Analysis of Blocking Probability in Noise- and
Crosstalk-Impaired All-Optical Networks
Outline
Introduction
Model
Iterative
technique
Yvan Pointurier1 ,
Maı̈té Brandt-Pearce2 , Suresh Subramaniam3
1 McGill
2 University
3 The
University, Montreal, QC, Canada
of Virginia, Charlottesville, VA, USA
George Washington University, Washington, DC, USA
May 7, 2007 – INFOCOM – Mini-symposium 3, Session 3
Simulation
results
Conclusions
and future
work
1
Introduction
Outline
Introduction
Model
2
Model
3
Iterative technique
Iterative
technique
Simulation
results
Conclusions
and future
work
4
Simulation results
5
Conclusions and future work
All-optical networks
Current high-speed optical networks
Bottleneck due to electrical conversions
Features of all-optical networks
Circuit switched → lightpaths; speed, flexibility, cost
New issues arise with all-optical networks
Nodes (OXCs) are subject to crosstalk
Node crosstalk is transmitted over extremely long paths
without electrical signal regeneration
Implementation
Crosstalk issues will be encountered in the near future
Motivation
Obtain order of magnitude of call blocking probability in
all-optical networks
Cross-layer optical network design
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
All-optical networks
Current high-speed optical networks
Bottleneck due to electrical conversions
Features of all-optical networks
Circuit switched → lightpaths; speed, flexibility, cost
New issues arise with all-optical networks
Nodes (OXCs) are subject to crosstalk
Node crosstalk is transmitted over extremely long paths
without electrical signal regeneration
Implementation
Crosstalk issues will be encountered in the near future
Motivation
Obtain order of magnitude of call blocking probability in
all-optical networks
Cross-layer optical network design
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
All-optical networks
Current high-speed optical networks
Bottleneck due to electrical conversions
Features of all-optical networks
Circuit switched → lightpaths; speed, flexibility, cost
New issues arise with all-optical networks
Nodes (OXCs) are subject to crosstalk
Node crosstalk is transmitted over extremely long paths
without electrical signal regeneration
Implementation
Crosstalk issues will be encountered in the near future
Motivation
Obtain order of magnitude of call blocking probability in
all-optical networks
Cross-layer optical network design
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
All-optical networks
Current high-speed optical networks
Bottleneck due to electrical conversions
Features of all-optical networks
Circuit switched → lightpaths; speed, flexibility, cost
New issues arise with all-optical networks
Nodes (OXCs) are subject to crosstalk
Node crosstalk is transmitted over extremely long paths
without electrical signal regeneration
Implementation
Crosstalk issues will be encountered in the near future
Motivation
Obtain order of magnitude of call blocking probability in
all-optical networks
Cross-layer optical network design
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
All-optical networks
Current high-speed optical networks
Bottleneck due to electrical conversions
Features of all-optical networks
Circuit switched → lightpaths; speed, flexibility, cost
New issues arise with all-optical networks
Nodes (OXCs) are subject to crosstalk
Node crosstalk is transmitted over extremely long paths
without electrical signal regeneration
Implementation
Crosstalk issues will be encountered in the near future
Motivation
Obtain order of magnitude of call blocking probability in
all-optical networks
Cross-layer optical network design
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
Node crosstalk model
[Deng/Subramaniam-Broadnets2004]
Demultiplexers
Switching fabric
Multiplexers
Outline
λ1 λ2
Introduction
LP1
LP2
Model
λ1
Iterative
technique
Simulation
results
λ2
..
..
..
Imperfect demultiplexing
“Self-crosstalk”
All channels are equivalent
No distinction between adjacent and non-adjacent channels
Conclusions
and future
work
Model
Assumptions:
fixed routing, random pick wavelength assignment
ISI, noise, node demultiplexer crosstalk
wavelength equivalence
Reuse published algorithm for blocking due to the
wavelength continuity constraint (wavelength blocking)
[Sridharan/Sivarajan-ToN2004]
QoS extensions are largely independent of the wavelength
blocking algorithm
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
Model
Assumptions:
fixed routing, random pick wavelength assignment
ISI, noise, node demultiplexer crosstalk
wavelength equivalence
Reuse published algorithm for blocking due to the
wavelength continuity constraint (wavelength blocking)
[Sridharan/Sivarajan-ToN2004]
QoS extensions are largely independent of the wavelength
blocking algorithm
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
Model
Assumptions:
fixed routing, random pick wavelength assignment
ISI, noise, node demultiplexer crosstalk
wavelength equivalence
Reuse published algorithm for blocking due to the
wavelength continuity constraint (wavelength blocking)
[Sridharan/Sivarajan-ToN2004]
QoS extensions are largely independent of the wavelength
blocking algorithm
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
Iterative technique
Bw
R|Xj =m
BR|X =m
j
U′ ′
R,R |Xj =m
UR|X =m
j
Outline
B
αj (m)
w
BR
q
R|Xj =m
XTR|X =m
j
Model
q
BR
BR
Introduction
XTR
UR
′
UR,R
′
Dashed box: wavelength blocking – Dotted box: QoS
blocking
Xj = number of free wavelengths on link j
BR , BRw , BRq are blocking probabilities
(BR = BRw + (1 − BRw )BRq )
αj (m) = state dependent arrival rate
Iterative
technique
Simulation
results
Conclusions
and future
work
Iterative technique
Bw
R|Xj =m
BR|X =m
j
UR|X =m
j
U′ ′
R,R |Xj =m
Outline
B
αj (m)
w
BR
q
R|Xj =m
Model
q
BR
BR
XTR|X =m
j
Introduction
XTR
UR
′
UR,R
′
BRw and BRq are interdependent
The respective algorithms to compute BRw and BRq ,
though, are largely independent
There are techniques in the literature to compute BRw
We reuse one of them to determine BRq
Iterative
technique
Simulation
results
Conclusions
and future
work
Per-link arrivals
α(C)
Λ:
Xj :
C
α(C − 1)
C–1
α(m)
...
m
α(1)
m–1
0
...
Outline
Introduction
M:
1
2
C −m+1
C
Birth-death process is known to accurately model link
states [Chung/Kasper/Ross-ToN1993]
Xj = number of free wavelengths on link j
Λ = arrival rate (parameter of a Poisson distribution)
M = service rate (parameter of an exponential
distribution)
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
Wavelength blocking (overview)
Bw
R|Xj =m
BR|X =m
j
UR|X =m
j
U′ ′
R,R |Xj =m
Outline
B
αj (m)
w
BR
q
R|Xj =m
Model
q
BR
BR
XTR|X =m
j
XTR
UR
′
UR,R
′
2-link correlation and wavelength equivalence assumptions
αj (m) ⇒ Pr(Xj = m) ⇒ βi,j ⇒ gR (i) ⇒ BRw
βi,j = Pr(given set of i wavelengths free on link j)
gR (i) = Pr(given set of i wavelengths free on route R)
Conditionals needed because: P
w
αj (m) =
ΛR 1 − BR|X
j =m
R:j∈R
Introduction
Iterative
technique
Simulation
results
Conclusions
and future
work
QoS blocking
q
0
BR → UR → UR,R
0 → XTR → BR → BR
UR (k) = probability that k = 0, . . . , C calls are
established on exactly route R
Establishing a call on R is modeled as a Bernoulli trial
with success pR :
ΛR 1 − BR
1 − BR
pR =
= ΛR
MR C
C
Assuming independence between the trials:
C k
UR (k) ≈
p (1 − pR )C −k , k = 0, 1, . . . , C .
k R
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
QoS blocking
q
0
BR → UR → UR,R
0 → XTR → BR → BR
nxt (R, R 0 ) = number of common nodes between routes R
and R 0 where crosstalk can occur
Recall: crosstalk from R 0 to R can occur at a node N when
R and R 0 share the link before N and the link after N
0
0
UR,R
0 (k) = probability that route R injects k crosstalk
components on route R
0
0
UR,R
0 (nxt (R, R )k) = UR 0 (k)
XTR (k) = probability that route R is subject to exactly k
crosstalk components
0
0
XTR = UR,R
∗ . . . ∗ UR,R
p
1
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
QoS blocking
q
0
BR → UR → UR,R
0 → XTR → BR → BR
Q factor for a system with crosstalk:
Outline
Introduction
QR =
µ1,R − µ0,R
µ1,R − µ0,R
q
=
σ0,R + σ1,R
2 + σ 2 + nσ 2
σ0,R + σi,R
n,R
x,R
Maximum number of crosstalks to keep Q below threshold:
NRmax


2
 µ1 −µ0
2 − σ2 
 Q − σ0,R − σi,R

n,R 
th

=

2
σx,R
QoS blocking:
BRq =
X
k>NRmax
XTR (k).
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
Iterative technique
Bw
R|Xj =m
BR|X =m
j
UR|X =m
j
U′ ′
R,R |Xj =m
Outline
B
αj (m)
w
BR
q
R|Xj =m
Model
q
BR
BR
XTR|X =m
j
Introduction
XTR
UR
′
UR,R
′
0
Computations of the conditionals UR|Xj =m , UR,R
0 |X =m ,
j
q
XTR|Xj =m , BR|Xj =m are very similar to the computations
q
0
of UR , UR,R
0 , XTR , BR .
Iterative
technique
Simulation
results
Conclusions
and future
work
Simulation parameters
Mesh-8 topology
Parameters
NSF topology
4
1
2
1
1
2
4
2
1
1
1
1
1
1
2
4
2
2
2 1
Description
Span length
Signal
peak power
Bit rate
Nonlinear
parameter
Pulse shape
Fiber type
Dispersion
2
Min. Q factor
Outline
Value
70 km
Introduction
Model
Iterative
technique
2 mW
10 Gbps
2.2 (W.m)−1
NRZ
SMF
100%
post-DC
6
Simulation
results
Conclusions
and future
work
Blocking probability: mesh of 8 nodes
0
10
Outline
Blocking probability due to QoS
−1
10
Introduction
Model
−2
10
Iterative
technique
−3
Simulation
results
10
−4
−5
10
0
Conclusions
and future
work
−25 dB; Simulation
−25 dB; Analysis
−30 dB; Simulation
−30 dB; Analysis
10
10
20
30
Total offered load (Erlang)
40
16 wavelengths, -25 dB and -30 dB crosstalk
red: analysis; black: simulation
50
Gain in load
Load in gain for the mesh of 8 nodes
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
−25
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work
−26
−27
−28
Crosstalk attenuation (dB)
−29
Target average call blocking probability of 0.001
(reference: gain=1 for -25 dB)
−30
Blocking probability: NSF topology
0
10
−1
Blocking probability
10
−2
10
B, simulation
B, analysis
Bq, simulation
Bq, analysis
Bw, simulation
Bw, analysis
Outline
Introduction
Model
Iterative
technique
−3
Simulation
results
10
Conclusions
and future
work
−4
10
5
10
15
20
25
30
35
Total offered load (Erlang)
40
45
NSF topology, 8 wavelengths, -30 dB crosstalk
red: analysis; black: simulation
50
Conclusions and future work
Physical parameters-dependent impact of crosstalk on
network performance
Extended an algorithm that computes wavelength
blocking, to include QoS blocking
But our work is independent of the wavelength blocking
calculations algorithm
Leads for future work
Adjacent vs. non-adjacent channel crosstalk
Other impairments (PMD, ...)
Questions ?
Outline
Introduction
Model
Iterative
technique
Simulation
results
Conclusions
and future
work