Optical Networks
Poompat Saengudomlert
Session 14
Traffic Grooming in WDM Networks (continued)
P. Saengudomlert (2018) Optical Networks Session 14 1 / 10
5.2.1 (Continued) Single-Hub Uniform Traffic
Grooming for a BLSR
Approach:
View working directed wavelengths of a BLSR as CW directedwavelengths for a UPSR
Modify the RWA solution of a UPSR to obtain a solution for a BLSR
Theorem:
For a BLSR-based feeder ring with the uniform single-hub traffic,
ABLSRmin = AUPSR
min = N +
⌈N
⌊g/r⌋
⌉
W BLSRmin = W UPSR
min = ⌈Nr/g⌉
P. Saengudomlert (2018) Optical Networks Session 14 2 / 10
Example:
N = 4, g = 7, r = 5,CW for working on λ1 and λ2, CCW for working on λ3 and λ4
⇒ W BLSRmin = ⌈4× 5/7⌉ = 3
λ4
λ1λ2λ3
(a) (b)Arrow labels are the traffic units.
EN5
5
2
EN5
2
1
5
55
5
AN 2
CCW: working CW: backup
λ4
λ1λ2λ3
(a) (b)Arrow labels are the traffic units.
EN5
5
2
EN5
2
1
5
55
5
AN 2
CCW: working CW: backup
NOTE: Only the RWA of traffic to/from AN2 is illustrated in the rightfigure.
P. Saengudomlert (2018) Optical Networks Session 14 3 / 10
Non-Uniform Single-Hub Traffic Grooming
Consider a UPSR (with results applicable for BLSR).
1 EN and N ANs
AN i transmits ri units to EN and receives ri units from EN
WA in order to minimize the number of ADMs
As before, traffic splitting does not help.⇒ focusing on WA with no traffic splitting
Example:
N = 4, g = 7, (r1, r2, r3, r4) = (3, 2, 5, 4): Greedy WA (on the left) not optimal
λ2λ3
λ1
(a) (b)
Arrow labels are the traffic units.
3
5
24
EN
AN 1
AN 2AN 3
AN 43
5
24
EN
AN 1
AN 2AN 3
AN 4λ2λ3
λ1
(a) (b)
Arrow labels are the traffic units.
3
5
24
EN
AN 1
AN 2AN 3
AN 43
5
24
EN
AN 1
AN 2AN 3
AN 4
P. Saengudomlert (2018) Optical Networks Session 14 4 / 10
ADM Allocation as Bin Packing Problem
Minimizing the number of ADMs viewed as bin packing problem
N objects of sizes r1, . . . , rN (with ri < g)
Each bin can contain objects up to total size g .
Use the minimum number of bins to hold all objects
Known to be NP-complete
Can be formulated as ILP problem
Given parameters
B: number of available bins (indexed from 1 to B)
N: number of objects (indexed from 1 to N)
g : size of bin
ri : size of object i
Variables
aij ∈ {0, 1}: equal to 1 iff object i is assigned to bin j
bj ∈ {0, 1}: equal to 1 iff bin j is used
P. Saengudomlert (2018) Optical Networks Session 14 5 / 10
Objective
Minimize the number of used bins
minimizeB∑
j=1
bj
Constraints
Assign each object to exactly one bin
∀i ∈ {1, . . . ,N},B∑
j=1
aij = 1
Bin usage and bin size limitation
∀j ∈ {1, . . . ,B},N∑
i=1
riaij ≤ gbj
Integer constraints
∀i ∈ {1, . . . ,N}, ∀j ∈ {1, . . . ,B}, aij ∈ {0, 1}∀j ∈ {1, . . . ,B}, bj ∈ {0, 1}
P. Saengudomlert (2018) Optical Networks Session 14 6 / 10
Additional comments on bin-packing
Can use the number of bins from first-fit heuristic as the value of B.
First-fit may not be optimal but uses no more than twice theminimum number of bins.
Example:
N = 5, g = 7, (r1, r2, r3, r4, r5) = (2, 4, 3, 2, 3).First-fit ⇒ 3 bins: {2, 4}, {3, 2}, {3}Optimization ⇒ 2 bins: {2, 3, 2} and {4, 3}
Theorem:
The number of bins used by the first-fit bin-packing heuristic is at mosttwice the minimum number of bins.
Proof: See notes.
P. Saengudomlert (2018) Optical Networks Session 14 7 / 10
5.2.2 Static Traffic Grooming with General Traffic
With general traffic, AUPSRmin and ABLSR
min may differ.Can use ILP to minimize the number of ADMs.Focus on using ILP for BLSR; see problem 4.5 for UPSR (optional)
Given information
W: set of wavelength channels in each fiber
g : capacity of each wavelength channel (e.g. in time slot)
N : set of nodes
L: set of links (one link equivalent to one fiber)
WDw ∈ {CW,CCW}: working direction of wavelength w
(w , t): time slot t on wavelength w in direction WDw1
S: set of s-d pairs with nonzero traffic
S(i ,·): set of s-d pairs whose source nodes are node i
S(·,j): set of s-d pairs whose destination nodes are node j1The term circle will be used to refer to such pair (w , t).P. Saengudomlert (2018) Optical Networks Session 14 8 / 10
Given information (continued)
ts : traffic demand (in time slot) for s-d pair s
psc : path for s-d pair s in ring direction c (CW or CCW)
Variables
f sw ,t ∈ {0, 1}: working traffic flow for s-d pair s on circle (w , t)
aiw ∈ {0, 1}: equal to 1 iff an ADM is used at node i for wavelength w
Objective
Minimize the number of ADMs used
minimize∑
i∈N
∑
w∈Waiw
P. Saengudomlert (2018) Optical Networks Session 14 9 / 10
Constraints
No collision on any link on any circle
∀l ∈ L, ∀w ∈ W , ∀t ∈ {1, . . . , g},∑
s: l∈psWDw
f sw ,t ≤ 1
Satisfaction of traffic demands
∀s ∈ S,∑
w∈W
∑
t∈{1,...,g}f sw ,t = ts
ADM termination capacity contraints (transmit and receive)
∀i ∈ N , ∀w ∈ W,∑
s∈S(i,·)
∑
t∈{1,...,g}f sw ,t ≤ gaiw
∀j ∈ N , ∀w ∈ W,∑
s∈S(·,j)
∑
t∈{1,...,g}f sw ,t ≤ gajw
Integer constraints
∀s ∈ S, ∀w ∈ W, ∀t ∈ {1, . . . , g}, f sw ,t ∈ {0, 1}∀i ∈ N , ∀w ∈ W, aiw ∈ {0, 1}
P. Saengudomlert (2018) Optical Networks Session 14 10 / 10
Top Related