5 traﬃc grooming in wdm networks 5.1 ilp formulation for...

Optical Networks

Poompat Saengudomlert

Session 13

Traffic Grooming in WDM Networks

P. Saengudomlert (2018) Optical Networks Session 13 1 / 16

5 Traffic Grooming in WDM Networks5.1 ILP Formulation for Traffic Grooming

Traffic unit smaller than one wavelength, i.e., subwavelength traffic⇒ two sets of decision variables for ILP

One for lightpath establishments

One for traffic flows on lightpaths

Given information

W: set of wavelength channels in each fiber

N : set of nodes

M: set of all node pairs (with distinct nodes)

L: set of linksαl : cost per wavelength channel in using link l

Fl : number of fibers on link l

S: set of s-d pairs (with nonzero traffic)

ts : traffic demand (in wavelength unit) for s-d pair s


Given information (continued)

Pm: set of candidate paths for a lightpath between node pair m,including the link between the node pair if it exists

P =∪

m∈M Pm: set of all paths

Pl : set of paths (from all node pairs) that use link l

P(n,·): set of paths that leave from node n

P(·,n): set of paths that go to node n

Variables

f p,sw ∈ R+: traffic flow on wavelength w on path p fors-d pair s

gpw∈ Z+: number of lightpaths established on wavelength w on path p

Objective

Minimize the total cost of used wavelength channels

minimize∑

l∈Lαl

∑

w∈W

∑

p∈Pl

gpw


Constraints

Limited number of wavelength channels on each link

∀l ∈ L, ∀w ∈ W ,∑

p∈Pl

gpw ≤ Fl

Flow conservation constraint

∀n ∈ N , ∀s ∈ S,∑

w∈W

∑

p∈P(·,n)

f p,sw −∑

w∈W

∑

p∈P(n,·)

f p,sw =

−ts , n = source of sts , n = dest. of s0, otherwise

Existence of lightpaths to support traffic flows

∀p ∈ P, ∀w ∈ W ,∑

s∈Sf p,sw ≤ gp

w

Nonnegativity and integer constraints

∀p ∈ P, ∀s ∈ S, ∀w ∈ W, f p,sw ∈ R+

∀p ∈ P, ∀w ∈ W, gpw ∈ Z+


5.2 Metropolitan WDM Rings

Metropolitan WDM rings

Commonly used for self-healing ability, i.e., 2-connectednessRing cover, i.e., connected rings, for general topologies

Unidirectional Path Switched Ring (UPSR)

Fibers used for working traffic in one direction onlyDedicated path protection

node 1

2

3

4

5

6

node 1

2

3

4

5

6λ1

λ1

λ1

λ1

CW CCW

node 1

2

3

4

5

6

node 1

2

3

4

5

6λ1

λ1

λ1

λ1

CW CCW

clockwise (CW) for working traffic

counterclockwise (CCW) for backup trafficP. Saengudomlert (2018) Optical Networks Session 13 5 / 16

Bidirectional Line-Switched Ring (BLSR)

Fibers in both directions used for working traffic

For BLSR/2, half of wavelengths for working in CW andfor backup in CCW (and vice versa for other half)

Shared link protection

Example:

Lightpaths for node pairs 1-3, 3-1, 3-4, 4-3, 4-6, 6-4

22

node 1

3

4

5

6

node 1

3

4

5

6λ1

λ1

λ1

λ2CW CCW

λ1

λ2

λ2

λ2

22

node 1

3

4

5

6

node 1

3

4

5

6λ1

λ1

λ1

λ2CW CCW

λ1

λ2

λ2

λ2


Typical Metropolitan WAN Networks

Feeder ring connecting distribution networks

single-home

distributionring

EN

AN

EN/AN

dual-homedistribution

ring

passive splitter oradd/drop multiplexer

customer premises(end users)

backbonenetwork

distributionbus

distributiontree

feederring

single-home

distributionring

EN

AN

EN/AN

dual-homedistribution

ring

passive splitter oradd/drop multiplexer

customer premises(end users)

backbonenetwork

distributionbus

distributiontree

feederring

Focus on a feeder ring with one egress node (EN) or more (for reliabiity)and several access nodes (ANs).


Electronics ADMs

For a metropolitan WDM ring, electronic add-drop multiplexers(ADMs) are used for traffic grooming (i.e., multiplexing)

Example:

Assume transmission rate of a wavelength channel is 10 Gbps. All connectionrates are 2.5 Gbps. An ADM can be used to drop and add any subset of 2.5-Gbpsconnections based on time division multiplexing (TDM).

ADMλ (1), λ (2), λ (4) λ (1), λ (3), λ (4)

λ (1), λ (2) λ (1), λ (3)

λ (k) corresponds tokthtime slot in wavelengthλ, k= 1, 2, 3, 4.Each time slot corresponds to the rate of 2.5 Gbps.

CW

CCW(for protection)

end users/equipment

ADMλ (1), λ (2), λ (4) λ (1), λ (3), λ (4)

λ (1), λ (2) λ (1), λ (3)

λ (k) corresponds tokthtime slot in wavelengthλ, k= 1, 2, 3, 4.Each time slot corresponds to the rate of 2.5 Gbps.

CW

CCW(for protection)

end users/equipment

NOTE: ADMs are needed at an AN only for the wavelengths that are dropped,

added, or both.


Example:

4-node UPSR with 2.5-Gbps connection rate,10-Gbps transmission rate for each wavelength channel, andtwo connections from each node to each of the other nodes

WA1 WA2λ1 : 1 ↔ 2, 3 ↔ 4 λ1 : 1 ↔ 2, 1 ↔ 3λ2 : 1 ↔ 3, 2 ↔ 4 λ2 : 2 ↔ 3, 2 ↔ 4λ3 : 1 ↔ 4, 2 ↔ 3 λ3 : 1 ↔ 4, 3 ↔ 4

3

node 1

24

λ1

ADM

λ2 λ3

λ1 λ2 λ3

λ1

λ2

λ3

λ1

λ2

λ3

WA 1

3

node 1

24

λ1 λ3

λ1 λ2 λ3

λ1

λ2

λ2

λ3

WA 2

3

node 1

24

λ1

ADM

λ2 λ3

λ1 λ2 λ3

λ1

λ2

λ3

λ1

λ2

λ3

WA 1

3

node 1

24

λ1 λ3

λ1 λ2 λ3

λ1

λ2

λ2

λ3

WA 2

Optimization of WA can reduce number of ADMs from 12 to 9.


5.2.1 Static Traffic Grooming in Feeder Rings with

Single-Hub Traffic

Consider a feeder ring with one EN and N ANs.

Assume for now a UPSR.

A wavelength in one direction (CW or CCW) is called a directedwavelength.

One wavelength has two directed wavelengths.

Transmission rate of g for each wavelength channel

Traffic rate r < g from each AN to EN and from EN to each AN,called uniform single-hub traffic

ENAN 1

…

AN 2

AN 3

AN N

AN N – 1

ENAN 1

…

AN 2

AN 3

AN N

AN N – 1


Theorem:

For a UPSR-based feeder ring, the minimum number of ADMs required tosupport the uniform single-hub traffic is

AUPSRmin = N +

⌈N

⌊g/r⌋

⌉

Proof: Focus on downstream working traffic; upstream traffic can follow samewavelengths (called circle-based routing).

EN

AN 2

EN

AN 2CWworkingcircle

CCWbackupcircle

EN

AN 2

EN

AN 2CWworkingcircle

CCWbackupcircle

circle-based routing for EN and AN2


Proof (continued):

Consider first no traffic splitting between each EN-AN pair.

Each CW directed wavelength supports working traffic for ⌊g/r⌋ ANs.

Use⌈

N⌊g/r⌋

⌉ADMs at EN and 1 ADM at each AN.

Argue that traffic splitting does not decrease the number of ADMs.

Theorem:

For a UPSR-based feeder ring, the minimum number of wavelengthsrequired to support the uniform single-hub traffic is

W UPSRmin = ⌈Nr/g⌉

Proof: Use the cut-set lower bound and greedy WA.


Can we minimize the number of ADMs and the number ofwavelengths at the same time?

Example:

Assume g = 4, r = 3, N = 4. The cut-set lower bound and the WA in figure (a)yields W UPSR

min = 3. Circle-based routing is used.

λ4

λ1λ2λ3

(a) (b)Arrow labels are the traffic units.

EN3

31

EN

3

11

3

3

3

λ4

λ1λ2λ3


EN3

31

EN

3

11

3

3

3

With 3 wavelengths allowed, at least 9 ADMs are needed. However, the minimum

number of ADMs is 8 and is obtained by using no traffic splitting and at least 4

wavelengths.

⇒ may not be possible to obtain both AUPSRmin and W UPSR

min togetherP. Saengudomlert (2018) Optical Networks Session 13 13 / 16

Minimizing ADMs Using W UPSRmin Wavelengths

D: number of CW directed wavelengths with unused capacities

g : remaining capacity left in these D CW directed wavelengths

N: number of ANs with traffic left to be supported

r : amount of traffic left at these N ANs

WA algorithm:

Use circle-based routing. Initialize D = W UPSRmin , g = g , N = N, r = r .

Fill each of D CW directed wavelengths with r units of traffic for up to⌊g/r⌋ ANs. Let the number of unsupported ANs be

N ′ = max

(0, N −

⌊g

r

⌋D

)

If N ′ = 0, terminate. Else (N ′ > 0), set the remaining capacity

g ′ = g −⌊g

r

⌋r < r


WA algorithm (continued):

NOTE: N ′ < D; otherwise, the remaining traffic rN ′ cannot be supportedon remaining capacity g ′D.

Fill the remaining capacity g ′ of N ′ CW directed wavelengths by traffic fromeach of the remaining N ′ ANs. The remaining traffic of each of N ′ ANsbecomes r ′ = r − g ′.

Repeat this step until r ′ < g ′. Let k denote the number of repetitions. Inparticular, after k repetitions,

r ′ = r − kg ′ < g ′

If r ′ = 0, terminate. Else (r ′ > 0), there are D ′ = D − kN ′ CW directedwavelengths with capacity g ′ left, and N ′ nodes with traffic r ′ left.

Update the parameters by setting D = D ′, g = g ′, N = N ′, r = r ′, andrepeat steps 1-3 until all traffic has been assigned, i.e. r ′ = 0.


Example:

Assume N = 4, g = 7, r = 5 ⇒ W UPSRmin = ⌈4× 5

7⌉ = 3

In step 1, each of 3 CW directed wavlengths can support ⌊7/5⌋ = 1 AN, fora total of 3 ANs. ⇒ g ′ = 7− ⌊7/5⌋5 = 2,N ′ = 4− 1× 3 = 1

In step 2, support 2 traffic units for the remaining AN on CW directedwavelengths. ⇒ k = 2, r ′ = 5− 2× 2 = 1

In step 3, set D = 3− 2× 1 = 1, g = 2, N = 1, r = 1, and move to 2ndround.

In step 1 (2nd round), support remaining 1 traffic unit for the remaining ANon the remaining CW directed wavelength. ⇒ N ′ = 0 ⇒ termination

λ2λ3

λ1


EN5

52

EN

5

21

55

5

5 AN 1

CW: working CCW: backup

λ2λ3

λ1


EN5

52

EN

5

21

55

5

5 AN 1

CW: working CCW: backup


5 traﬃc grooming in wdm networks 5.1 ilp formulation for...

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