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
P. Saengudomlert (2018) Optical Networks Session 13 2 / 16
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
P. Saengudomlert (2018) Optical Networks Session 13 3 / 16
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+
P. Saengudomlert (2018) Optical Networks Session 13 4 / 16
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
P. Saengudomlert (2018) Optical Networks Session 13 6 / 16
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).
P. Saengudomlert (2018) Optical Networks Session 13 7 / 16
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.
P. Saengudomlert (2018) Optical Networks Session 13 8 / 16
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.
P. Saengudomlert (2018) Optical Networks Session 13 9 / 16
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
P. Saengudomlert (2018) Optical Networks Session 13 10 / 16
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
P. Saengudomlert (2018) Optical Networks Session 13 11 / 16
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.
P. Saengudomlert (2018) Optical Networks Session 13 12 / 16
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
(a) (b)Arrow labels are the traffic units.
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
P. Saengudomlert (2018) Optical Networks Session 13 14 / 16
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.
P. Saengudomlert (2018) Optical Networks Session 13 15 / 16
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
(a) (b)Arrow labels are the traffic units.
EN5
52
EN
5
21
55
5
5 AN 1
CW: working CCW: backup
λ2λ3
λ1
(a) (b)Arrow labels are the traffic units.
EN5
52
EN
5
21
55
5
5 AN 1
CW: working CCW: backup
P. Saengudomlert (2018) Optical Networks Session 13 16 / 16