Survivable Telecommunication Network Design Under Different Types of Failures

Hanan Luss and Richard T. Wong

Presented by Huan-Ting Chen, OPLab, IM, NTU2007/3/19

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS, VOL. 34, NO. 4, JULY 2004

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Author

- Hanan Luss received the the Ph.D. degree in operations research from the University of Pennsylvania,Philadelphia, in 1973.- He is an Adjunct Professor at Columbia University, New York.

- Richard T. Wong received the Ph.D. degrees from the Cambridge, 1978.- He is currently a Senior Operations Research Analyst with United Parcel Service.

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Outline

Introduction - Principal Issues for Survivable Network Design - Message of Paper Three approaches - Under Partial Link Failure - Under Link Failure - Under Node Failure Conclusions

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Outline

Introduction - Principal Issues for Survivable Network Design - Message of Paper Three approaches - Under Partial Link Failure - Under Link Failure - Under Node Failure Conclusions

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Introduction

Principal Issues for Survivable Network Design

- Reroute the traffic of a failure of a network element - Restoration protocols

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Introduction

Message of Paper - Augmenting capacities - Under a single failure

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Outline

Introduction - Principal Issues for Survivable Network Design - Message of Paper Three Approaches - Under Partial Link Failure - Under Link Failure - Under Node Failure Conclusions

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Three Approaches

Three different scenarios - Restoration under a single partial link failure - Restoration under a single link failure - Restoration under a single node failure

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Under Partial Link Failure

Augments network capacity Under a single partial link failure - A link component failed on one link

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Notation

G(N , A) A network with a set of nodes N and a set of

links A .

i,j,k,l Indices for nodes. Links are denoted by their end nodes, e.g., link (i , j) .

C

Capacity of a single-link component. All link components have the same capacity. Each component on link (i , j) provides capacity of C units from i to j and of C units from i to j .

s(i , j) Spare capacity on link (i , j) .

f(i , j)The maximal traffic that can be routed from node i to j (or from node j to i ), using spare capacities in G(N , A) .

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Under Partial Link Failure Guarantees the network will survive a single

partial link failure on any link of G(N , A). Goal - Constructs a spanning tree V(N , A) where each link (i , j) V(N , A) has f(i , j) C.

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Under Partial Link Failure

[C – s(k,l) ] + [s(k,l) – s’(k,l) ] = C – s’(k,l)

C – s’(k,l) Traffic units that need be rerouted.

s(k,l) – s’(k,l)Traffic units that can be absorbed by the remaining spare on other components of link (k,l).

C – s(k,l)

Traffic units that can be routed between nodes k and l using spare capacity on paths comprised of other links.

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Under Partial Link Failure

6

7

6

6

10

10 10

Add (1,4) and (1,5) to the spanning treeAdd capacity C to (1,3) and add it to the spanning tree

7

7

10

Add capacity C to (1,2) and add it to the spanning tree

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Under Partial Link Failure

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Under Link Failure

Augments network capacity Under a single link failure

g(i , j) ： Traffic on link (i , j) that needs to be restored in the event that link (i , j) A fails.

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Under Link Failure

3

4

2

15

2

1

1

22

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Under Link Failure

3

4

2

15

Add C to these links and decrease the original g(i,j) by 1

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Under Link Failure

3

4

2

15

1 1

1

0

0

Two subnetworks

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Under Link Failure

3

4

2

15

Add C to these links and decrease the original g(i,j) by 1

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Under Link Failure

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Under Node Failure

Augments network capacity Under a single node failure Construct a restoration ring

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Notation

t(i,i1,i2…..il

.j)

Transit traffic between end nodes i and j which is routed through intermediate nodes i,i1,i2…..il.j.

t(i , j)Aggregated transit traffic between end nodes iand j over all routes.

N(il)The set { t(i,i1,i2…..il.j) } (with the corresponding traffic volumes) that use node il

as an intermediate node.

RThe set of nodes that are the origin/destinationof some transit traffic that needs to be restoredin the event of some node failure.

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Under Node Failure

t(1,4) = 4

t(3,5) = 2

t(1,3) = 1

t(1,2,3,4) = 1t(1,3,4) = 1t(1,5,4) = 2

t(1,2,3) = 1

t(3,4,5) = 2

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Under Node FailureN(3) = {t(1,2,3,4) , t(1,3,4)}

t(1,2,3,4) =1 is reroute on link (1,4)

Update N(3) = {t(1,3,4) =1}

N(4) = {t(3,4,5) }

t(3,4,5) =1 is reroute on link (3,5)

Update N(4) = {t(3,4,5) = 1}

N(5) = {t(1,5,4)}

t(1,5,4) =1 is reroute on link (1,4)

Update N(5) = {t(1,5,4) = 1}

N(2) ＝ {t(1,2,3,4) , t(1,2,3)}t(1,2,3,4) =1 is reroute on link (1,4) (1,4) + 1

t(1,2,3) = 1 is reroute on link (1,3) (1,3) + 1

Update N(2) ＝

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Under Node Failure

11

1

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Under Node Failure

After one iteration the updated traffic value are

t (1,4) = 2 t (3,5) = 1

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Under Node Failure

11

1

N(3) ＝ {t(1,3,4) }

t(1,3,4) =1 is reroute on link (1,4) (1,4) + 1

Update N(3) =

N(4) = {t(3,4,5) }t(3,4,5) =1 is reroute on link (3,5) (3,5) + 1

Update N(4) ＝

N(5) = {t(1,5,4)}

t(1,5,4) =1 is reroute on link (1,4)

Update N(5) =

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Under Node Failure

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Outline

Introduction - Principal Issues for Survivable Network Design - Message of Paper Three approaches - Under Partial Link Failure - Under Link Failure - Under Node Failure Conclusions

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Conclusions

The goal of this paper is to present several survivable designs by augmenting capacities along prudently selected variants of spanning tree and ring structures.

Future work may evaluate the designs by comparing the results to those obtained by other heuristics.

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Thanks for your listening

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Consider a network with multiple disconnected subnetworks and suppose a spanning tree can be constructed on the complementary graphs of subnetworks m = 1 , 2 . The number of links comprising the two spanning trees is less than the number of links of a spanning tree on the complementary graph of a subnetwork that is the union of the two.

Consider two disconnected subnetworks. A spanning tree always exists on the complementary graph of a subnetwork that is the union of the two.

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Under Partial Link Failure C – s’(k,l) : traffic units need be rerouted. s(k,l) – s’(k,l) : traffic units can be absorbed

by the remaining spare on other components of link (k,l).

C – s(k,l) : traffic units can be routed between nodes k and l using spare capacity on paths comprised of other links.

[C – s(k,l) ] + [s(k,l) – s’(k,l) ] = C – s’(k,l)