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Architectures and Algorithms for Resource Allocation. Mounire El Houmaidi * , Mostafa A. Bassiouni * , and Guifang Li # * School of Electrical Engineering and Computer Science # School of Optics/CREOL University of Central Florida. Outline. Motivation What is a Minimum Dominating Set (MDS)

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architectures and algorithms for resource allocation

Architectures and Algorithms for Resource Allocation

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

*School of Electrical Engineering and Computer Science

#School of Optics/CREOL

University of Central Florida

slide2
Outline
  • 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 placement
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Motivation- Resource placement

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

(U.S Long Haul Net.)

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)

Optimize overall network performance by using the dominating nodes (U.S Long Haul topology)

  • G. Li et. al., JON, 2:6, 2003
  • G. Li et. al., JOE, 43:1, 2004
  • G. Li et. al., IEEE/ACM MASCOTS, 2003
what is mds
What is MDS
  • 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, 1972

2. Lund, et. al., J. ACM, 1994

slide5
Definitions
  • 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.
slide6
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 mk-Neighbor(v))
slide7
k-WMDS 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 network
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U.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}

comparing k mds vs k loss k blk
Comparing k-MDS vs. k-LOSS (k-BLK)

load=60,k-MDSk-BLK

k=3 17% (32%) 20% (20%)

k=2 13% (48%) 19% (24%)

k=17% (72%) 10% (60%)

We can achieve almost 50% improvement

with only 5 nodes

slide10
NSFNET: nationwide backbone network

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Weighted MDS (k-WMDS)

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

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

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

3-WMDS (NSF) = {14}

k loss k blk vs k wmds
k-LOSS (k-BLK) vs. k-WMDS

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

Node Weight

0 6

1 12

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3 12

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7 11

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9 2

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11 15

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placement of limited owc
Placement of Limited OWC

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

g nodes placement t grooming
G-nodes placement: T-Grooming

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)

G-nodes placement for traffic Grooming

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

slide14
OBS switch design with FDLs/OWCs

MAIN CONTROL

Input Link 1

DMX

1

Converter Bank

A 1

B 1

C 1

1

MUX

Output Link 1

OWC

W

1

C 2

C 1

A 1

.

.

.

W

W

OWC

O X C

Input Link 2

DMX

Converter Bank

i

MUX

Output Link 2

1

A 2

B 2

C 2

OWC

B 1

A 2

B 2

F.W

.

.

.

W

OWC

F.W + 1

F.W + 1

DMX: De-multiplexor

MUX: Multiplexor

OWC: any-to- Converter

FDL: Fiber Delay Line

F.W + 2

F.W + 2

FDL Bank

2

FDL

1

FDL

fiber delay line design
λ1

.

.

.

λW

λ1

.

.

.

λW

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21

20

2(max_d)

OWC

OWC

OWC

OWC

Fiber Delay Line design

Variable delay: [0…MAXD], where MAXD = (20 + 21 +… +2(max_d)) x b

benefits of fdls and owcs
Benefits of FDLs and OWCs

FDLs vs. OWCs with JET signaling and W=16

slide17
Efficient FDLs/OWCs placement
  • 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.
conclusion
Conclusion
  • 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.
slide20
Discussion

and

Questions

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