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 Networks 5.1 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 links α l : cost per wavelength channel in using link l F l : number of fibers on link l S : set of s-d pairs (with nonzero traffic) t s : traffic demand (in wavelength unit) for s-d pair s P. Saengudomlert (2018) Optical Networks Session 13 2 / 16 Given information (continued) P m : set of candidate paths for a lightpath between node pair m, including the link between the node pair if it exists P = ∪ m∈M P m : set of all paths P l : 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,s w ∈ R + : traffic flow on wavelength w on path p for s-d pair s g p w ∈ Z + : number of lightpaths established on wavelength w on path p Objective Minimize the total cost of used wavelength channels minimize ∑ l ∈L α l ∑ w ∈W ∑ p∈P l g p w P. Saengudomlert (2018) Optical Networks Session 13 3 / 16 Constraints Limited number of wavelength channels on each link ∀l ∈ L, ∀w ∈ W, ∑ p∈P l g p w ≤ F l Flow conservation constraint ∀n ∈ N , ∀s ∈ S , ∑ w ∈W ∑ p∈P (·,n) f p,s w − ∑ w ∈W ∑ p∈P (n,·) f p,s w = −t s , n = source of s t s , n = dest. of s 0, otherwise Existence of lightpaths to support traffic flows ∀p ∈ P , ∀w ∈ W, ∑ s ∈S f p,s w ≤ g p w Nonnegativity and integer constraints ∀p ∈ P , ∀s ∈ S , ∀w ∈ W, f p,s w ∈ R + ∀p ∈ P , ∀w ∈ W, g p w ∈ Z + P. Saengudomlert (2018) Optical Networks Session 13 4 / 16
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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
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
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