Ignatenko Oleksii Institute of Software System NAS UkraineInstitute of Software System NAS Ukraine

Today network model are related to veryToday network model are related to very different areas◦ Information networks◦ Information networks◦ Telecommunications◦ Energy systemsgy y◦ Distributed production processesModeling for the purposes of control and the g p pdevelopment of control techniques for truly complex networks has become a major research activity over the past two decades.

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SpamDenial of service attacksDenial of service attacksUnauthorized intrusionS li f i f iStealing of informationFishingViruses and worms

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)(t)(1 tu

)(1 tw

)(tw )(2 tu)(2 tw )(2 tu

)(3 tw

)(3 tu)(tp

)(3 tw

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)(1 tq - queuing time

)( k t i l t)(tα - packets arrival rate

)(tu routing policy)(1 tu - routing policy

)()( 11 tutq +α=& )()( 11q

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We consider two constraint types for modelWe consider two constraint types for model

Geometric constraintsGeometric constraints

max)(0 α≤α≤ tmax11 )(0 qtq ≤≤

Integral constraint

max11 )( qq

int0

)( α≤α∫∞

tdtt

0∫t

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)(2 tq - attack power

)()()()( 211 tqktuttq ⋅+−α=&

)()(2 tvtq =&

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)()( tkt +&

)(tαServer

Buffers

)()()()(

1

21

tuttqktq

−α+⋅=)(1 tu)(1 tq

k )()( 1 tutα

)()()( 22 tutvtq −=&)(tv )(2 tu)(2 tq )()()( 22q

)()( μ≤+ )()( 21 tutu

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2))0((qkv>μ

max1int

21

))0((2

)0( qqkq ≤α+ν−μ

+

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60

80

100

значення

Stochastic model

50 100 150 200 250крок

20

40Real Network

)()())(()()1( tVtAtZBtQtQ +++=+

Deterministic discrete model

OMNeT++ model)()())(()()1( tvtatubtqtq +++=+

80

100

position

50 100 150 200 250step

20

40

60

Deterministic fluid model

)()())(( tvttuBq +α+=&

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Defense systemDefense systemDefense systemDefense systemUsersUsers

Network

ModelingModelingModeling environmentModeling environment

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AttackerAttacker

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Th kThanks

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