Failure Localization in All-Optical Networks Jnos Tapolcai - - PowerPoint PPT Presentation

Failure Localization in All-Optical Networks

János Tapolcai Budapest University of Technology and Economics

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• The goal is to provide fast link failure (cable cuts)

localization in All-Optical Networks

• Link monitoring
• a naive solution by having an active alarm for each link
• the number of monitors is |E|
• Alarm storm due to multi-hop lightpaths and multi-layer

networks

Motivation

2 STTL SNFC CHCG NYCM LSAN LSVG SLKC DNVR KSCY TULS CLEV STLS WASH BSTN CHRL DTRT TRNT ATLN IPLS HSTN DLLS ELPS NSVL MIAM MPLS NWOR

• Out-of-the band monitoring
• Using dedicated supervisory lightpath
• Monitoring-trail/cycle

þ Simpler and more reliable implementation þ Fast failure localization û Bandwidth requirements

• In-band-monitoring

þ Minimal bandwidth requirements

• Taping operating connections only

û Less precision on failure localization

• Combining with out-of-band monitoring
• Dealing with imprecision of failure localization

How to localize failures?

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• The network topology is known
• At least 2-connected
• The goal is to localize single cable cut
• With minimal number of monitors
• Linear combination of cover length and # of monitors

γ * (#monitors) + (total cover length)

Localize Single Link Failure with Monitoring Cycles

1 2 3

Alarm code table c2

c1 c0

0-1 0 0 1 0-2 0 1 0 0-3 0 1 1 1-2 1 0 0 1-3 1 0 1 2-3 1 1 0

c0 c1 c2

0-3 0 1 1

#monitors= 3 Cover length = 9 #monitors ≥ ⎡log2(#links+1)⎤

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• If a node has degree 2 the neighboring links can not be

distinguished with cycles:

• Using monitoring-trails instead of cycles

Optical Link Failure Monitoring with Trails

(M-Trail)

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2 3 1 4 (b) An m-trail solution t1 t0 t2 (0,1) 1 1 5 (0,2) 1 1 1 7 (0,3) 1 4 (1,2) 1 1 3 (1,3) 1 1 6 (2,4) 1 1 (3,4) 1 2 t2 t1 t0 Link (c) Alarm code table Decimal (a) m-trail R T a b c d e

No optical loopback switching

• N. Harvey, M. Patrascu, Y. Wen, S. Yekhanin, and V. Chan,

“Non-Adaptive Fault Diagnosis for All-Optical Networks via Combinatorial Group Testing on Graphs,” in IEEE INFOCOM, 2007, pp. 697–705.

• Bm-trail is a connected sub-graph
• Euler constraint is relaxed

Optical Link Failure Monitoring with Bi- directional M-Trails (BM-Trails)

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Optical loopback switching

Architecture - Summary

• A supervisory path (SP) is used to probe status of

a group of fibre segments and components

• Each SP corresponds to a monitor which may

alarm when any irregularity is identified

• By collecting all the flooded alarms in a failure

event, the network controller can identify the failed SRLG instantly

• Objective: achieve fast unambiguous

failure localization (UFL) under any shared risk link group (SRLG) failure event

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| 2011 | RNDM

UNAMBIGUOUS FAILURE LOCALIZATION

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• Given: an undirected 2 connected graph
• 1. bm-trail – connected components
• 2. m-trail – trail (Euler subgraph)
• 3. m-cycle – closed trail
• SRLG:
• A. Single link
• B. Dense SRLG: dual, triple link failures
• C. Sparse SRLG: Some multi-link failures
• Goal: find a minimum number of m-trail/m-

cycle/bm-trail in the graph, such that there are no pair of SRLGs with exactly the same m-trail/m-cycle/bm-trail passing through.

• Goal: We assign non-zero alarm codes to the

links, such that each SRLG has unique alarm code, and the in each bit position the 1 bits form.

Unambiguous failure localization (UFL) under any shared risk link group (SRLG) failure event

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#monitors≥ ⎡log (# SRLGs +1) ⎤

1 2 3

001 010 011 100 101 110

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• Number of bm-trails is ⎡#links/2⎤
• To distinguish the failure of link e and f we need

an bm-trail terminating in node n.

• Each bm-trail can terminate at most two nodes,

thus 2*[#bmtrails] ≥ [#nodes] Ring networks single failure

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f e n

• J. Tapolcai1, Bin Wu, Pin-Han Ho, "On Monitoring and Failure

Localization in Mesh All-Optical Networks", in IEEE INFOCOM ’09

• J. Tapolcai, B. Wu, and Pin-Han Ho, L. Rónyai, “A Novel Approach for

Failure Localization in All-Optical Mesh Networks”, in IEEE/ACM Transactions on Networking, Feb 2011.

• Ring topology: #mtrails= ⎡#links/2⎤
• Well-connected topologies (e.g. complete graph):
• Decompose the graph into disjoint spanning trees

and code them separately

• Nash-Williams and Tutte: a 2k connected graph

has k disjoint spanning tree #bm-trails= ⎡log2(#links +1)⎤=k More bounds for single link failure

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• 2⎡log(élszám+1)⎤ összefüggő gráf (m-tree)
• Monitorok száma =⎡log(élszám+1)⎤
• Nash-Williams és Tutte tétele: minden 2k él-összefüggő gráf k

diszjunkt feszítőfát tartalmaz

• 2⎡log(élszám+1)⎤ összefüggő

Nagyon összefüggő gráf

12 | 2011 | RNDM

• b=⎡log(élszám+1)⎤ független feszítőfa
• i. feszítőfához rendelt kódban az i. bit 1
• Ekkor az i. bithez tartozó élek garantáltan összefüggőek

lesznek (sőt kifeszítik az egész gráfot)

• A b hosszú bináris kódokat b vödörbe csoportosítjuk, és

minden vödörben legalább és legfeljebb kód kerül.

• Indukció: rekurzív konstrukció
• b=1,2 jó
• b-re van megoldásunk

Nagyon összefüggő gráf

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1 2 b

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• Csapjunk a végére 0 bitet b+1 bites kódjaink
• Csapjunk a végére 1 bitet a maradék b+1 bites kódjaink
• A második csoportból tegyünk át megfelelő darab kódot az

utolsó vödörbe.

• Ha b ≥ 3

a független feszítő fák miatt igaz

• Teljes gráfra igaz ha V ≥ 18

Nagyon összefüggő gráf

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1 2 b b+1

• Randomly generated

5320 network topology

• with 20, 30, 40, 50, 60

nodes

• Ring networks and

randomly adding chords

• 30 random graph series
• In order to achieve 95%

confidence interwal

Analyzing Different Network Topologies

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• The m-trails are calculated with heuristics

Simulation Results

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1770

• Bin Wu, P.-H. Ho, and K. Yeung, “Monitoring trail: a new paradigm for fast link failure

localization in WDM mesh networks,” in IEEE GLOBECOM ’08

• The problem has been formulated as an Integer Linear

Program (ILP)

The Concept of Monitoring Trails

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ILP running *me= 9573.47 sec ~ 2:30hours Gap to the op*mality = 20.41% #monitors = 11 Total cost =98 where

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t0

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t1

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t2

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t3

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t4

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t5

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t6

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t7

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t8

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t9

1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

t10

γ=5

Constraint 1: Every link most have a unique alarm code

• Unambiguous Failure Localization (UFL)

Constraint 2: The ”1” bits at each bit-position must form a trail

• S. Ahuja, S. Ramasubramanian, and M. Krunz, “SRLG Failure Localization in

All-Optical Networks Using Monitoring Cycles and Paths,” in IEEE INFOCOM ‘08

• The heuristic is proposed a structure where constraint 2 is

ensured and the goal is to fulfill constraint 1.

• Cycle Accumulation (CA)
• Our concept is provide a structure where constraint 1 is

ensured and our goal is to fulfill constraint 2.

• Much faster for minimizing the m-trails

The Heuristic Algorithm I.

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• Randomly generate unique alarm

code for each link

• For each bit position we treat the

m-trail shaping problem separately

• We start with the smallest bit

position and mark the links that has bit „1” at that position

• The goal is to shape it as a trail

The Heuristic Algorithm II.

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This link has no pair. 0001 1 1 0010 0111 1 1 1 1 1110

• Each link has a pair for bit position i
• The binary alarm codes are the same except at bit position i
• One of the links is marked the other is not
• If we change the alarm codes assigned to these links there would be no

change in other positions

• Some links might not have a pair
• Because 0000 alarm code can not be chosen (valid for 1 link only)
• Its code pair was not assigned to any link (don’t care links)

• Greedy code swapping
• Based on Euler’s theorem

we try to shape the links into a trail

• Nodes with odd degree

must be reduced to 2

• The edge set must be

connected

• We repeat it for every bit

position

• Until trails are shaped for

every bits

• If we stuck we generate

new random codes

The Heuristic Algorithm III.

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This link has no pair. : 0001 1 1 0010 0111 1 1 1 1 1110 1 1 1 1

The performance of the heuristic compared to ILP

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• The theoretical minimum ⎡log(#links+1)⎤

was almost always achieved if the network had no nodes with degree 2

• The number of nodes with degree 2

strongly influences the number of m-trails

A Rule of Thumb of Topology Analysis

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1 2 3 4 5 6 7 8 9 12 14 10 11 13 15 16 17 18 20 19

• Counter example
• Every node has degree 3
• The number of bm-trails is linear respect the

number of links Lack of 2 degree nodes is not guarantee

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• Previous results on square Lattice
• N. Harvey, M. Patrascu, Y. Wen, S. Yekhanin, and V. Chan, “Non-Adaptive Fault

Diagnosis for All-Optical Networks via Combinatorial Group Testing on Graphs,” in IEEE INFOCOM, 2007

• Essentially Optimal solution
• Close to the information theory lower bound

Two Dimensional Lattice

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≥ ⎡log2(#links+1)⎤ 4 + ⎡log2(#links+1)⎤ ≥ #mtrails

3x5

• Planar
• Nodal degree is 4
• Large diameter

Moebius ladder

• We add two m-trails

Construction of Chocolate Bar Graph for M-trail

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[11] [10] [01] [00] Unique codes Unique codes Unique codes

• We generate n bitvectors r1,r2,…,rn of lenght b

Construction on Chocolate Bar Graph

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• 1. The bitvectors ri are all non-zero and pairwise different
• 2. The bitvectors ri ⊕ ri+1 are all non-zero and pairwise

different

• 3. The first coordinate of ri and rn are the same
• Abstract algebra
• Galois Field
• Two operators: addition and multiplication
• It has q=2b elements

Generating Bitvectors r1,r2,…,rn

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100 010 001 110 011 111 101 110 011 111 101 100 010 001

• We represent the elements as polynomials of degree strictly

less than b in F2

• E.g. [1 0 1] represented with 1+ x2
• We select an irreducible polynomial R of degree b over F2.
• For F8 it can be
• Operator ⊕ is performed by summing up two polynomials in

modulo R over F2

• It would be bitwise OR

[1 1 1] ⊕ [1 0 1] = [0 1 0]

• Operator * is performed by multiplying two polynomials in

modulo R over F2

• It has a primitive element α such that all the powers are pair

wise different

Constructing Galois Field

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• If for any i ≠ j
• However 1 ⊕ α ≠ 0, thus αi= αj which is a contradiction.

Verification of the required properties

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• We generalize the chocolate bar construction
• First part of the code for horizontal axis
• Second part of the code for vertical axis

Construction for 2 Dimensional Lattice for M- tree

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Benchmarks

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• Relatively sparse

graphs with low nodal degree

• Large diameter
• Benchmarking
• It is much

stronger than any general method we have examined

• J. Tapolcai, L. Rónyai, and Pin-Han Ho,

“Optimal Solutions for Single Fault Localization in Mesh Topologies”, in IEEE Infocom 2010 Mini-conf, and extended for IEEE/ACM Transaction on Communications

MULTIPLE FAILURES

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• Dedicated path protection is the only widely

accepted solution

• 1+1+1
• The chance of having a dual failure is very small
• Shared protection is too complex for multiple failures
• The network connectivity is often limited
• Failure Dependent Protection could be a strong

alternative

• Great capacity efficiency Stub-reuse
• Great flexibility to sparse topologies

Multiple failures

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• With multi-link SRLGs, each SRLG should be uniquely coded
• Code of an SRLG is the bitwise OR of the codes of all the

links contained in the SRLG

• to ensure that “an SRLG failure is a failure event that all the links in the

SRLG failed”

• Note: routing of m-trails is performed on links in the topology,

but code uniqueness should be ensured for every SRLG

Multiple Failures

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1 2 3 Alarm code table

c2 c1 c0

0-1 0 0 1 0-2 0 1 0 0-3 0 1 1 1-2 1 0 0 1-3 1 0 1 2-3 1 1 0

c0 c1 c2

0 1 1 0-2 0-1

• Non-adaptive
• 1942 Washington, DC
• Searching for syphilitic antigen in blood samples with chemical analysis
• It might be economical to pool the blood samples, since there are only a

few blood samples with syphilitic antigen

• Annals of Mathematical Statistics
• Statistical „group test”
• 1973 Gyula O. H. Katona emphasized the combinatorial aspect of

group testing

• Strongly union-free sets
• The alarm code is the characteristic vector of a set
• We need codes where the bitwise or of any two codes is unique
• Péter Frankl, Zoltán Füredi, Pál Erdős, Miklós Ruszinkó
• 1987 F. K. Hwang, V. T. Sós :number of tests O(d2 log |E|), where |

E| is the number of elements

• 2007 Eppstein, Goodrich, Hirschberg : more efficient code for real

size problems

• Superimposed Codes

Combinatorial Group Testing (up to d failures)

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Dense SRLG

• The code swapping mechanism was improved
• Generate CGT codes
• Code swapping is implemented among codes with

Hamming distance > 1

• At least Binomial(|E|,2) possible code swaps
• Special data structure for fast decision on the cost of a

code swapping

• For each bit position we have
• 1. A link is added and an other is removed
• 2. A link is added
• 3. A link is removed
• Evaluate the change in the number of m-trails in constant

time

• Finally, select the best code swapping
• J. Tapolcai and Pin-Han Ho, et. al. “Failure Localization for Shared Risk Link Groups

in All-Optical Mesh Networks using Monitoring Trails”, accepted in IEEE/OSA Journal of Lightwave Technology in Feb. 2011.

Dense SRLG - Greedy Code Swapping (GCS)

| 2011 | RNDM

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• Random maximal planar graphs
• CA – Cycle Accumulation
• DSTC – Disjoint Spanning Tree Coding
• Theoretical, often not feasible
• Found that when d = 3, link monitoring (a

special and trivial solution for the problem) becomes the best solution most of the time

Dense SRLG - Simulation

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Sparse SRLG

• Failure localization for bi-directional m-trails for a

small set of SRLGs

• Identified necessary and sufficient conditions for

the existence of the problem solution

• Use a graph partition method and re-invoke the

random code swapping mechanism to solve

• Proved that the solution also yield the least

cover length

• P. Babarczi, J. Tapolcai, and Pin-Han Ho, “Adjacent Link Failure Localization

with Monitoring Trails in All-Optical Mesh Networks”, IEEE/ACM Transactions on Networking, vol. 19, no. 3, pp. 907 - 920, 2011

• P. Babarczi, J. Tapolcai, Pin-Han Ho, "SRLG Failure Localization with

Monitoring Trails in All-Optical Mesh Networks", In Proc. International Workshop on Design Of Reliable Communication Networks (DRCN), 2011 39

NETWORK-WIDE LOCAL UFL (NWL-UFL)

Signaling free failure localization

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• Drawbacks of the alarm dissemination process
• Electronic signaling is required
• Increase the failure localization latency
• Achieving UFL all-optically at each node (Local-Unambiguous

Failure Localization)

• Any node along an m-trail can obtain the on-off status of

the m-trail via optical signal tapping

• Achieve UFL according to these status information
• Alarm dissemination is no longer needed
• For every node: Network Wide L-UFL (NWL-UFL)
• Simplification in our current work
• It is very complex to consider the general case (open trails)
• We consider bidirectional m-trails

Signaling free failure localization

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• The number of

alarms is no longer a concern

• Minimize the

cover length

NWL-UFL solution

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t3 t1 t4 t2

• Stars
• The cover length ≥ |E|⎡log (|E|+1)⎤
• in each leaf node at least ⎡log (|E|+1)⎤ m-trails must terminate
• The cover length ≤ |E|⎡1+log (|E|+1)⎤
• Random alarm codes of ⎡1+log (|E|+1)⎤ bits, and the

complement for each m-trail is added

• The lower bound generally true

≥​|𝑊|/2 ⌈​log⁠(|𝐹|+1) ⌉

• Line graph
• The cover length is m2

Bounds on cover length

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• J. Tapolcai and Pin-Han Ho, et. al. “Network-Wide Local Unambiguous

Failure Localization (NWL-UFL) via Monitoring Trails” review in IEEE/ACM Transactions on Networking

• Complete graphs
• The cover length is (|V|-1)2
• Lower bound is ≥2|𝐹|(1−​1/|𝑊| )
• Singular link: a link is traversed by

single m-trail

• The number of singular link is σ
• An m-trail may have at most one

singular link

• 1. Cover length is ≥2|𝐹|−𝜏
• An m-trail with a singular link must

span the graph

• 2. Cover length is ≥𝜏(|𝑊|−1)
• If 𝜏≥​2|𝐹|/|𝑊| 1. holds, otherwise 2

holds

Bounds on cover length

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• Idea: we focus on solutions

where the m-trails are spanning tree

• We generate b random

spanning trees

• b is sufficiently large
• We need to make the alarm

codes unique

• If there is a code collusion

perform Greedy Link Swapping

• Until UFL

Random Spanning Tree Assignment (RSTA) and Greedy Link Swapping (GLS)

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The GAP to the optimality is ~20%

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Performance

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• The idea to use the spare capacity resources for

monitoring until there is a failure in the network

• Cover length is no longer a concern
• Shared protection
• Failure Dependent Protection
• Each node performs L-UFL parallel
• We have a longer failure localization phase but

shorter connection setup

• Still less than 100ms
• P-cycle based mechanism
• Much better capacity efficiency
• Much better flexibility on topology diversity

Integration with Protection mechanism

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Example

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t3 t1 t4 t2 w1

• Depends on traffic
• Depends on the number of WL on each link
• With 50 WL the cost of m-trail is relatively small

Simulation Results

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working protection m-trail

Comparison with other schemes

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• Optical layer rerouting is a strong candidate

for achieving high end-to-end connection availability

• Capacity efficient
• Flexible
• Easy to calculate
• It should provide fast restoration
• Failure localization is the main difficulty
• With alarm dissemination
• Without alarm dissemination

Conclusions

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