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I@YASSUME: B1<B12<B<B2

R

R1

H d

R2

{L2,B2}

{L1,B1}

{L12,B12}

<D,H,L,B>

STEP 1

R2 :R <D,R,L’+L2,min{B,B2}>

{L12,B12}

R

R1

H d

R2

{L2,B2}

{L1,B1}

STEP 3

{L12,B12}

R

R1

H d

R2

{L2,B2}

{L1,B1}

STEP 2

<D,R,L+L1,B1>τ1

<D,R,L+L2,B>τ2

τ2 dominates τ1 : L2 < L1 AND B > B1

R R1 : <D,R,L’+L1,min{B,B1}>

<D,R2,L’+L2+L12,min{B,B12}>R2 R1 :

R1 R2 : <D,R1,L’+L1+L12,min{B1,B12}>

L’ = L + L(R,H)

�&Kd>Oa57%1JYX� � R � ! , �a5<8`d1��)r5C:48=@N5>@1

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IUL

ViableTuples

NextHopSelection

Dst1

Dst2

Dstn

R1

R2

R3

Src Dst1

5R2 2

Selected Tuple

Set of Tuples for (Src,Dst1)

Routing Table

10R1

10R1 3 8R3 3

8R3 3

8R3 3

3

Bottleneck BWPath LengthNext Hop

Tuple Format

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L �

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5

Ratio of g to smallest link capacity (LCC)

Lo

ad T

hre

sho

ldLCC

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L@Y

0.0001

0.001

0.01

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Offered Load

Fra

ctio

n R

ejec

ted

(B

DP

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CM

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BDP

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0.0001

0.001

0.01

0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Offered Load

Fra

ctio

n R

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ted

(L

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LDG

0.0001

0.001

0.01

0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Offered Load

Fra

ctio

n R

ejec

ted

(R

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uti

ng

)

LCC LCC+R

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LUH

0

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0.2

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0.4

0.5

0.6

0.7

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Torus Path Choices for PP

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

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Intra-domain Path Choices for PP

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HUH

ERw

GEO: L[ERx,ERy] = Euclidean DistanceSTAT: Cost[ERx,ERy] = Physical Path LengthTRU: Cost[ERx,ERy] = C[ERx,ERy]

2

Domain

4

1

ERy

ERx

Dst

Src

Domain

Domain

3

Domain

Combined Cost Metric(C[ERw,ERx])

ERz

TOP−LEVEL PATH SELECTED:SRC−ERw−ERx−ERy−ERz−DST

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MUM

0.0001

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0.01

0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Offered Load

Fra

ctio

n R

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(LF

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PP

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0.0001

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Offered Load

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n R

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(150

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0)

PP

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GEO

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M?U

0.0001

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0.1

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Offered Load

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(600

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0

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0.3

0.4

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0.6

0.7

5 10 15 20 25 30 35 40

Request Bandwidth (Mbps)

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ad T

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M W

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

5 10 15 20 25 30 35 40

Request Bandwidth (Mbps)

Lo

ad T

hre

sho

ld(L

F<1

50 M

bp

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PP

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0

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0.3

0.4

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0.6

0.7

5 10 15 20 25 30 35 40

Request Bandwidth (Mbps)

Lo

ad T

hre

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ld(1

50<L

F<6

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bp

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PP

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

5 10 15 20 25 30 35 40

Request Bandwidth (Mbps)

Lo

ad T

hre

sho

ld(6

00<L

F<2

400

Mb

ps)

TRU

PP

GEO

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5

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Peering Link Degradation Factor (Load = 0.4)

Rat

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ract

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Ratio of Update Period to MHT

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ad T

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sho

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UUI

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0 0.5 1 1.5 2 2.5

Ratio of g to default (TRU)

Lo

ad T

hre

sho

ld

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UDG

0.15

0.16

0.17

0.18

0.19

0.2

0 0.5 1 1.5 2

Ratio of αααα to Default(TRU)

Lo

ad T

hre

sho

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UUL

0.001

0.01

0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Offered Load

Fra

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n R

ejec

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GEO G-SP G-PP G:(PP+SP) TRU PP

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# d �

0.0001

0.001

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Offered Load(α=β=0.5)

Fra

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Sim(5) DRES(5) NDRES,1032�4 �.�X5 � #�# " , �!@�QT> 0 -�U �e���=�GQT>=�GD]@*>%�+-'� # 4 �R;=> 0 U��G;.;

0.0001

0.001

0.01

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Offered Load(α=β=0.05)

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Sim(5) DRES(5) NDRES,1032�4 �.�X5 � # � " , �!@�QT> 0 -�U���� �GQT>=�GDP@*>$�]�GD 034 / # 4 �R;=> 0 U��G;.;, �.-�/ ,I0[2�4 �.�v5 � # 5 8 �:�P;=� �]>.�_@*><�)�pQ @�U 2 � >�; 0[2 U 0 x_Q @�Us>?@�DAD 0 > 0 -�UA@�F 0 /6HA�.- J��G/6�GUY><ksO0 UAQT�!�G@�; 0 U 2 >.���}D�� Lc� ��> 0 /b�KLV�!-�/ 7 >=- # d � ,I0[2�4 �!�K5 � # 5M;.��-'��;%����� �{� 0 >.�p@?D�� Lc� �kl- 4 U_DM-�L # d4 U 0 >.;S- 4 >=Hl� �.LV-��R/ 0 U 2 � ����� ��k9O������ � U ,I0[2�4 �.�e5 � # 798 �)� 0 UY>=�.-ED 4 QT��@BU�� ��/6� >=� 0 Q�Q @�F3F[�GDb>.�A� �6#�� � � ����� �� 0 Q!� 0 ;:D�� x_U��GD<@�;>.���`�!@*> 0 -y-�L�>.���XF[-�@�D{@*>)��� 0 Q!������� �<; 4 HAHl-��.>.;)@}�.��� �GQT> 0 -�U{LV�!@�QT> 0 -�U<-�L # d � � >=-6>.���XF[-�@�D�����GU

# d 5

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Offered Load(α=β=0.005)

Fra

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Sim(5) DRES(5) NDRES,I0[2�4 �!�X5 � #�� " , �R@�QT> 0 -�U���� �GQT>=�GDp@*> � 032 ��# 4 �!;=> 0 UA�G;.;

0.0001

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Offered Load(α=β=0.5)

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Offered Load

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Ratio of Defer Bound to MHT

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Case 1: Multiple Last Hops

Admit

Case 2: Unique Last Hop

Receiver Last Hop Router

Exchange

Probes

Probe

LAN

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