781
1 INTRODUCTION
CriticalInfrastructure(CI)systemsprotectionagainst
accidents,naturaldisasters,andactsofterrorism,has
become key point of many public institutions and
entrepreneursactivities(Dziulaetal.2015).Theneed
forensuringhighsecurityandresilienceofCIassets
and services appears as strategic and critical for
running
vital activities, and ensuring proper
functioning of industries, populations, natural
environment and national security (Lazari 2014).
Thus, works on critical infrastructure systems
protection are concentrated mainly on formulating
procedures and building resources, able to monitor
level of threats, capable of lowering their negative
impactif needed,and restoringtheir full
functionality,incaseofdisruptionscausedbyinternal
or external hazards (Blokus‐Roszkowska & Dziula
2015).
Remarkable number of works concerning CIs
protection, show that many of them feature some
interactions and interconnections. Disruptions,
affectingoneinfrastructurecandirectlyandindirectly
influence other infrastructures, impact large
geographicregions,andsendripples
throughoutthe
Safety Analysis of Interdependent Critical
Infrastructure Networks
A.Blokus&P.Dziula
GdyniaMaritimeUniversity,Gdynia,Poland
ABSTRACT: Certain critical infrastructure networks show some interconnections, relations and interactions
withotherones,mostfrequentlywhenlocatedandoperatingwithinparticularareas.Failuresarisingwithin
onecriticalinfrastructurenetwork,canthen negatively impact notonlyonassociatedsystems, societies and
natural environment, but also on
mutual critical infrastructure networks. Therefore, interdependent critical
infrastructurenetworkscanbedeterminedasnetworkofcriticalinfrastructurenetworks(networkofnetworks
approach).
The paper presents safety analysis of the network of critical infrastructure networks, taking into account
interconnections, relations and interactions between particular ones. Critical infrastructures networks as
multistatesystems
are considered, by distinguishingsubsets ofno‐hazardssafety states, and crisis situation
states,andbyanalysingtransitionsbetweenparticularones.
Issuesintroducedinthearticlearebasedontheassumptionthatonekeycriticalinfrastructurenetworkimpacts
onfunctioningofothercriticalinfrastructurenetworks‐canreducetheirfunctionalityandchange
leveloftheir
safetyandinoperability,furthermore,othernetworkscanimpacteachother,too.
Safetycharacteristicsofnetworkofcriticalinfrastructurenetworks:safetyfunction,meanvaluesandstandard
deviationsoflifetimesinparticularsafetystatesubsets,aredetermined,takingintoaccountinterdependencies
betweenparticularnetworks.Theresultsarerelatedto
variousvaluesofcoefficientsdefiningthesignificanceof
influenceofinterdependenciesamongnetworks.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 13
Number 4
December 2019
DOI:10.12716/1001.13.04.10
782
nationalandglobaleconomy.Thedegreetowhichthe
infrastructures are coupled or linked, strongly
influences their functionality (Rinaldi et al. 2001).
That makes, interacted and interconnected CIs are
often classified as critical infrastructure networks
(Yustaetal.2011,Utneetal.2011,Huangetal.2014).
Consequently, CI networks,
operating within
certain area, interacting, and being also
interconnected, can be classified as a Network of
Critical Infrastructure Networks (Network of CI
Networks).
Asthe example,theresultof analysisofspecifics
related to the Baltic Sea region, its location and
geographic conditions, concentration of various
installations qualified as critical
infrastructure,
distinguishingfollowingCINetworkswithinthearea,
canbeshown(Dziula&Kołowrocki2017a):
BalticITCINetwork;
BalticPortCINetwork;
BalticShippingCINetwork;
BalticOilRigCINetwork;
BalticWindFarmCINetwork;
BalticElectricCableCINetwork;
BalticGasPipelineCINetwork;
BalticOilPipelineCINetwork.
Interconnections and interactions among above
mentioned networks, havethen led to formulate the
concept of Global Baltic Network of Critical
Infrastructure Networks (GBNCIN), that is used in
this paper for safety analysis of network of
interdependentcriticalinfrastructurenetworks.
2 INTERDEPENDENCIESAMONGCRITICAL
INFRASTRUCTURES
ANDCRITICAL
INFRASTRUCTURENETWORKS
CIsandCInetworkscanberelatedinmultipleways.
Most widely, literature concerning this issue,
indicates dependencies and interdependencies as
frameworkcharacterisation oftheir relations.
Dependencies usually concern unidirectional
relationships, while interdependencies in general
indicatebidirectionalinteractions(Rinaldi etal.2001).
However it can be noted,
dependencies usually are
regarded as interdependencies, unless specially
referred(Ouyang2014).
There are several approaches to classification of
interdependencies among critical infrastructures and
critical infrastructure networks. One of frequently
cited proposals (Rinaldi et al. 2001), specifies four
types of interdependencies: physical (concerns
material flows between CIs), cyber (refers to
information
flows), geographic (related to physical
proximity), and logical (mechanisms other than
physical, cyber or geographic). Another one,
proposed by Zimmermann (2001) divides relations
into functional (operation of one infrastructure is
necessaryfortheoperationofanotherinfrastructure)
and spatial (proximity between infrastructures).
Dudenhoeffer (2006), indicates physical (direct
linkages between infrastructure systems),
geospatial
(co‐location of infrastructure components within the
same footprint), policy (binding of infrastructure
components due to policy or high level decisions),
andinformational(bindingorrelianceoninformation
flow between infrastructure systems) interactions.
Interdependencies distinguished by Wallace et al.
(2003),andLeeetal.(2007),are:input(infrastructure
systems
require as input one or more services from
another infrastructure), mutual (activities of each
infrastructure system is dependent upon each of the
other infrastructure systems), shared (physical
componentsoractivitiesoftheinfrastructuresystems
are shared with one or more other infrastructure
systems),exclusive(onlyoneoftwoormoreservices
canbeprovidedbyaninfrastructuresystem),andco‐
located (components of two or more systems are
situated within a prescribed geographical region).
Zhang & Peeta (2011), suggested relations like
functional(functioningofonesystemrequiresinputs
from another system, or can be substituted, to a
certainextent,bythe
othersystem),physical(systems
are coupled through shared physica l attributes),
budgetary(infrastructuresystemsinvolvesomelevel
of public financing), plus market and economic
(infrastructuresystemsinteractwitheachotherinthe
sameeconomicsystem).
As it can be read out of above, there are quite
many different proposals of classification. Adoption
of particular one depends mainly on character of
interdependenciesexistingamonganalysedCIsorCI
networks(Ouyang2014).
3 MODELLINGOFINTERDEPENDENCIESIN
CRITICALINFRASTRUCTURES
As described in the above chapter, relations among
critical infrastructures and critical infrastructure
networks, can be identified and described according
to different approaches. Numerous modelling
methods,thatcanbefoundintheliteraturerelatedto
thatsubject,areintroducedinthischapter.
Usually,thefirststageisidentificationofpossible
interconnections among particular entities forming
critical infrastructure, and determining their mutual
impact in case of their failure. The impact can be
definedbyspecifyingpotentialinitiating
events,and
behaviourofparticularCIobjectsbefore, duringand
after each initiating event (Bloomfield et al. 2017,
Huangetal.2014,Utneetal.2011).
Identification of critical infrastructure objects
interconnections, and their mutual impacts, leads to
build a model, representing specified
interdependencies. Nagurney & Qiang (2008), for
critical
networkefficiencymeasure,usemodelshown
inFig.1.
Figure.1. Critical infrastructure network structure model
usedforefficiencymeasure(Nagurney&Qiang2008).
783
They identify network nodes (1,2,…,7), and links
(a,b,…,k).Then,by specifyinglink costfunctions,the
importance and the rankings of particular links and
thenodes,canbedetermined.Theapproachallowsto
find the significance of particular network
components, and determine the most and least
importantlinks.
Another approach is a multilayer infrastructure
network model showing infrastructure
interdependencies (Fig. 2), proposed by Zhang &
Peeta (2011). Individual infras tructure systems are
represented as network layers I(1), I(2) and I(3). All
infrastructurenetworkshavethesamesetofnodes.A
node represents a geographical region at a spatial
scale,
which can range from a city zone to a city,
county,state,orcountry.The(horizontal)linkswithin
eachnetworklayerrepresenttheflowconnectivityin
that infr astructure system, manifesting primarily
through the physical facilities enabling the flow. As
different infrastructure systems have different
physicalnetworkconfigurations,flowcharacteristics,
and institutional
organization, the set of links may
varyacrossinfrastructuresystems,asindicatedinFig.
1bythedifferentsetsoflinksconnectingthenodesin
thevariousinfrastructurenetworklayers.
Figure.2. Multilayer infrastructure network framework
(Zhang&Peeta2011).
Vertical links denote the infrastructure
interdependenciesinthesamegeographicalregion,as
nodes are common to the va rious MIN network
layers. The interdependencies between one
infrastructure system in a region and another
infrastructure system in another region are captured
through a combination of horizontal and vertical
links.Exampleofsuchan
interdependency,involving
systemsI(1)andI(2),isrepresentedbynodesAandB.
ItmanifestsfirstasbeingtransmittedfromnodeBin
infrastructure I(2) to node A in I(2) through the
horizontallinks, and then to node A in I(1) through
theverticallinks.
Rueda & Calle (2017), introduce
interdependency
matrices to analyse interdependencies between
interconnected critical i nf rastructures. They consider
twoundirectednetworksG
1andG2(Fig.3),eachwith
setsofnodesandlinks,respectively.WhenG
1andG2
interact, a set of bidirectional interlinks, joining the
twonetworks,appears.
Figure.3. Mutual interactions of interdependent networks
incaseofnodesfailures(RuedaandCalle2017).
By generating interdependency matrices: High
Centrality Interdependency Matrix (correspondence
between high centrality nodes in G
1 and high
centrality nodes in G
2), Low Centrality
Interdependency Matrix (correspondence between
lowcentralitynodesinG
1andlowcentralitynodesin
G
2), and Random Interdependency Matrix
(correspondencebetweennodesinG
1andnodesinG2
without their centrality measures), the impact of
failure of one network element on another network
canbedetermined,asshowninFig.3(a)andFig.3(b).
Methodology submitted by Reed et al. (2009), is
delivering network model illustrated in Fig. 4.,
derived from the eleven‐system interdependent
infrastructure.
Figure.4. Interdependencies coefficients between selected
subsystems(Reedetal. 2009).
One central node (X1 – Power System), has been
determined, and the other (X
2 – X11) interdependent
onessuchastelecommunications,transportation,etc.,
have been pointed. Interdependencies ( a
ij), between
various subsystems are related to probability of
inoperabilitythatonesubsystemcontributestoother
one. The approach lets to evaluate engineering
resilience and interdependency for subsystems of a
multi‐system networked infrastructure for extreme
naturalhazardevents.
The approaches introduced above, show slight
differences, concerning modelling of
interdependencies within
CI network, or among CI
networks. They all let however to specify the
784
approach for the purpose of this article, that is
introducedinthenextchapter.
4 ASSUMPTIONSFORMODELLINGSAFETY
RELATEDTOINTERDEPENDENCIES
For the analysis of GlobalBaltic Network of Critical
Infrastructure Networks, we adopt model proposed
by Reed et al. (2009), enhanced however with
interdependencies among particular networks,
besides
relationsrelatedtocentraloneonly(Fig.5).
Figure.5. Interdependencies among particular networks
withinGBNCIN.
TheBalticITCINetwork,isassumedasone,that
most significantly impacts on other networks. Baltic
CI networks specified in Chapter 1 are denoted as
follows:
BalticITCINetwork–BCIN1;
BalticPortCINetwork–BCIN2;
BalticShippingCINetwork–BCIN3;
BalticOilRigCINetwork–BCIN4;
BalticWindFarmCINetwork–BCIN5;
BalticElectricCableCINetwork–BCIN6;
BalticGasPipelineCINetwork–BCIN7;
BalticOilPipelineCINetwork–BCIN8.
Theinterdependenciesamongparticularnetworks
can be both unidirectional and bidirectional, as also
indicated in the Fig. 5. The impact of malfunctions
within BCIN
j, j ϵ {1,2,...,8} network, on BCINi,
iϵ{1,2,...,8} network, related to their safety states, is
denoted by coefficient q
ij, where i ϵ {1,2,...,8} and
jϵ{1,2,...,8}. The q
ij coefficients can take values from
the range [0;1). If there is no influence of BCIN
j
network on BCIN
i network, the coefficient equals to
zero.
Forthepaperpurposes,themultistateapproachis
adopted for the safety analysis of the GBNCIN
(Blokus‐Roszkowskaetal.2018,Dziula&Kołowrocki
2017b). Following four safety states, of the GBNCIN
and BCIN
i, i ϵ {1,2,...,8} networks, have been
distinguished:
GBNCIN/ BCIN network state of full ability –
z3=3;
GBNCIN/BCIN network impendency over safety
state–z2=2;
state of GBNCIN/ BCIN network unreliability –
z1=1;
stateoffullinabilityofGBNCIN/BCINnetwork–
z0=0.
ThesafetyfunctionofBCIN
i,i={1,2,...,8}network
is defined by the vector (Blokus‐Roszkowska et al.
2018,Dziula&Kołowrocki2017b):
(,)
i
St
3
(,0), (,1), (,2), , (, ),
iii i
St St St Stz
(1)
),,0
t
1,2,...,8.i
By the assumption the coordinates of the above
safety function are exponential, they take following
forms:
( , ) exp[ ( ) ],
ii
Stu ut
3
1, 2, , ,uz
,8,...,2,1i
(2)
where λ
i(u), u = 1,2,...z3, are the intensities of
departurefromthesafetystatesubset{u,u+1,...,z
3}–
subset of safety states not worse than the state u,
u=1,2...,z
3,andSi(t,0)=1.
WeassumethattheGBNCINisamultistateseries
network.ThatmeansthattheGBNCINisinthesafety
statessubset{u,u+1,...,z
3},u=1,2,...z3,ifandonlyif
all BCIN
i, i = 1,2,…,8, networks are in this subset of
safetystates.
5 SAFETYANALYSISOFGLOBALBALTIC
NETWORKOFCRITICALINFRASTRUCTURE
NETWORKS
For the purposes of the GBNCIN safety analysis,
takinginto account interdependenciesamong
particularBCIN
i,i=1,2,…,8,networks,themultistate
approach(Blokus‐Roszkowska etal.2018,Kołowrocki
2014)is applied. The approachstates, that impact of
BCIN
j, j=1,2,…,8 network, on functioning of the
BCIN
i, i=1,2,…,8 network, means that transition of
the BCIN
j safety state from better to worse one (i.e.
fromz
3=3,toz2=2orz1=1),resultswithtransitionof
theBCIN
isafetystatealsofrom bettertoworse. Itis
comingoutoffactthatlifetimesofBCIN
i,iϵ{1,2,...,8}
network, within subset of safety states, shorten, and
itssafetycharacteristicsgetworse.Inmoredetails,if
the BCIN
j, jϵ1,2,…,8, network exceeds subset
{u,u+1,...,z
3},u=1,2,...,z3,ofsafetystates,itresultsthe
BCIN
i, i=1,2,…,8 network lifetimes and their mean
values in the subset {υ,υ+1,...,z
3}, where υ=1,2,…,u,
andu=1,2,...,z
3‐1,decreaseaccordingtotheformulas
givenbyBlokus‐Roszkowskaetal.(2018):
/
()
ij
T
[1 ( , , )] ( ),
jii
q BCIN BCIN T

(3)
/
[ ( )] [1 ( , , )] [ ( )],
ij j i i
E T q BCIN BCIN E T


,8,,2,1
i
,8,,2,1
j (4)
where q(υ, BCIN
j, BCINi), i,j=1,2,…,8, i≠j, are the
coefficients of BCIN
j network impact on functioning
ofBCIN
inetwork,
785
(, , ) 0,
ii
q BCIN BCIN
,8,...,2,1i
(5)
and
0(, , )1
ji
BCIN BCqIN
 (6)
fori,j=1,2,…,8,υ=u,u‐1,...,1,andu=1,2,...,z
3‐1.
T
i(υ)andTi/j(υ),givenbyformulae(3)and(4)are
independentrandomvariablesrepresentinglifetimes
of BCIN
i, i ϵ {1,2,...,8} network in the safety state
subset {υ,υ+1,...,z
3}, respectively before and after
BCIN
j, j ϵ {1,2,...,8} network departures states subset
{u,u+1,...,z
3}, u = 1,2,...,z3. Similarly, E[Ti(υ)] and
E[T
i/j(υ)] are respectively mean values of lifetimes
T
i(υ)andTi/j(υ).
Duetofactithasbeenassumed,thattheGBNCIN
isaseriesnetwork,wedonotconsiderimpactontime
ofstayofBCIN
inetworkinthebeststate(z3).Thatis
becauseseriesnetworkisinthebeststatez
3onlyifits
all BCIN
i, i = 1,2,...,8, networks, are in the state z3.
Thus,departureofoneofBCIN
j,jϵ{1,2,...,8}networks
from subset { z
3}, automatically results with the
GBNCINdeparturefromthestatez
3.Weanalyseonly
influenceonothernetworksBCIN
i,iϵ1,2,...,8,timeof
staywithinsubsets{1,2,...,z
3},{2,...,z3},...,{z3‐1,z3}.
In further safety analysis, we replace z
3 by 3, as
assumed before. Under the assumption about the
exponentialdistribution,theconditionalintensitiesof
the network BCIN
i departure from the subset
{υ,υ+1,…,3},afterthedepartureofthenetworkBCIN
j,
by(4),are:
/
()
() ,
1(, , )
i
ij
ji
q BCIN BCIN

(7)
fori,j=1,2,…,8,υ=u,u‐1,...,1,andu=1,2.
Assuming the GBNCIN is a multistate series
network and interdependences among BCIN
networks, expressed in (3)‐(4), in case the BCIN
networks have exponential safety functions (1)‐(2),
and considering (7), the safety function of
the
GBNCIN is given by the vector (Blokus‐Roszkowska
&Kołowrocki2017):
(,) [1, (,1), (,2), (,3)],ttttSSSS
(8)
where
8
1
(,1) exp[ (2)]
i
i
tt

S
8
88
1
11
(2) (1)
(2) (1)
jj
j
ii
ii



8
1
(1)
[exp[ ]
1(1, , )
i
i
ji
t
q BCIN BCIN

88
11
exp[ ( (2) (1)
ii
ii




8
1
(1)
) ]],
1(1, , )
i
i
ji
t
qBCINBCIN
(9)
8
1
( ,2) exp[ (3) ]
i
i
tt

S
8
88
1
11
(3) (2)
(3) (2)
jj
j
ii
ii



8
1
(2)
[exp[ ]
1(2, , )
i
i
ji
t
q BCIN BCIN

88
11
exp[ ( (3) (2)
ii
ii




8
1
(2)
) ]],
1(2, , )
i
i
ji
t
qBCINBCIN
(10)
8
1
(,3) exp[ (3)],
i
i
tt

S
(11)
fort≥0.
Table1.Coefficientsq(υ,BCINj,BCINi),i,j=1,2,…,8,υ=1,2,
of the BCIN
j network impact on lifetimes and their mean
valuesinthesubsets{1,2,3}and{2,3}oftheBCIN
inetwork.
_______________________________________________
j|I BCIN1BCIN2BCIN3BCIN4BCIN5BCIN6BCIN7BCIN8
BCIN1 0 0 0 0 q q 0 0
BCIN2 q 0 q 0 0 q q q
BCIN3 q q 0 q q 0 0 0
BCIN4 q 0 q 0 0 q q q
BCIN5 q 0 q 0 0 q 0 0
BCIN6 q q 0 q q 0 q q
BCIN7 q q 0 q 0 q 0 0
BCIN8 q q 0 q 0 q 0 0
_______________________________________________
CoefficientsofimpactofparticularBCINnetworks
on the GBNCIN network, formulated according to
model introduced in Fig. 5, are shown in Table 1.
Table 2 presents intensities of particular BCIN
i, i =
1,2,...,8, networks departures from the safety states
subsets {1,2,3}, {2,3}, and {3}. The BCINs lifetimes in
thesafetystatesareexpressedinyears.
Table2. Intensities λ
i(1), λi(2) and λi(3) of the BCINi,
i=1,2,…,8, networks departure from the safety states
subsets{1,2,3},{2,3},and{3},respectively[year
‐1
].
__________________________________________
BCIN
i λi(1) λi(2) λi(3)
__________________________________________
BCIN
1 0.2  0.5 1
BCIN2 0.1 0.2 0.5
BCIN3 0.1 0.2 0.5
BCIN4 0.1 0.2 0.5
BCIN5 0.2 0.5 1
BCIN6 0.067 0.1 0.2
BCIN7 0.067 0.1 0.2
BCIN8 0.067 0.1 0.2
__________________________________________
ByenteringintensityvaluesgiveninTable2,into
the formulas (8)‐(11), and assuming that coefficients
of impact of particular BCIN networks q(1, BCIN
j,
BCIN
i) = q(2, BCINj, BCINi), i,j=1,2,…,8, indicated in
Table 1, take the values 0 and q = 0.50 (exemplary
value),weobtainsafetyfunctionoftheGBNCIN.
786
Figure.6.SafetyfunctioncoordinatesoftheGBNCINfor
q=0.
Figure.7. Safety function coordinates of the GBNCIN for
exemplaryvalueq=0.50.
The graph of safety function coordinates of the
GBNCINforq=0isshowninFig.6,andforq=0.50in
Fig. 7. In case the coefficients q(υ,BCIN
j,BCINi),
i,jϵ{1,2,…,8}, υ=1,2, equal to zero, the results are
identical to the results for GBNCIN assuming
independenceofBCINnetworks.
Table 3 shows mean values and standard
deviations of the GBNCIN lifetimes in safety states
subsets{1,2,3},{2,3}, and{3},obtained for
q(υ,BCIN
j,BCINi)=q, i,jϵ{1,2,…,8}, υ=1,2,
coefficientsvaryingfromzeroto0.99,demonstrating
howrelationslevelinfluencesonthewholeGBNCIN
network. The results are calculated in years by
applying GBNCIN safety function (8)‐(11), for
intensitiesλ
i(1),λi(2)andλi(3),giveninTable2.
Table 3. Mean values and standard deviations of the
GBNCINlifetimesinsafetystatessubsets{1,2,3}, {2,3}, and
{3}, for coefficients q(υ, BCIN
j, BCINi) = q, i,j ϵ {1,2,...,8},
υ=1,2,rangingfromzeroto0.99.
_______________________________________________
q
 μ(1) σ(1) μ(2) σ(2) μ(3) σ(3)
_______________________________________________
0
1.1101.110 0.5260.526 0.2440.244
0.1 1.0641.0490.507 0.500 0.2440.244
0.2 1.0150.9870.485 0.473 0.2440.244
0.3 0.9630.9200.462 0.443 0.2440.244
0.4 0.9070.8490.437 0.411 0.2440.244
0.5 0.8460.7740.409 0.377 0.2440.244
0.6 0.7800.6960.378 0.340 0.2440.244
0.7 0.7100.6190.344 0.301 0.2440.244
0.8 0.6360.5520.306 0.265 0.2440.244
0.9 0.5670.5170.269 0.240 0.2440.244
0.99 0.5270.525 0.2450.242 0.2440.244
_______________________________________________
The impact of interdependencies among BCIN
networks,expressedby(3)‐(4), on meanvalues μ(1),
μ(2), μ(3) of the GBNCIN lifetimes in safety states
subsets {1,2,3}, {2,3}, and {3} respectively, is also
illustratedinFig.8.
Figure.8. Mean values of the GBNCIN lifetimes in safety
states subsets {1,2,3}, {2,3}, and {3}, given in years for
coefficients q(υ,BCIN
j, BCINi) = q, i,j ϵ {1,2,...,8}, υ=1,2,
rangingfromzeroto0.99.
It can be noticed that values of coefficients
q(υ,BCIN
j, BCINi), i,j ϵ {1,2,...,8}, υ=1,2, have no
influence on the GBNCIN lifetime in safety state 3.
Thisisduetothefactthatincaseofaseriesnetwork
structure, as previously pointed out, the safety
function coordinate S( t,3) does not depend on the
value of
these coefficients and is the same as for
independentseriesnetwork.
6 CONCLUSIONS
Thepaperpresentsmultistateapproachtomodelling
safety of network of CI networks related to
interdependencies.Proposedmodelofsafety analysis
for series network is applied to determine safety
function of the GBNCIN, taking into account
interdependencies
among particular BCIN networks,
forming the GBNCIN. By use of the safety function,
meanvaluesandstandarddeviationsoftheGBNCIN
lifetimesinsafetystatessubsets,aredetermined.The
resultsarecomparedfordifferentvaluesofcoefficient
expressinginterdependenciesamongparticular
networks within GBNCIN. The proposed method
allows to assess
the influence level of
interdependencies among CI networks on the whole
GBNCINnetworklifetimesinsafetystatessubsets.
REFERENCES
Blokus‐Roszkowska,A.&Dziula,P. 2015. Anapproachto
identification of critical infrastructure systems. In T.
Simos, Ch. Tsitouras (eds.), ICNAAM 2015. AIP Conf.
Proc.1738.Rhodes:AIPPublishing,pp.440006.10‐13.
Blokus‐Roszkowska, A., Dziula, P. & Kołowrocki, K. 2018.
SafetyandresilienceofGlobalBalticNetwork
ofCritical
Infrastructure Networks related to cascading effects.
787
JournalofPolishSafetyandReliabilityAssociation,Summer
SafetyandReliabilitySeminars,Vol.9,no2,pp.79‐86.
Blokus‐Roszkowska, A. & Kołowrocki, K. 2017. Modelling
safety of interconnected critical infrastructure network
cascading. Journal of Polish Safety and Reliability
Association, Special Issue on EU‐CIRCLE Project Critical
Infrastructure
Impact Models for Operation Threats and
ClimateHazards,Part1,CriticalInfrastructureConnections,
Vol.8,no3,pp.97‐114.
Bloomfield, R., Popov, P., Salako, K., Stankovic, V. &
Wright,D. 2017. Preliminaryinterdependencyanalysis:
An approach to support critical‐infrastructure risk‐
assessment. Reliability Engineering & System Safety, Vol.
167,
Elsevier,pp.198‐217.
Dudenhoeffer,D.,Permann,M.&Manic,M.2006.CIMS:a
framework for infrastructure interdependency
modelling and analysis. In L. Felipe Perrone, Barry G.
Lawson, Jason Liu, Frederick P. Wieland (eds.),
Proceedings of the 2006 winter simulation conference,
Monterey:ACMDigitalLibrary,pp.478–485.
Dziula,P.&
Kołowrocki,K.2017a.Modellingtheoperation
processofGlobalBalticNetworkofCritical
Infrastructure Networks. In Marko Cepin, Radim Bris
(eds.), Safety and Reliability. Theory and Applications:
ESREL 2017. London: CRC Press/Balkema, pp. 2445‐
2451.
Dziula, P. & Kołowrocki, K. 2017b. Modelling safety of
Global Baltic Network of
Critical Infrastructure
Networks. Journal of Polish Safety and Reliability
Association,SummerSafetyandReliabilitySeminars,Vol.8,
no3,pp.73‐98.
Dziula, P., Kołowrocki, K. & Rosiński, A. 2015. Issues
concerning identification of critical infrastructure
systems within the Baltic Sea area. In Luca Podofillini,
Bruno Sudret, Bozidar
Stojadinovic, Enrico Zio,
WolfgangKröger(eds.),Safetyand Reliabilityof Complex
Engineered Systems: ESREL 2015. Leiden:CRC
Press/Balkema,pp.119‐126.
Huang, C., Liou, J. & Chuang, Y. 2014. A method for
exploring the interdependencies and importance of
criticalinfrastructures.Knowledge‐Based Systems, Vol. 55,
pp.66‐74.
Koł
owrocki, K. 2014. Reliability of Large and Complex
Systems.London:Elsevier,2014.
Lazari, A. 2014. European Critical Infrastructure Protection.
Cham:Springer.
Lee, E., Mitchell, J. & Wallace, W. 2007. Restoration of
services in interdependent infrastructure systems: a
network flows approach. IEEE Transactions on systems,
Man, and Cybernetics — part C:
Application and Reviews,
Vol.37(6),pp.1303–1317.
Nagurney, A. & Qiang, Q. 2008. A network efficiency
measure with application to critical infrastructure
networks.JournalofGlobalOptimization,Vol.40,Springer,
pp.261–275.
Ouyang, M. 2014. Review on modelling and simulation of
interdependentcriticalinfrastructuresystems.Reliability
Engineering&SystemSafety,
Vol.121,pp.43‐60.
Reed, D., Kapur, K. & Christie R. 2009. Methodology for
Assessing the Resilience of Networked Infrastructure.
IEEESystemsJournal,Vol.3,no.2,pp.174‐180.
Rinaldi, S., Peerenboom, J. & Kelly, T. 2001. Identifying,
Understanding, and Analysing Critical Infrastructure
Interdependencies.IEEEControlSystems
Magazine21(6),
pp.11‐25.
Rueda,D.&Calle,E.2017.Usinginterdependencymatrices
tomitigatetargetedattacksoninterdependentnetworks:
A case study involving a power grid and backbone
telecommunications networks. International Journal of
Critical Infrastructure Protection, Vol. 16, Elsevier, pp. 3‐
12.
Utne, I.B., Hokstad, P. & Vatn,
J. 2011. A method for risk
modelingofinterdependenciesincriticalinfrastructures.
ReliabilityEngineering&SystemSafety,Vol.96,Issue6,pp.
671‐678.
Wallace,W.,Mendonca,D.,Lee,E.,Mitchell,J.&Wallace,J.
2003. Managing disruptions to critical interdependent
infrastructures in the context of the 2001 World Trade
Centerattack. InMondayJ.(ed.), BeyondSeptember11th:
an account of post‐disaster research, University of
Colorado,pp.165–198.
Yusta, J., Correa, G. & Lacal ‐Arantegui, R. 2011.
Methodologies and applications for critical
infrastructure protection: State‐of‐the‐art. Energy Policy,
Vol.39,Issue10,pp.6100‐6119.
Zhang, P. & Peeta, S. 2011. A generalized modeling
framework to analyze interdependencies among
infrastructure systems. Transportation Research part B:
Methodological,Vol.45(3),Elsevier,pp.553–579.
Zimmerman, R. 2001. Social implications of infrastructure
networkinteractions.JournalofUrbanTechnology,Vol.8,
pp.97–119.