csc 778 presentation waveband switching neil d’souza jonathan grice

CSC 778 Presentation

Waveband Switching

Neil D’souzaJonathan Grice

What is Waveband Switching?

• Grouping wavelengths into bands– Switch as groups rather than individual

wavelengths – Using a single port

• Only demultiplex to add/drop traffic– 75% of traffic is bypass

Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004

Wavelength

Why Waveband Switching?

• $$$

• Reduced Port Count

• Size

• Power


So how does this reduce port count???


No waveband switching:

Node A: 1 incoming fiber port8 incoming wavelength ports8 outgoing wavelength ports2 outgoing fiber ports

Total: 19 ports



No waveband switching:

Node A: 1 incoming fiber port2 incoming waveband ports2 outgoing waveband ports2 outgoing fiber ports

Total: 7 ports – over 50% reduction!

A 3-Layer MG-OXC w/ WLC

Switch a wavelength

Switch a waveband

Switch a fiber

Wavelength conversion


Wavelength Conversion

• Input/Output on different wavelength– Expensive, signal degradation

• In waveband switched networks:– Even if ports & converters available,

conversion requires demultiplexing to wavelength level.


Waveband Assignment with Path Graph

• An algorithm to satisfy a new request– Minimize use of wavelength conversion– Maximize benefit of wavebanding

• Assumes:– Fixed routing– Intraband wavelength conversion


• Our example:



Wavelength conversion

New Path

Existing Path

Fibers have 4 wavelengths in 2 bands

• Step 1: Split nodes by wavelength



• Step 2: Add converters



• Step 3: Draw available wavelengths



• Step 4: Assign weights



Wavelengths = λConverters = # wavelengths x # hops

1 1

2 2

3 3

4 44

3

2

16 16

16 16

• Step 5: Create logical source & destination



1 1

2 2

3 3

4 44

3

2

16 16

16 16

0

0

0

0

0

0

0

0

Dijkstra’s Algorithm:

• With the weighted links will:

1. Try to find a wavelength continuous path

2. Try to find a path using the minimum number of wavelength converters.


• Step 6: Find path



1 1

2 2

3 3

4 44

3

2

16 16

16 16

0

0

0

0

0

0

0

0

• Another Example:



1 1

2

3

4 4

3

16 16

16 16

0

0

0

0

0

0

0

0

16 16

16

16

16

16

16 16

• Another Example: Random Fit



1 1

2

3

4 4

3

16 16

16 16

0

0

0

0

0

0

0

0

16 16

16

16

16

16

16 16

• Another Example: First Fit



1 1

2

3

4 4

3

16 16

16 16

0

0

0

0

0

0

0

0

16 16

16

16

16

16

16 16

• Another Example: Path Graph



1 1

2

3

4 4

3

16 16

16 16

0

0

0

0

0

0

0

0

16 16

16

16

16

16

16 16

Performance Results:

• With no conversion same as First Fit– Fixed routing – path already set

• Less blocking than First Fit or Random Fit

• Intraband conversion – nearly as good as full– High cost to demux two bands

• Large reduction in wavelength conversion

• Even better when not all fibers can be demuxed


Waveband Aggregation techniques

• Source to End Switching

• Intermediate Waveband Switching – Intermediate to Destination (ITD-WBS) – Source to Intermediate (STI-WBS)* – Both-end-to-Intermediate (BETI-WBS)

Terms used

• Waveband granularity is defined as the number of wavelengths that can be grouped or aggregated into a waveband.

• Uniform waveband switching if the granularity of all the wavebands is an arbitrary constant g.

Wavelength Grooming

• Problem is to groom wavelengths into wavebands such that the number of ports saved is maximized.

• Depends on Uniform or Non-uniform waveband switching.

• Depends on the location of aggregation.

Intermediate-to-destination uniform waveband switching: (ITD-UWBS)

• Inputs : – Graph G=(V,E)

– Routed Demands Pd={p1,p2,……..,pk}

– Lightpaths for each demand• C={c1,c2 ……..ck}

– Destination : d– Waveband granularity : g

Limitations

• Connections that have the same destination.

• Complete set of paths can be partitioned into sub-sets based on their destination nodes.

• Waveband grooming only occurs among paths within a partition and not across partitions

Notations

• Waveband B of granularity g is denoted by

(Q, s, d, g)

• Q = {(p1, b1), (p2, b2), . . . (pm, bm)}

• Set of tuples (pi, bi) – pi is a routed-demand

– bi is the number if units (lightpaths) of the routed-demand.

Notations

• number of wavelength ports used by a waveband of length L and granularity g is 4g + 2(L + 1).

• number of ports required for routing g wavelength level connections of length L is 2g(L + 1)

• number of ports saved by a waveband route of length L and granularity g is

2(L + 1)(g − 1) − 4g.

Algorithm (ITD-WBS)• Algorithm 1• 1: Input: (G, Pd, C)

– Pd = {p1, p2, . . . , pm}– C = {c1, c2, . . . , cm}

• 2: Output: Destination-rooted capacitated tree T• 3: compute graph T using paths in the set Pd• 4: transform T into a tree by deleting cycles in T and modifying

paths accordingly• 5: compute the height hi for each node i in the tree T• 6: initialize the residual capacity Rj of the leaf node j to ni where j the

source node of the path pi• 7: compute the residual capacity Ri of each intermediate node i as

the sum of the residual capacities of its child nodes

ABDest

Source2

Source1

4

9

9

9

4 4

Paths

p1 : dabs1; c1 = 4

p2 : dbas2; c2 = 9

Subset of Graphwith Cycles

ABDest

Source2

Source1

9

9

5

4 4

Paths

p1 : dbs1; c1 = 4

p21 : das2; c21 = 4

p22 : dbas2; c22 = 5

With No Cycles

Dest

Source21

9

4

54

Assign Heights

Source1

Source22

B

A

4

5

A

G = 3

0

1

1

2

2

3

2

Dest

Source21

Calculate Residual Capacities

Source1

Source22

A

A

G = 3

0,13

1,4

1,9

2,5

2,4

3,5

2,4

B

Algorithm 2• 1: Input:(G, Pd, C, g)• 2: Output: Waveband set B • 3: run Algorithm 1 on input (G, Pd, C)• 4: for i = h; i ≤ 2; i−− do• 5: for each u where hu = i, and Ru ≥ g do• 6: if ((Su = 2(i + 1)(g − 1) − 4g) > 0) then• 7: form waveband B = (Q, u, d, g) from node u to root node d and

add to B • 8: update the residual capacities Ru of all the nodes along the paths

included in the waveband• 9: end if• 10: end for• 11: end for

Dest

Source21

Iteration 1

Source1

Source22

A

A

G = 3

0,13

1,4

1,9

2,5

2,4

3,5

2,4

B

Source21

Iteration 2

Source1

Source22

A

A

G = 3

0,10

1,4

1,6

2,2

2,4

3,2

2,4

B

Dest

Waveband:

B1=s2-a-b-d

Source21

Iteration 3

Source1

Source22

A

G = 3

0,7

1,4

1,3

2,2

2,1

3,1

2,4

B

Waveband:

B1=s2--a--b---d

B2= s1—b---d

A

Dest

Source21

Iteration 4

Source1

Source22

A

G = 3

0,4

1,1

1,3

2,2

2,1

3,2

2,1

B

Waveband:

B1=s2--a--b---d

B2= s1—b---d

B3= s2---a---d

A

Dest

Source21

Iteration 5

Source1

Source22

A

G = 3

0,1

1,1

1,0

2,2

2,1

3,2

2,1

B

Waveband:

B1=s2--a--b---d B4= b-d

B2= s1—b---d

B3= s2---a---d

A

Dest

Algorithm for BETI waveband switching

• Create a Destination-rooted capacitated tree and Source rooted capacitated tree.

Algorithm 3 The Initialization Algorithm for the BETI problem.

• 1: Input: (G, P,C)• 2: compute graphs Tt and Ts using paths in the set P• 3: add super destination node d and super source node s to trees Tt

and Ts respectively• 4: add edges from node d to all the destination nodes in tree Tt• 5: add edges from node s to all the source nodes in tree Ts• 6: transform Tt and Ts into a trees by deleting cycles in Tt and ts

and modifying paths accordingly• 7: compute the height hi for each node i in the tree T• 8: initialize the residual capacity Rj of the leaf node sj of the tree Tt

to ni where sj the source node of the path pi• 9: initialize the residual capacity Rj of the leaf node tj of the tree Ts

to ni where tj the source node of the path pi• 10: compute the residual capacity Ri of each intermediate node of

the trees Tt and Ts as the sum of the residual capacities of its child nodes

• Algorithm 4 The BETI Algorithm for computing the wavebands.

• 1: Input:(G, P,C)• 2: Output: Waveband set B 3: run Algorithm 3 on input (G, P,C) to

compute trees Tt and Ts• 4: let ht and hs be the heights of the trees• 5: let h be the maximum of the heights hd and ht• 6: for i = h; i ≤ 2; i−− do• 7: for each u in Tt and Ts where hu = i in the corresponding tree,

and Ru ≥ g do• 8: if ((Su = 2(i + 1)(g − 1) − 4g) > 0) then• 9: form waveband B = (Q, u, d, g) from node u to root node d/s

corresponding to tree Tt/Ts and add to B 10: update the residual capacities Ru of all the nodes along the paths in included in the waveband in both the trees Tt and Ts

• 11: end if• 12: end for• 13: end for

HAPPY HALOWEEN

BACKUP

Wavelength Assignment Methods:

• Always start with lowest wavelength

• If there is a continuous path – TAKE IT!

• Else:– Random fit: Randomly choose next wavelength– First fit: Choose the first available wavelength– Path Graph: Use dijkstra’s algorithm to find path



• An simple example:– 1 fiber – 64 wavelengths – 8 bands– Need to drop 1 wavelength


Traditional OXC Waveband Switching

BXC Ports: 0 8 in – 8 out

OXC Ports: 64 in – 64 out 8 in – 8 out

Total: 128 32

csc 778 presentation waveband switching neil d’souza jonathan grice

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