On Survivable Routing of Mesh Topologies in

IP-over-WDM Networks

Maciej Kurant, Patrick ThiranEPFL, Switzerland

Infocom 2005, March 13-17, Miami

2

Mapping

• Logical topology GL - mesh of IP links

• Physical topology GΦ - mesh of physical links (fibers)

• Each logical link is mapped on the physical topology as a physical path called a lightpath.

• We assume infinite capacities of fibers

• Mapping M - a set of lightpaths associated with a set of logical links

GL

GΦ

M

3

Survivability

How to deal with failures?

There are several methods

• Protection vs restoration

• WDM layer vs IP layer

We use only the IP restoration approach:(The failures are detected at the IP layer,

and a new route is found dynamically.)

GL

GΦ

M

4

Link-survivability example

GL

GΦ

GL

GΦ

GL

GΦ

The logical topology remains conneceted after any single physical link failure

The mapping is link-survivable

5

Node-survivability example

GL

GΦ

GL

GΦ

GL

GΦ

The failure of node v* disconnects the remaining logical topology GL\{v*}

The mapping is not node-survivable

v*

v*

Connected Connected Not connected!!

6

The problem of finding a survivable mapping is not new…

E. Modiano and A. Narula-Tam, Survivable lightpath routing: a new approach to the design of WDM-based networks, IEEE Journal on Selected Areas in Communications, vol. 20, no. 4, 2002

F. Giroire, A. Nucci, T. Taft, and C. Diot, Increasing the Robustness of IP Backbones in the Absence of Optical Level Protection, Proc. of IEEE INFOCOM 2003.

L-W. Chen and E. Modiano, Efficient Routing and Wavelength Assignment for Recongurable WDM Networks with Wavelength Converters, Proc. of IEEE INFOCOM’03.

…

J. Armitage, O. Crochat, and J. Y. Le Boudec, Design of a Survivable WDM Photonic Network, Proceedings of IEEE INFOCOM 97, April 1997.

Our solution

8

Contraction

a

b

c

e

d

g

h

f

Contraction ofC={a, b, c}

e

d

g

h

f

GC=G CG

9

The SMART algorithm (link-survivability example)

GL

GΦ

GL

GΦ

GL

GΦ

GCGC GC

A single node!

Iteration 1 Iteration 2 Iteration 3Theorem 1: If the contracted logical topology GC converges to a single node, then the mapping is (link/node)-survivable.

a

b

cd

f

g

h

e

a

b

cd

f

g

h

e

a

b

cd

f

g

h

e

a

b

cd

f

g

h

e

f

g

h

e

d

e

d

10

Verification of mapping existence

GL

GΦ

GL

GΦ

GL

GΦ

GCGC GC

Iteration 1 Iteration 2 Iteration 3

a

b

cd

f

g

h

e

a

b

cd

f

g

h

e

a

b

cd

f

g

h

e

a

b

cd

f

g

h

e

f

g

h

e

d

e

d

Theorem 2: A (link/node)-survivable mapping of GL on GΦ exists iff any contracted topology GC can be mapped on GΦ in a (link/node)-survivable way.

A node-survivable mapping of the contracted topology GC={e,d} does not exist.

A node-survivable mapping of the logical topology GL

on GΦ does not exist.

Seq

uen

ce o

f cy

cles

do

es n

ot

mat

ter!

11

SMART applied to the verification of the existence of a link/node-

survivable mapping

Application 1

12

Verification of mapping existence (2)

SMART- physical topology- logical topology

Survivablemapping

Survivable mappingnot possible (proof)

SMARTconverges

Exhaustivesearch for GC

Survivablemapping found

SMART doesnot converge

Survivablemapping not found

Contracted logicaltopology GC

13

Random graph on NSFNET

NSFNET

1

2

4 7

8

3 6

5

9

11

10 14

13

12

Random graph (2-node-connected)

1

2

4 7

8

3 6

5

9

11

10 14

13

12

(a) Random graph on NSFNET

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2.3 2.5 2.7 2.9 3.1 3.3 3.5

Average node degree of random graph

Fra

cti

on

of

ma

pp

ed

to

po

log

ies

Unknown

14

SMART applied to the fixing a vulnerable topology (enabling link/node-survivable mapping)

Application 2

15

Where to introduce a new link?

GL

GΦ

GC

a

b

d

f

g

h

e

e

d

A new logical link which is a self-loop in the contracted topology GC will never help.

Only a new logical link between two different nodes in GC might help.

i

i

i

i

In simulations (up to 64 nodes):

• New logical link introduced at random rarely helped (<10%)

• New logical link between two different nodes in GC helped in more than 80% of cases.

16

Applications of SMART (summary)

• The formal verification of the existence of a link/node-survivable mapping,

• a tool tracing and repairing the vulnerable areas in network,

• a fast heuristic.

17

Thank you!