Architectures and Algorithms for Architectures and Algorithms for Resource AllocationResource Allocation

Mounire El HoumaidiMounire El Houmaidi**, Mostafa A. Bassiouni, Mostafa A. Bassiouni**, and Guifang Li, and Guifang Li##

**School of Electrical Engineering and Computer ScienceSchool of Electrical Engineering and Computer Science##School of Optics/CREOLSchool of Optics/CREOL

University of Central FloridaUniversity of Central Florida

OutlineOutline Motivation What is a Minimum Dominating Set (MDS) How to find k-MDS

– Algorithm– Example– What is Weighted MDS

Applications of k-MDS– Sparse placement of wavelength conversion

• k-LOSS(k-BLK) and F-SEARCH• Weighted k-MDS for non-uniform traffic• Limited wavelength conversion

– Placement of G-nodes for traffic grooming– Placement of FDLs

Conclusions

Motivation- Resource placementMotivation- Resource placement

Optimize overall network performance by using dominating nodes [1-4]

1. M. El Houmaidi et. al., J. Opt. Net., 2:6, (OSA, 2003)2. M. El Houmaidi et. al., Proc. MASCOTS, (IEEE/ACM, 2003)3. M. El Houmaidi et. al., J. Opt. Eng., 43:1, (SPIE, 2004) 4. M. El Houmaidi et. al., Proc. OFC, (IEEE, 2004)

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(U.S Long Haul Net.)

What is What is MDSMDS Given a graph G(V,E), determine a set with minimum

number of vertices D V such that every vertex in the graph is either in D or is at distance k or less from at least one member in D.

NP-Complete problem [1,2] .

Heuristic algorithms for sub-optimal solution.

Highly connected nodes dominate the entire topology.

1. Karp, Pl. Press, 19722. Lund, et. al., J. ACM, 1994

DefinitionsDefinitions

Neighbor (v): is the set of nodes sharing a link with v.

k-Neighbor (v): is the set of nodes that are at most within k hops away from a node v.

For k equals 0, 0-Neighbor(v) contains the node v only.

Definitions (Cont.)Definitions (Cont.) k-Connect(v): the connectivity index based on nodes within k hops of v is :

k-Master (v): represents the node p, member of k-Neighbor(v), with the highest k-Connect value over all nodes m that are at most k hops away from node v (i.e., all nodes mk-Neighbor(v))

)Neighbor(v m

(m) Connect-1)-(k + (v) Connect-1)-(k = (v) Connect-k

:as (v) Connect-k define y weRecursivel

)Neighbor(v m(m) Connect-0 + (v) Connect-0 = (v) Connect-1

(v)) (Neighbory Cardinalit = (v) Degree = (v) Connect-0

k-WMDSk-WMDS Algorithm Algorithm Initialize the dominating set k-WMDS to .

For all nodes v in G, Compute k-Connect (v).

Each node v sends CON(v) with computed k-Connect(v) to all nodes in k-Neighbor (v).

Each node v finds its k-Master(v), denoted node m, based on the values received in CON messages.

Each node v sends VOTE(v) message to m=k-Master(v). The VOTE message informs node m that it is a master node .

Each node that receives VOTE(v) adds itself to k-WMDS.

U.S Long Haul networkU.S Long Haul network

1-MDS (USLH) = {1, 3, 4, 5, 8, 10, 12, 15,17, 20, 22, 25, 27} 2-MDS (USLH) = {4, 8, 12, 17, 25} (double circled in graph)3-MDS (USLH) = {8, 12, 17}4-MDS (USLH) = {12}

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Comparing Comparing k-MDSk-MDS vs. vs. k-LOSS k-LOSS ((k-BLKk-BLK))Figure 2: U.S. Long Haul Topology

k-BLK vs k-MDS

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4-MDS:12

4-BLK:8

3-MDS:8,12,17

3-BLK:8,12,27

2-MDS:4,8,12,17,25

2-BLK:3,8,12,26,27

1-MDS:1,3,4,5,8,10,1215,17,20,22,25,27

1-BLK: 3,8,12,18,19,2021,22,23,24,25,26,27

All Converters

load=60, k-MDS k-BLKk=3 17% (32%) 20% (20%)k=2 13% (48%) 19% (24%) k=1 7% (72%) 10% (60%)

We can achieve almost 50% improvement with only 5 nodes

Weighted Weighted MDSMDS ( (k-WMDSk-WMDS))

1-WMDS (NSF) = {1, 4, 5, 6, 9, 11, 14}2-WMDS (NSF) = {1, 4, 9, 14}

3-WMDS (NSF) = {14}

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NSFNET: nationwide backbone network

0-Connect (v) = Cardinality (Neighbor (v)) * Weight(v)

k-LOSS (k-BLK) k-LOSS (k-BLK) vsvs. k-WMDS. k-WMDS Figure 6: NSFNET topology

k-BLK vs k-WMDS

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3-WMDS:14

3-BLK:5

2-WMDS:1,4,9,14

2-BLK:5,4,15,14

1-WMDS:1,4,5,6,9,11,14

1-BLK:5,4,15,14,13,12,11

All Converters

Under a load of 70, we simulated non-uniform traffic pattern between node pairs:

Node Weight0 61 122 73 124 55 86 17 118 79 210 711 1512 313 1514 915 2

Placement of Limited OWCPlacement of Limited OWC

Figure 6: U.S Long Haul LIMITED vs F-SEARCH (50 Erlang, W=8)

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F-S:Flexible Node-Sharing

LIM:Flexible Node-Sharing

Figure 8: U.S Long Haul LIMITED vs F-SEARCH (50 Erlang, W=8)

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Number of wavelength ConvertersBl

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F-S:Static Mapping

LIM:Static Mapping

LIMITED has better performance than F-SEARCH for Flexible node-sharing and Static mapping optical switch designs.

G-nodes placement: T-G-nodes placement: T-GroomingGrooming

NSF Network (W=8)

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1-WMDS

1-BLK

2-WMDS

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NSFNET topology (W=8)

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2-WMDS: r=16

2-BLK: r=16

2-WMDS: r=8

2-BLK: r=8

We can achieve with 2-WMDS members as G-nodes (r=16) the same throughput as if all nodes in the network had the grooming capability (r is the grooming ratio)

OBS switch design with FDLs/OWCsOBS switch design with FDLs/OWCs

Input Link 2

DMX

MUX

MAIN CONTROL

DMX: De-multiplexor

MUX: Multiplexor

OWC: any-to- Converter

FDL: Fiber Delay Line

DMX

MUX

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Output Link 1

Output Link 2

Input Link 1

OWC

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Converter Bank

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F.W + 2 F.W + 2

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FDL1

F.W + 1F.W + 1

FDL Bank

OWC

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Converter Bank

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A 1

B 1

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B 2

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Fiber Delay Line designFiber Delay Line design

Variable delay: [0…Variable delay: [0…MAXDMAXD], where ], where MAXDMAXD = (2 = (200 + 2 + 211 +… +2 +… +2(max_d)(max_d)) x b) x b

λ1

. . .λW

λ1

. . .λW

…

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2(max_d)OWC

OWC OWC

OWC

Benefits of FDLs and OWCsBenefits of FDLs and OWCsSwitch design benefits with NSFNET Topology

FDLs vs. OWCs in 2-WM DS nodes (W=16)

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OWCs only

FDLS only

FDLs and OWCs

FDLs vs. OWCs with JET signaling and W=16

In a fully connected network (all nodes are connected), OWC has no effect on the blocking performance but FDLs do.

FDLs and OWCs capabilities must be used judiciously and placed in nodes that maximize the performance.

k-LOSS heuristic [JIM99, MSS02]: Via simulation, Place OWC in nodes experiencing the highest blocking rates.

Efficient FDLs/OWCs placementEfficient FDLs/OWCs placement

k-WMDSk-WMDS vs. vs. k-LOSS (NSFNET)k-LOSS (NSFNET)Burst loss for the NSFNET Topology

k-WM DS vs k-LOSS (W=16)

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3-LOSS

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1-BLK

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All FDLs

ConclusionConclusion

k-MDS provides an efficient sparse OWC placement.

k-WMDS models non-uniform traffic patterns.

k-MDS allows efficient placement of limited OWC.

It applies to G-nodes selection for traffic grooming.

k-WMDS efficiently place FDLs.

Discussion Discussion

and and

QuestionsQuestions