Multi-Layer versus Single-Layer MGOXC for WBS
Xiaojun Cao
In collaboration with
Vishal Anand and Chunming Qiao
1
Outline
Concept of Waveband Switching (WBS)
Multi-Layer MG-OXC and Single-Layer MG-OXC
architecture
Offline WBS algorithms
Reconfigurable MG-OXC for Online case
Online WBS algorithms
Conclusions
2
The Optical Cross-connect (OXC)
– Size, management
complexity, cost …
optical
switch fabric
Called Ordinary-OXC here
DeMux/Mux: split/combine
the wavelengths in a fiber
Switch: connects the
wavelengths to one another
using ports
requiring one port for each
wavelength
As the number of
wavelength or fiber
increase, it also brings up
add traffic
drop traffic
3
Waveband Switching (WBS)
Up to 60%~80% of the total traffic in the backbone is
bypass (i.e. transit) traffic
Waveband: a group of several wavelengths
All the wavelengths in a band will be switched as a
single entity (port)
Major merits of WBS
- reduce port count
- reduce complexity
- simplify network management
- better scalability
Need new cross-connects architecture: MultiGranularity optical cross-connect (MG-OXC)
4
MG-OXC Architecture
A new switching hierarchy
with multiple granularities
– Fiber, band, wavelength
Three layer, three switching
fabric
Advantage:
1
2
..
1
2
..
FXC
n
n
BTF Mux
..
..
..
..
BXC
..
.. FTB
Demux
FXC
Layer
BXC
Layer
– flexible
BTW
Demux
Fadd B d r o p
..
..
..
..
W add
WXC
..
..WTB
Mux
W d r o p B add
WXC
Layer
Fdrop
Three-Layer MG-OXC
5
Single-Layer MG-OXC
One common switching
fabric, includes three logical
divisions
Only designated
fibers/bands can be
demuxed/muxed
Advantage:
– Simple
– better signal quality
1
2
..
...
FXC
..
1
2
...
BXC
n
...
F a d d Ba d d Wa d d
WXC
n
...
Wdrop
B d r o p Fd r o p
6
Three-Layer versus Single-Layer
1
2
..
1
2
..
FXC
FXC
n
Layer
n
BTF Mux
BTW
Demux
F add B d r o p
..
..
..
..
..
BXC
..
..
..
W add
..
WXC
..
Wdrop
1
2
..
..
FXC
..
.. FTB
Demux
BXC
Layer
Mux
B add
WXC
Layer
2
..
BXC
n
..
..WTB
1
F a d d Ba d d Wa d d
WXC
n
..
Wdrop
B d r o p Fd r o p
Fdrop
In WBS networks with Single-Layer MG-OXC, an appropriate
WBS algorithm needs to make sure that dropped lightpath will
be assigned wavelengths belong to a designated fiber/band.
In the following, Consider Fixed band size as well as fixed set
of wavelengths per band
7
Offline WBS
Given static traffic, network topology, the number of
wavelength etc, how to satisfy the demands while
minizing the size of MG-OXCs.
Optimal ILP model, BPHT appeared in InfoCom’03
and OptiComm’02
– Too time-consuming
Near-Optimal ILP model (Off-ILP)
– Limit the number of possible routing
– To reduce the computation complexity
8
Off-ILP model
Primary Notation:
– In,On,An,Dn:
set of incoming/outgoing fibers
– B,W, Lb:
number of band/wavelength, set of λ in band b.
– P, T[p], K, Rk,p: traffic matrix and K-shortest path set
Variables:
– V, S, W, B, F: lightpaths going through which switching fabric
– FTB/BTF, BTW/WTB: describe which demux/mux to use
Objective: minimize the total MG-OXC ports in the network
min imize[∑WXCn + ∑ BXCn + ∑ FXCn ]
n
n
n
9
Constraints
Traffic flow constraints
– Satisfy all the traffic demands
Waveband switching
– Appropriately switch the lightpaths through the switch
fabrics at a node
Mux/Demux
– Appropriately Mux/Demux the lightpaths at a node
Detailed formulations refer to Papers
10
Performance Metrics
Total port number ratio T:
Total ( FXCn + BXCn + WXCn ) u sin g MG − OXC
Total (OXCn ) u sin g ordinary − OXC
Max port number ratio M:
Max ( FXCn + BXCn + WXCn )u sin g MG − OXC
Max (OXCn ) u sin g ordinary − OXC
Used wavelength-hop ratio WH:
λ − hop used by WBS a lg orithm
λ − hop used by optimal RWA without WBS
11
Numerical Results
14-node Network with random traffic, K=3
1.2
1.2
Three-Layer,BPHT
Three-Layer,Off-ILP
Single-Layer,BPHT
Single-Layer,Off-ILP
1.1
1.0
1.0
0.9
0.8
Ratio: M
Ratio: T
0.9
Three-Layer,BPHT
Three-Layer,Off-ILP
Single-Layer,BPHT
Single-Layer,Off-ILP
1.1
0.7
0.6
0.8
0.7
0.6
0.5
0.4
0.5
0.3
0.4
0
5
10
15
Number of wavlength per band
20
0
5
10
Number of wavlength per band
12
Summary for Offline case
Near-optimal ILP model perform better
Single-Layer MG-OXC requires up to 20% fewer
ports than Multi-Layer MG-OXC
With appropriate wavelength granuularity (W=4),
MG-OXC can achieve more than 50% ports reduction
when compared to ordinary OXCs
– The maximum size of a node over all the nodes also has
similar reduction
Tradeoff between wavelength-hops and port count
13
Online WBS
Given MG-OXC and network topology, how to
process lightpath request without knowledge of any
future requests.
– Incremental, non-rearrangeable
Unlike offline case, which can have as many port as
needed to guarantee all demands
In online case, MG-OXCs may have a predetermined
limited port count
– How to minimize request blocking probability
– How to efficiently use the network resources (e.g.
minimize active ports)
14
Reconfigurable MG-OXC
X: the number of incoming
fibers
α(≤1): the ratio of fibers can
be demuxed to bands
Wa d d
..
– Any α·X fibers can be
demuxed to bands
Y: the number of BXC ports
from FTB demux
β (≤1): the ratio of bands
can be demuxed to λs
– Any β ·Y bands can be
demuxed to λs
Wd r o p
WXC
...
...
..
BXC
..
...
WXC
Layer
WTB
Y
BTF
..
BXC
Layer
...
FTB
FXC
..
..
..
BTW
βY
..
...
FXC
Layer
αX
X
..
Total number of ports:
MG − OXCn = (1 + α ) ⋅ X + (1 + β ) ⋅ Y + β ⋅ Y ⋅ W + Wadd / drop
15
T for Reconfigurable MG-OXC
T3: ratio of the port count in a Three-Layer MG-OXC to the
port count in an ordinary-OXC
(1 + β ) ⋅ α
MG − OXC n
≈ β ⋅α +
T3 =
OXC
W
n
Similarly, T1: the ratio for
Single-Layer MG-OXC
(1 − β ) ⋅ α
T1 ≈ β ⋅ α +
W
For single-fiber systems, it’s
necessary to set α=1, otherwise
the blocking is too high
Wa d d
n
βY
..
..
..
αX .
.
1
WXC
..
..
2
Wd r o p
..
..
..
..
..
BXC
FXC
n
..
..
2
..
1
16
Online ILP model (On-ILP)
Additional constraints for Three-Layer MG-OXC
– δ:node degree
n ,b
WTB
∑ o ≤δ ⋅β
∀n
o ,b
n ,b
BTW
∑ i ≤δ ⋅β
∀n
i ,b
Additional constraints for Single-Layer MG-OXC
– The choice of the designated bands is critical: the traffic carried by a
designated band at one node may bypass at another node.
– EWTB/EBTW: the setting of designated bands: randomly select β ·Y
bands as designated bands.
WTBon ,b ≤ EWTBon ,b ∀n, o, b
BTWi n ,b ≤ EBTWi n ,b ∀n, i, b
Since α=1, no constraint on the number of FTB/BTF ports
17
Online heuristics
Random-Fit
– Combine the K-shortest path routing with random wavelength assignment
First-Fit
– Use K-shortest path routing and assign the wavelength sequentially
Maximum Overlap Ratio (MOR)
– Model a WBS network as a band-graph having B layers
– Find K-shortest path in each layer corresponding to band b
– Intuitively, to minimize the blocking coming with limitation of ports and
wavelength resource
• Route along the path that has max links in common with existing lightpaths
• Avoid the wastage of wavelength resources
– Set the weight of each (k,b) pair as Q kb = ∑
where L is the overlap
H
length, H is the number of hops, choose the maximum weight to route the
new demand
L
18
MOR example
1
R1
0
1
0
8
2
9
3
10
11
7
0
R3
4
5
6
8
2
9
λ0
3
10
b0
11
4
5
6
1
S2
S3
8
9
10
λ2
11
4
5
6
1
2
3
7
b1
S7
R2
(a)
New demand: 0→7
Compute weight
3
1
b0
b2
Q k2 =
Q k1 =
4
4
0
8
4
Q kb31
3
=
5
New lightpath: 0→4→5→6→7
(λ5)
9
10
5
existing lightpaths
λ4
b2
11
7
6
λ5
new demand
(b)
19
Results of Three-Layer MG-OXC
For medium load, MOR is
better than First-Fit, On-ILP,
much better than Random-Fit.
When β≈0.45 (i.e. T3≈0.60),
MOR achieves the lowest
blocking probability
– One may build 45% (but not more)
BTW ports
– 40% savings on port count
0.3
0.4
0.5
0.6
β
0.7
0.8
0.9
1.0
0.14
0.12
Blocking Probability
– MOR takes waveband grouping
into consideration
– On-ILP minimize additional ports,
random λs assignment to the
initial traffic set hurts its
performance
0.10
Random-Fit
On-ILP
First-Fit
MOR
0.08
0.06
0.04
0.02
0.00
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Ratio: T3 (Three-Layer MG-OXC - Med load)
20
1.3
Results of Three-Layer MG-OXC cont.
β
For high load, First-Fit is the
best when T3>0.75
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.20
0.18
0.16
Blocking Probability
– Assign λs sequentially
– Prefer to use shortest path
0.3
Random-Fit
On-ILP
MOR
First-Fit
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
Ratio: T3 (Three-Layer MG-OXC - High load)
1.5
1.4
Wavelength Hops
MOR consumes more
wavelength recourses,
experience more blocking due
to the lack of wavelength
resources
1.3
1.2
Random-Fit
On-ILP
MOR
First-Fit
1.1
1.0
0.3
0.4
0.5
0.6
0.7
0.8
β (Three-Layer MG-OXC)
0.9
1.0
1.1
21
Results of Single-Layer MG-OXC
– At low loads, noneligible blocking
– At high loads, blocking probability
close to 1
0.3
0.4
0.5
0.6
β
0.7
0.8
0.9
1.0
0.6
0.5
Blocking Probability
The designated bands are
allocated randomly at different
nodes, greatly reduces the
chance of wavebanding and
hence increase the blocking
Random-Fit
On-ILP
First-Fit
MOR
0.4
0.3
0.2
0.1
0.0
0.4
0.5
0.6
0.7
0.8
0.9
Ratio: T1 (Single-Layer MG-OXC - Low load)
22
1.0
Three-Layer versus Single-Layer
Under medium load, the blocking probability using Three-Layer MG-OXC
is much lower
– Three-Layer MG-OXC is more suitable for online traffic
β
0.4
0.5
0.6
0.7
0.9
0.3
1.0
0.4
0.5
0.6
β
0.7
0.8
0.9
1.0
0.14
0.7
Random-Fit
On-ILP
MOR
First-Fit
0.6
Blocking Probability
0.8
0.5
0.12
Blocking Probability
0.8
0.3
0.4
0.3
0.2
0.10
Random-Fit
On-ILP
First-Fit
MOR
0.08
0.06
0.04
0.02
0.1
0.00
0.0
0.4
0.5
0.6
0.7
0.8
0.9
Ratio: T1 (Single-Layer MG-OXC - Med load)
1.0
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
Ratio: T3 (Three-Layer MG-OXC - Med load)
23
Conclusion
Proposed feasible ILP model for offline case and
efficient heuristics for online case
Compared Three-Layer MG-OXC and Single-Layer
MG-OXC for both online case and offline case
– For the offline case, Single-Layer MG-OXC is better in
terms of reducing port count when building network from
scratch
– For the online case, Three-Layer MG-OXC is more flexible
and results in lower blocking probability
– The ratio (β) and waveband granularity have a great effect
on the performance of WBS networks
24