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Architectures and Algorithms for Resource Allocation

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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)
- 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

- Sparse placement of wavelength conversion
- Conclusions

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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

- 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

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.

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))

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.

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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}

load=60,k-MDSk-BLK

k=317% (32%) 20% (20%)

k=213% (48%) 19% (24%)

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

We can achieve almost 50% improvement

with only 5 nodes

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}

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

NodeWeight

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

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)

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

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C 2

C 1

A 1

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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

λ1

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λW

λ1

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λW

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2(max_d)

OWC

OWC

…

…

OWC

OWC

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

FDLs vs. OWCs with JET signaling and W=16

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.

k-WMDS vs. k-LOSS (NSFNET)

- 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

and

Questions