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Hierarchical Traffic Groomingin WDM Networks
George N. Rouskas
Department of Computer Science
North Carolina State University
Joint work with: Rudra Dutta (NCSU), Bensong Chen (Google Labs), Huang Shu (RENCI)
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.1
Upcoming Book
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.2
Outline
Motivation and problem definition
Complexity results and implications
Hierarchical grooming in rings
Hierarchical grooming for general topology networks
clustering and hub selection
logical topology design and traffic routing
RWA
Results and discussion
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.3
Optical Networking Trends
Increasing data ratesOC-48 (2.5 Gbps) → OC-768 (40 Gbps) and 100 GbE
Increasing fiber capacityDense WDM → 100s of λs per fiber
Improving fiber technologyOptical signals may travel longer without regeneration (OEO)
Improving OXC technologyHigher port counts, faster configuration times
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.4
Optical Network Design Considerations
Fine traffic granularityMost traffic demands are sub-wavelength in magnitude
High cost of OEO componentsCost scales faster than linearly with the number of ports
Optical bypass of intermediate nodes has benefits:
most traffic travels more than200 Km
most links shorter than 200 Km
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.5
Traffic Grooming in WDM Networks
What is traffic grooming?
Efficiently set up lightpaths and groom (i.e., pack/unpack,switch, route, etc.) low-speed traffic onto high capacitywavelengths so as to minimize network resources
Requires MUX/DEMUX and ADM/OADM devices
But: involves much more than simple multiplexing techniques
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.6
Traffic Grooming as Optimization Problem
Inputs to the problem:
physical network topology (fiber layout)
traffic matrixT = [tsd] → int multiples of unit rate (e.g., OC-3)
Output:
logical topology
lightpath routing and wavelength assignment (RWA)
traffic grooming on lightpaths
Objectives:
minimize total # of OEO ports in the network (↔ # of lightpaths)
limit the number of required wavelengths
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.7
Traffic Grooming Subproblems
1
2
3
4
5
6
Logical topology design → determine the lightpaths to be established
Lightpath routing → route the lightpaths over the physical topology
Wavelength assignment → assign wavelengths to lightpaths w/o clash
Traffic grooming→ route traffic on virtual topology
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.8
Traffic Grooming Subproblems
1
2
3
4
5
6
Logical topology design → determine the lightpaths to be established
Lightpath routing → route the lightpaths over the physical topology
Wavelength assignment → assign wavelengths to lightpaths w/o clash
Traffic grooming→ route traffic on virtual topology
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.8
Traffic Grooming Subproblems
1
2
3
4
5
6
Logical topology design → determine the lightpaths to be established
Lightpath routing → route the lightpaths over the physical topology
Wavelength assignment → assign wavelengths to lightpaths w/o clash
Traffic grooming→ route traffic on virtual topology
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.8
Traffic Grooming Subproblems
1
2
3
4
5
6
Logical topology design → determine the lightpaths to be established
Lightpath routing → route the lightpaths over the physical topology
Wavelength assignment → assign wavelengths to lightpaths w/o clash
Traffic grooming→ route traffic on virtual topology
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.8
Traffic Grooming Subproblems
1
2
3
4
5
6
Logical topology design → determine the lightpaths to be established
Lightpath routing → route the lightpaths over the physical topology
Wavelength assignment → assign wavelengths to lightpaths w/o clash
Traffic grooming→ route traffic on virtual topology
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.8
Outline
Motivation and problem definition
Complexity results and implications
Hierarchical grooming in rings
Hierarchical grooming for general topology networks
clustering and hub selection
logical topology design and traffic routing
RWA
Results and discussion
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.9
Problem Complexity
Optimization problem:
can be formulated as integer linear problem (ILP)
is NP-hard in general → ILP solvable for toy networks only
Difficulty arises due to RWAsubproblem:
solvable in polynomial time for path (linear) and star networks
NP-hard for other topologies (including rings and trees)
But what about the traffic groomingsubproblem?
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.10
Traffic Grooming Complexity [JSAC 2006]
. . . . . .S 1 2 3 n n+1 n+2 n+3 n+4 2n+1 D
Problem instance:
unidirectional linear (path) network
logical topology and RWA is given
traffic either bifurcated or not bifurcated
Objective: find a grooming of traffic onto the lightpaths
Result: problem is NP-complete → reduction from Subset Sums
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.11
Implications
The problem is not simplified by assuming
fixed routing
large numbers of wavelengths
full wavelength conversion
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.12
Traffic Grooming in Stars
4
1
2
3
Switching and grooming: only at hub
Two types of lightpaths
1-hop: to/from the hub
2-hop: optically bypass the hub
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.13
Star Grooming Complexity [JSAC 2006]
RWA subproblem solvable in polynomial time
But: the grooming subproblem is NP-Complete
Greedy heuristic:
obtain an all-electronic solution → 1-hop lightpaths only
greedily reroute large demands onto direct (2-hop) lightpaths
O(WN 2) running time
Experiments show good performance
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.14
Outline
Motivation and problem definition
Complexity results and implications
Hierarchical grooming in rings
Hierarchical grooming for general topology networks
clustering and hub selection
logical topology design and traffic routing
RWA
Results and discussion
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.15
Hierarchical Grooming in Rings
[Gerstel 2000]: single-hub, double-hub architectures, etc.
[Chen 2005]: ring embeddings
[Simmons 1999]: super-node archtecture
[Dutta 2002]: generalized hub archtecture
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.16
Ring Embeddings
access nodes
backbonewavelengths
wavelengthsaccess
backbone nodes
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.17
Super-Node Archtecture
Supe
rnod
e 2
Supernode 1
Supernode 3
Supe
rnod
e 4
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.18
Generalized Hub Archtecture
(a) (b)
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.19
Outline
Motivation and problem definition
Complexity results and implications
Hierarchical grooming in rings
Hierarchical grooming for general topology networks
clustering and hub selection
logical topology design and traffic routing
RWA
Results and discussion
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.20
Grooming in General Topology Networks
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2011
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3031
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Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.21
Approaches
1. Solve the ILP directly
2. Apply classical optimization tools to solve the ILP suboptimally
LP-relaxation techniques
meta-heuristics (simulated annealing, genetic algorithms)
3. Apply decomposition methods
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.22
Airline Analogy
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.23
Airline Traffic Analogy (2)
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.24
Hierarchical Grooming Phases [ToN 2008]
1. Clustering and hub selection
2. Logical topology design and traffic routing
reduction: set up direct and direct-to-hub lightpaths
intra-cluster grooming: 1st level virtual stars
inter-cluster grooming: 2nd level virtual star
3. Lightpath routing and wavelength assignment (RWA)
existing LFAP algorithm [Siregar et al, 2003]
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.25
Illustration: Clustering
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2011
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Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.26
Illustration: Clustering
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Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.26
Illustration: Reduction
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Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.27
Illustration: Reduction
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Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.27
Illustration: Intra-Cluster Grooming
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Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.28
Illustration: Intra-Cluster Grooming
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Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.28
Illustration: Intra-Cluster Grooming
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3031
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.28
Illustration: Intra-Cluster Grooming
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Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.28
Illustration: Inter-Cluster Grooming
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Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.29
Illustration: Inter-Cluster Grooming
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Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.29
Benefits of Hierarchical Design
Hierarchical control and management
RWA on physical topology relatively independent of logical topologydesign
Only hubs have grooming capability
Efficient handling of small traffic components
Limited number of electronic hops
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.30
Clustering and Hub Selection
Widely studied problem in network design and other domains
Many algorithms exist, but do not address grooming considerations
K-Center problem → good match
minimizes max distance from any node to nearest center
does not take into account:traffic matrixnodal degrees
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.31
Clustering Algorithm for Grooming [CN 2008]
Grooming considerations for clustering:
Effect of number of clusters on hub size and cost objectives
Composition of each cluster → group nodes with dense traffic
Effect of cut links connecting to other clusters
Physical shape of each cluster → avoid linear topology
Selection of hubs → prefer high degree nodes
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.32
The “Virtual” Star Concept
61
2
3
45
Any arbitrary topology
View as star to determine logical topology / traffic routing
Star topology not used for RWA
Perform RWA on original topology
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.33
The “Virtual” Star Concept
4
1
2
3
45
6
6
1 5
2 3
Any arbitrary topology
View as star to determine logical topology / traffic routing
Star topology not used for RWA
Perform RWA on original topology
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.33
The “Virtual” Star Concept
4
1
2
3
45
6
6
1 5
2 3
Any arbitrary topology
View as star to determine logical topology / traffic routing
Star topology not used for RWA
Perform RWA on original topology
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.33
The “Virtual” Star Concept
4
1
2
3
45
6
6
1 5
2 3
Any arbitrary topology
View as star to determine logical topology / traffic routing
Star topology not used for RWA
Perform RWA on original topology
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.33
Computational Considerations
Running time complexity:
1. Clustering: O(N 4)
2. Logical topology design and traffic routing:O(WN 2)
3. RWA: O(WN 2M)
Algorithm scales well to large networks
a few seconds for 128-node network
permits “what-if” analysis
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.34
Lower Bounds
For evaluating algorithm effectiveness
Lightpath lower bounds:
nodal aggregate traffic demands
ILP relaxation
Wavelength lower bound:
bisection of physical topology forms cut of size k with traffictgoing through → bound = t/kC
used METIS tool to generate good cut
Bounds independent of grooming method
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.35
Outline
Motivation and problem definition
Complexity results and implications
Hierarchical grooming in rings
Hierarchical grooming for general topology networks
clustering and hub selection
logical topology design and traffic routing
RWA
Results and discussion
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.36
Results: 32-Node Network, Locality Traffic
900
1000
1100
1200
1300
1400
1500
0 5 10 15 20 25 30
No.
of L
ight
path
s
Problem Instance
Lower Bound1 Cluster
2 Clusters4 Clusters8 Clusters
30
40
50
60
70
80
90
0 5 10 15 20 25 30
No.
of R
equi
red
Wav
elen
gths
Problem Instance
Lower Bound based on BisectionTopology-specific Lower Bound
1 Cluster2 Clusters4 Clusters8 Clusters
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.37
Results: 32-Node Network, Random Traffic
800
900
1000
1100
1200
1300
1400
0 5 10 15 20 25 30
No.
of L
ight
path
s
Problem Instance
Lower Bound1 Cluster
2 Clusters4 Clusters8 Clusters
40
45
50
55
60
65
70
75
0 5 10 15 20 25 30
No.
of R
equi
red
Wav
elen
gths
Problem Instance
Lower Bound Based on BisectionTopology-specific Lower Bound
1 Cluster2 Clusters4 Clusters8 Clusters
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.38
Results: 32-Node Network, Random Traffic
#Clusters Avg LP Length Avg Max Hub Degree Wavelengths
1 3.17 266 60
2 3.07 228 60
4 2.93 183 59
8 2.84 143 56
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.39
Results: 47-Node Network, Locality Traffic
1.36
1.38
1.4
1.42
1.44
1.46
1.48
1.5
0 5 10 15 20 25 30
Nor
mal
ized
ligh
tpat
h co
unt
Problem Instance
K-Center, 4 clustersK-Center, 6 clusters
MeshClustering, 3.52 clustersMeshClustering, 5.45 clusters
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30
Nor
mal
ized
wav
elen
gth
requ
irem
ents
Problem Instance
K-Center, 4 clustersK-Center, 6 clusters
MeshClustering, 3.52 clustersMeshClustering, 5.45 clusters
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.40
Results: 128-Node Network, Rising Traffic
1.45
1.46
1.47
1.48
1.49
1.5
0 5 10 15 20 25 30
Nor
mal
ized
ligh
tpat
h co
unt
Problem Instance
K-Center, 9 clustersK-Center, 10 clusters
MeshCluster, 9.03 clusters
1
1.5
2
2.5
3
0 5 10 15 20 25 30
Nor
mal
ized
wav
elen
gth
requ
irem
ents
Problem Instance
K-Center, 9 clustersK-Center, 10 clusters
MeshClustering, 9.03 clusters
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.41
Conclusions
Hierarchical grooming framework is effective for the objectives
Star logical topology design applied to two levels of hierarchy
Clustering algorithm addresses grooming considerations
Topologies of more than 100 nodes handled easily
Open issues:
integrating RWA
logical topologies other than star at each level
dynamic hierarchical grooming
waveband grooming
Hierarchical Traffic Grooming in WDM Networks May 8, 2008 – p.42
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