Undersea Cable Network Capt Matthew Bohman & LCDR Charles Burton OA 4202 Network Flows & Graphs June 7, 2012.

Undersea Cable Network

Capt Matthew Bohman & LCDR Charles BurtonOA 4202 Network Flows & Graphs

June 7, 2012

Network Overview

• Physical structure • Number of Cables• Operations & Ownership

Network Capacity

• Cable design capacity• Lit capacity• Capacity increases

Scope of the Project

Cat Island, Bahamas

Crooked Island, Bahamas

Isla Verde, Puerto Rico,

Nassau, Bahamas

North Miami Beach, Florida

Turks & Caicos Islands

Puerto Plata, Dominican Republic

Punta Cana, Dominican Republic

ARCOS

Cat Island, Bahamas

Clarence Town, Bahamas

Cockburn Town, Bahamas

Crooked Island, Bahamas

Duncan Town, Bahamas

Fresh Creek, Bahamas

George Town, Bahamas

Governors Harbor, Bahamas

Hawksbill, Bahamas

Matthew Town, Bahamas

Mayaguana, Bahamas

Nassau, Bahamas

Port Nelson, Bahamas

Port-au-Prince, Haiti

Sandy Point, Bahamas

BDNSi

BICS

Boca Raton, Florida

Spanish River, Florida

Caves Point, Bahamas

Current, Bahamas

Hawksbill, Bahamas

Sandy Point, Bahamas

America Movil (2012)Americas II (2006)

South America I (2001)

BICS (2001)

ARCOS(2001)

BDNSi (2006)

Problem Statement

• Examine connectivity – Caribbean Islands to Florida– Inter-Island Connectivity

• Resiliency vs. threats– Natural disaster– Accidental disruptions– Terrorist attack– Additional Cables

• Measure of Effectiveness– Number of disconnected islands

Model Choices

• Nodes• Edges• Formulation ?– Shortest Path– Maximum Flow– Minimum Cost– Multi-commodity Flow

Multi-Commodity Flow Formulation

• Every node has both production & demand– Has its own commodity “place name”– Has demand for all other commodities “other places”

• Arcs are cables connecting islands– Two way flow– Cost = 1 unit per edge

• Multi-Commodity Combines– Producer-Consumer – Minimum Cost Flow

Assumptions

• If any physical connection is maintained– Insignificant delay– No monetary difference for users

• Satellite communications – not modeled• Capacities– Traffic on arcs never exceeded

• Equal demand for all vs. population driven

Formulation

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k ji

kjijiji

kji

yUnsatDmd

nCYXDCMin

kji 2:

,,,,,

,,

kji

jiji

kji

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kji

k

ji

kia

ji

kai

Y

EjiuY

kEjiuY

kVadUnsatDemanyUnsatSupplabYY

,

,,

,

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0

),(

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,

Scenario 1: Mainland ConnectivityFLORIDA

CockburnTownData: -1

CockburnTownData: 1

Turks&CaicosData: -1

PuertoPlataData: -1

PuntaCanaData: -1

Turks&CaicosData: 1PuertoPlataData: 1PuntaCanaData: 1Etc…

C=1, Y={0,1}

GAMS

StartNode EndNode Commodity CostFlorida Jacksonville PPlataData 0Florida Jacksonville PrtoRicoData 0Florida Jacksonville HawksbillData 0

StartNode EndNode CapacityFlorida Jacksonville 1000Jacksonville AM1Junc 1000AM1Junc PuertoPlata 1000

Florida JacksonvilleJacksonville AM1JuncAM1Junc PuertoPlataAM1Junc SanJuan

Jacksonville AM1JuncAM1Junc PuertoPlataAM1Junc SanJuanPuertoPlata SanJuan

PPlataDataPrtoRicoDataHawksbillDataSandyPtDataCurrentData

FloridaJacksonvilleAM1JuncPuertoPlataSanJuan

Node Commodity SupplyDemandFlorida PPlataData 1Florida PrtoRicoData 1Florida HawksbillData 1

attack_arcs_set

arc_set

arcs_data

arcs_commodity_data commodities nodes Nodes_data

GAMS Implementation

Mainland Connectivity

Mainland Connectivity

1 2 3 4 5 60

5

10

15

20

25

Dis

conn

ecte

d Is

land

s

Number of Attacks

Scenario 2: Inter-Island Connectivity

CockburnTownData: -21

CockburnTownData: 1GeorgeTownData: 1Etc…

GeorgeTownData: -21

C=1, Y={0,1}GovernorsHarborData: -21

CockburnTownData: 1GovernorsHarborData: 1Etc…

GeorgeTownData: 1GovernorsHarborData: 1Etc…

Inter-Island Attacks

Flo

rid

a

Pu

erto

Pla

ta

Peu

rto

Ric

o

Haw

ksb

ill

San

dyP

oin

t

Cu

rren

t

Cav

esP

oin

t

Nas

sau

Cat

Isla

nd

Cro

oke

dIs

lan

d

Cai

cosI

slan

d

Pu

nta

Can

a

Go

vern

ors

Har

bo

r

Fres

hC

reek

Co

ckb

urn

Tow

n

Cla

ren

ceTo

wn

Po

rtN

elso

n

Geo

rgeT

ow

n

Du

nca

nTo

wn

Matt

hew

Tow

n

May

agu

ana

Po

rtA

uP

rin

ce

Tota

l Dis

con

nec

ts

PuertoPlata 1PeurtoRico 1Hawksbill 1SandyPoint 1Current 1CavesPoint 1Nassau 1CatIsland 1CrookedIsland 1CaicosIsland 1PuntaCana 1GovernorsHarbor 1FreshCreek 21CockburnTown 1ClarenceTown 1PortNelson 1GeorgeTown 1DuncanTown 1MatthewTown 1Mayaguana 1PortAuPrince 1

Average Disconnects: 2

Flo

rid

a

Pu

erto

Pla

ta

Peu

rto

Ric

o

Haw

ksb

ill

San

dyP

oin

t

Cu

rren

t

Cav

esP

oin

t

Nas

sau

Cat

Isla

nd

Cro

oke

dIs

lan

d

Cai

cosI

slan

d

Pu

nta

Can

a

Go

vern

ors

Har

bo

r

Fres

hC

reek

Co

ckb

urn

Tow

n

Cla

ren

ceTo

wn

Po

rtN

elso

n

Geo

rgeT

ow

n

Du

nca

nTo

wn

Matt

hew

Tow

n

May

agu

ana

Po

rtA

uP

rin

ce

Tota

l Dis

con

nec

ts

PuertoPlata 4PeurtoRico 4Hawksbill 4SandyPoint 4Current 4CavesPoint 4Nassau 4CatIsland 4CrookedIsland 4CaicosIsland 4PuntaCana 4GovernorsHarbor 4FreshCreek 4CockburnTown 4ClarenceTown 4PortNelson 4GeorgeTown 4DuncanTown 17MatthewTown 17Mayaguana 17PortAuPrince 17

Average Disconnects: 6.5

Inter-Island Attacks

Flor

ida

Puer

toPl

ata

Peur

toRi

co

Haw

ksbi

ll

Sand

yPoi

nt

Curr

ent

Cave

sPoi

nt

Nas

sau

CatI

slan

d

Croo

kedI

slan

d

Caic

osIs

land

Punt

aCan

a

Gov

erno

rsH

arbo

r

Fres

hCre

ek

Cock

burn

Tow

n

Clar

ence

Tow

n

Port

Nel

son

Geo

rgeT

own

Dun

canT

own

Matt

hew

Tow

n

May

agua

na

Port

AuP

rince

Tota

l Dis

conn

ects

PuertoPlata 6PeurtoRico 6Hawksbill 6SandyPoint 6Current 6CavesPoint 6Nassau 6CatIsland 6CrookedIsland 6CaicosIsland 6PuntaCana 6GovernorsHarbor 6FreshCreek 6CockburnTown 6ClarenceTown 15PortNelson 15GeorgeTown 15DuncanTown 15MatthewTown 15Mayaguana 15PortAuPrince 15

Average Disconnects: 9

Increasing Resiliency of Network

• Summary of interdiction analysis – Two nodes can be disconnected with single attacks– Mainland and Inter-Island interdiction is identical– Nested solutions

• Adding new cables– Majority of network is resilient to multiple attacks– Laying new cables is expensive– Focus on inexpensive fixes

New Lines - One Attack FLORIDA

Placement of Additional Cables

Mainland Connectivity

Interdicted MainlandNetwork Results with

Added Cables

Revised Performance

Resiliency with Added Cables

1 2 3 4 5 60

5

10

15

20

25

Resiliency Graph of Network

Original

Added

Dis

conn

ecte

d Is

land

s

Number of Attacks

Inter-Island Connectivity

Interdicted Inter-IslandNetwork Results with

Added Cables

Inter-Island (Added Cables)- One Attack

Flor

ida

Puer

toPl

ata

Peur

toRi

co

Haw

ksbi

ll

Sand

yPoi

nt

Curr

ent

Cave

sPoi

nt

Nas

sau

CatIs

land

Croo

kedI

sland

Caico

sIsla

nd

Punt

aCan

a

Gove

rnor

sHar

bor

Fres

hCre

ek

Cock

burn

Tow

n

Clar

ence

Tow

n

Port

Nel

son

Geor

geTo

wn

Dunc

anTo

wn

Matt

hew

Tow

n

May

agua

na

Port

AuPr

ince

Tota

l Disc

onne

cts

PuertoPlata 1PeurtoRico 1Hawksbill 1SandyPoint 1Current 1CavesPoint 1Nassau 1CatIsland 1CrookedIsland 1CaicosIsland 1PuntaCana 1GovernorsHarbor 1FreshCreek 21CockburnTown 1ClarenceTown 1PortNelson 1GeorgeTown 1DuncanTown 1MatthewTown 1Mayaguana 1PortAuPrince 1

Average Disconnects: 2Fl

orid

a

Puer

toPl

ata

Peur

toRi

co

Haw

ksbi

ll

Sand

yPoi

nt

Curr

ent

Cave

sPoi

nt

Nas

sau

CatIs

land

Croo

kedI

sland

Caico

sIsla

nd

Punt

aCan

a

Gove

rnor

sHar

bor

Fres

hCre

ek

Cock

burn

Tow

n

Clar

ence

Tow

n

Port

Nel

son

Geor

geTo

wn

Dunc

anTo

wn

Matt

hew

Tow

n

May

agua

na

Port

AuPr

ince

Tota

l Disc

onne

cts

PuertoPlata 0PeurtoRico 0Hawksbill 0SandyPoint 0Current 0CavesPoint 0Nassau 0CatIsland 0CrookedIsland 0CaicosIsland 0PuntaCana 0GovernorsHarbor 0FreshCreek 0CockburnTown 0ClarenceTown 0PortNelson 0GeorgeTown 0DuncanTown 0MatthewTown 0Mayaguana 0PortAuPrince 0

Average Disconnects: 0

Original Added Cables

Original Added Cables

Flor

ida

Puer

toPl

ata

Peur

toRi

co

Haw

ksbi

ll

Sand

yPoi

nt

Curr

ent

Cave

sPoi

nt

Nas

sau

CatIs

land

Croo

kedI

sland

Caico

sIsla

nd

Punt

aCan

a

Gove

rnor

sHar

bor

Fres

hCre

ek

Cock

burn

Tow

n

Clar

ence

Tow

n

Port

Nel

son

Geor

geTo

wn

Dunc

anTo

wn

Matt

hew

Tow

n

May

agua

na

Port

AuPr

ince

Tota

l Disc

onne

cts

PuertoPlata 4PeurtoRico 4Hawksbill 4SandyPoint 4Current 4CavesPoint 4Nassau 4CatIsland 4CrookedIsland 4CaicosIsland 4PuntaCana 4GovernorsHarbor 4FreshCreek 4CockburnTown 4ClarenceTown 4PortNelson 4GeorgeTown 4DuncanTown 18MatthewTown 18Mayaguana 18PortAuPrince 18

Average Disconnects: 6.7Fl

orid

a

Puer

toPl

ata

Peur

toRi

co

Haw

ksbi

ll

Sand

yPoi

nt

Curr

ent

Cave

sPoi

nt

Nas

sau

CatIs

land

Croo

kedI

sland

Caico

sIsla

nd

Punt

aCan

a

Gove

rnor

sHar

bor

Fres

hCre

ek

Cock

burn

Tow

n

Clar

ence

Tow

n

Port

Nel

son

Geor

geTo

wn

Dunc

anTo

wn

Matt

hew

Tow

n

May

agua

na

Port

AuPr

ince

Tota

l Disc

onne

cts

PuertoPlata 2PeurtoRico 2Hawksbill 2SandyPoint 2Current 21CavesPoint 21Nassau 2CatIsland 2CrookedIsland 2CaicosIsland 2PuntaCana 2GovernorsHarbor 2FreshCreek 2CockburnTown 2ClarenceTown 2PortNelson 2GeorgeTown 2DuncanTown 2MatthewTown 2Mayaguana 2PortAuPrince 2

Average Disconnects: 3.8

Inter-Island (Added Cables)- Two Attacks

Original Added Cables

Flor

ida

Puer

toPl

ata

Peur

toRi

co

Haw

ksbi

ll

Sand

yPoi

nt

Curr

ent

Cave

sPoi

nt

Nas

sau

CatIs

land

Croo

kedI

sland

Caico

sIsla

nd

Punt

aCan

a

Gove

rnor

sHar

bor

Fres

hCre

ek

Cock

burn

Tow

n

Clar

ence

Tow

n

Port

Nel

son

Geor

geTo

wn

Dunc

anTo

wn

Matt

hew

Tow

n

May

agua

na

Port

AuPr

ince

Tota

l Disc

onne

cts

PuertoPlata 6PeurtoRico 6Hawksbill 6SandyPoint 6Current 6CavesPoint 6Nassau 6CatIsland 6CrookedIsland 6CaicosIsland 6PuntaCana 6GovernorsHarbor 6FreshCreek 6CockburnTown 6ClarenceTown 16PortNelson 16GeorgeTown 16DuncanTown 16MatthewTown 16Mayaguana 16PortAuPrince 16

Average Disconnects: 9.3Fl

orid

a

Puer

toPl

ata

Peur

toRi

co

Haw

ksbi

ll

Sand

yPoi

nt

Curr

ent

Cave

sPoi

nt

Nas

sau

CatIs

land

Croo

kedI

sland

Caico

sIsla

nd

Punt

aCan

a

Gove

rnor

sHar

bor

Fres

hCre

ek

Cock

burn

Tow

n

Clar

ence

Tow

n

Port

Nel

son

Geor

geTo

wn

Dunc

anTo

wn

Matt

hew

Tow

n

May

agua

na

Port

AuPr

ince

Tota

l Disc

onne

cts

PuertoPlata 4PeurtoRico 4Hawksbill 4SandyPoint 4Current 4CavesPoint 4Nassau 4CatIsland 4CrookedIsland 4CaicosIsland 4PuntaCana 4GovernorsHarbor 4FreshCreek 4CockburnTown 4ClarenceTown 4PortNelson 4GeorgeTown 4DuncanTown 18MatthewTown 18Mayaguana 18PortAuPrince 18

Average Disconnects: 6.7

Inter-Island (Added Cables)- Three Attacks

Summary

• Multi-Commodity Flow• Caribbean network is robust• Recommend short additions to improve

resiliency of isolated islands• Future modeling– Other regions– Global model– Time & cost estimates for satellite connections

Questions?