modelling the
operation process of the BPSSTPOICIN has been
proposed.
ACKNOWLEDGEMENTS
Thepaperpresentstheresults developedinthescope
of the EU‐CIRCLE project titled “A pan – European
framework for strengthening Critical Infrastructure
resilience to climate change” that has received
funding from the European Union’s Horizon 2020
research and innovation programme
under grant
agreementNo653824.http://www.eu‐circle.eu/
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