NETWORK RECOVERY BY EMBRACING THEUNCERTAINTY

D. Z. TOOTAGHAJ†, S. CIAVARELLA∗ , H. KHAMFOROUSH†, S. HAYES†, N. BARTOLINI∗, T. LA PORTA††THE PENNSYLVANIA STATE UNIVERSITY, USA, ∗SAPIENZA UNIVERSITY, ITALY

OBJECTIVES AND MOTIVATION

A

C

H

L

M

Flow =1 unit

Demand pair

S

B

E

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K

I

F

D

J

D

Flow =1 unit

Gray area

Demand pair

S

0.1

0.3

0.1

0.7

0.9

0.7

0.1

0.1

0.6

0.1

0.8

0.2

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0.1

0.6

D

(a) (b)

Figure 1: Netwrok failurewith full information (a),partial-information (b).

Figure 2: ITC Deltacomfrom the internet topol-ogy zoo [3].

Motivation:1. Large-scale network failures,2. Natural disasters:

• Hurricane Katrina (2005),• Hurricane Rita (2005),

3. Malicious attacks,4. Uncertain failures,

Objectives:1. Proggressive and timely network recovery,2. Minimize losses, facilitate rescue mission,3. Minimize the expected recovery cost (ERC).

PROPOSED ALGORITHMWe use an iterative approach to place monitors andgain more information at each recovery step.

Start

(1)Find afeasiblesolution

set St

St = ∅? End

(2)Selectcanidate

nodeni ∈ St

(3)Monitoron ni,

discoveryphase

(4)Repairni and itsadjacent

edges ∈ St

(5)Updateexpected

costs

yes

no

Finding a feasible solution set (1) is based on oneof the following algorithms:

1. An iterative shortest path algorithm (ISRT),2. An iterative split and prune (ISP),3. An approximate branch and bound (IBB),4. An iterative imulticommodity LP relaxation

(IMULT).Selecting the best candidate node (2) is based onone of the following criterias:

1. Maximum failure probability,2. Maximum betweeness centrality.3. Maximum information gain.

EXPERIMENTS (2)Scenario3: Trade-off execution time and number of re-pairs (DeltaCom).

40

60

80

100

120

140

0 20 40 60 80

Nu

mb

er

of

tota

l re

pa

irs

Percentage of Gap from OPT

ISP Total

ISP Necessary

IMULT Total

IMULT Necessary

IBB Total

IBB Necessary

ISRT Total

ISRT Necessary

OPT

0.1

1

10

100

1000

10000

0 20 40 60 80

Tim

e (

s)

Percentage of Gap from OPT

ISP Total

IMULT

IBB Property3

IBB

ISRT

OPT

Scenario4: Synthetic Erdos-Renyi topology with 100nodes:

20

25

30

35

40

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Nu

mb

er

of

tota

l re

pa

irs

Edge probability

OPT IMULT IBB

0*100

5*104

1*105

2*105

2*105

2*105

3*105

4*105

4*105

5*105

5*105

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Exe

cu

tio

n t

ime

(s)

Edge probability

OPT

IBB

IMULT

Scenario5: Trade-off between number of repairs anddemand loss (Deltacom)

0

20

40

60

80

100

1 2 3 4 5 6

Num

ber

of to

tal r

epairs

Number of demand pairs

ISP Total

ISP Necessary

IMULT Total

IMULT Nesessary

IBB Total

IBB Nesessary

ISRT Total

ISRT Nesessary

OPT

70

75

80

85

90

95

100

105

110

1 2 3 4 5 6

Perc

enta

ge o

f sa

tisfie

d d

em

and

Number of demand pairs

ISP

IMULT

IBB

ISRT

OPT

REFERENCES[1] N. Bartolini, S. Ciavarella, T. F. La Porta, and S. Silvestri. Network

recovery after massive failures.[2] J. Wang, C. Qiao, and H. Yu. On progressive network recovery after

a major disruption. In INFOCOM, 2011 Proceedings IEEE, 2011.[3] The internet topology zoo. http://www.topology-zoo.org/,

accessed in May, 2015.

PROBLEM FORMULATIONRecovery problem can be formulated as follows:

minimizeδi,δi,j

Eζ

∑(i,j)∈EU∪EB

keijζ

eijδ

eij +

∑i∈VU∪VB

kvi ζvi δvi

(1a)

subject to cij .δij >|EH |∑h=1

fhij + f

hji ∀(i, j) ∈ E (1b)

δi.ηmax >∑

(i,j)∈EBδij ∀i ∈ V (1c)∑

j∈Vfhij =

∑k∈V

fhki + b

hi ∀(i, h) ∈ V × EH (1d)

fhij > 0 ∀(i, j) ∈ E, h ∈ EH (1e)

δvi , δ

ei,j ∈ {0, 1} (1f)

Where the binary variables δij and δi represent thedecision to repair link (i, j) ∈ E and node i ∈ V .

EXPERIMENTS (1)NetworkName

# ofnodes

# ofedges

AverageNodedegree

Repairs(ISP-partial-info)

Repairs(Progres-sive ISP)

BellCanada 48 64 2.62 79 45.39Deltacom 113 161 2.85 112 55.5

Table 1: Network characteristics used in our evaluation.

Scenario1: Increasing demand pairs and flows (Bell-Canada).

0

10

20

30

40

50

60

0 2 4 6 8 10

Nu

mb

er

of

tota

l re

pa

irs

Number of demand pairs

ISP Total

ISP Necessary

IMULT Total

IMULT Nesessary

IBB Total

IBB Nesessary

ISRT Total

ISRT Nesessary

OPT

10

20

30

40

50

60

2 4 6 8 10

Nu

mb

er

of

tota

l re

pa

irs

Number of flows

ISP Total

ISP Necessary

IMULT Total

IMULT Nesessary

IBB Total

IBB Nesessary

ISRT Total

ISRT Nesessary

OPT

Scenario2: K-hop discovery and increasing disruption(BellCanada).

10

20

30

40

50

60

70

80

90

0 1 2 3 4 5

Nu

mb

er

of

tota

l re

pa

irs

K-hop discovery

ISP Total

ISP Necessary

IMULT Total

IMULT Nesessary

IBB Total

IBB Nesessary

ISRT Total

ISRT Nesessary

OPT

0

10

20

30

40

50

20 40 60 80 100 120 140 160 180 200

Nu

mb

er

of

tota

l re

pa

irs

Variance of disruption

ISP Total

ISP Necessary

IMULT Total

IMULT Nesessary

IBB Total

IBB Nesessary

ISRT Total

ISRT Nesessary

OPT

CONCLUSIONWe consider for the first time a progressive net-work recovery algorithm under uncertainty. Ourextensive simulation shows that our algorithmoutperforms the state-of-the-art recovery algo-rithm while we can configure our choice of trade-off between:

1. Execution Time,2. Demand Loss,3. Number of repairs (cost).

Our iterative recovery algorithm reduces the totalnumber of repairs’ gap with full-knowledge andpartial knowledge from 79 repairs to 45.39 repairsin Bellcanada topology which is the smallest topol-ogy in our experiments.

FUTURE RESEARCH1. Tomography techniques to reveal more infor-

mation,2. Uncertain traffic analysis of the network,3. Dependable networks.