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Analysis and simulation of Optical Networks
Xin Liu
Outline• Analytic Approach
Probability: Expectation values, Variance
Network Global Expectation Model
Stochastic Process: Markov chain
Packet Delay in OCS networks
• Simulation
Discrete Event Simulation Model
OCS and OBS extension on NS
Analytic Approach
• Methods: formal derivation, considered approximation,semi-empirical observation.
• Intent:To formulate analytic or closed form;To complement, not supplant more accurate, but computationally intensive tools based on numerical simulation.
Simulation
• Methods:
To implement discrete event simulation model using generic languages;
To extend known simulation platform.
• Intent:
To be close to the real network.
Network Global Expectation Model
• Key idea: Use expectation values to describe required quantities of key network and network element resources.
• Significance: Provide approximate results for the preliminary evaluation and design of dynamic networks.
• Assumption: single-tier backbone networks, location-independent traffic demands.
Network Global Expectation Model
the total network cost
the number of network elements of type i
the unit cost of network element of type i.
T ii
C c
TC
iv
ic
T i ii
C v c Challenge: iv
Network Global Expectation Model
• Expectation value
• Example: L is the number of links and N is the number of nodes.
1
1 m
ii
q qm
T l nC L c N c
Primary Model Variables (Input)
• Network graph
adjacent matrix
• Network traffic
T : the total ingress/egress traffic
D : the number of demands
: demand matrix
( , )G L N
[ ]ijg
[ ]ijd
Primary Model Variables
• Specify the difference between one-way and two-way links
2 1
2 1
2 1
Links: 2
Total Traffic: 2
Total Demands: 2
L L L
T T T
D D D
Output
• Number of Demands
• Traffic Demand Bit-Rate
• Degree of Node
1,
N
ij ni j
D d N d
1 2
1 2
T T
D D
1L
N
Output
• Number of Hops
well known a demand model 1[ ] [ ]
D
ij ij iji j
g h h hD
Number of Hops
1 nodes
N
2
1
Nh
4
Divide the network into 4 sectors centered on the selected node
square root relation
Number of Hops
0-hop 1-hop 2-hops D=3-hops
1
The Moore bound results from the construction of a tree whose root is the parent of vertices and each subsequent vertex is itself the parent ofvertices.
max
max 1 1
Logarithmic relation
Number of Hops
1 maxmax max max
max1
( 1) 11 ( 1) 1
2
D Dh
h
n
max
maxmin
max
2ln 1 ( 1)
ln( 1)
n
D
2ln 1 ( 1)
ln( 1)
nh
Output• Demands on Link
• Restoration Capacity
11
Do
iji j
D h d hW h
L L
(1 )k oW W k
a bk
b
Inverse dependency upon the degree of the nodes
Output
• Traffic on Link
• Number of Ports
D TW h h
L L
ADD DROP THRUP P P P
Number of ports
Drop+Thru Add+Thru
Add Drop d d
ADD DROPP P d
( 1)THRUP d h
Packet Delay in OCS Networks
• The paper first presents the queue length distribution and the packet delay distribution in a single logical buffer of the edge router, and then extends that discussion to a network of edge routers.
• To ensure computational tractability, the framework approximates the evolution of each buffer independently.
Model Formulation
• A circuit is a unidirectional lightpath connecting a pair of source-destination edge routers capable of transmitting C b/s uninterruptedly for a period of T seconds.
• Circuits are allocated to the logical buffers using a policy R based on the queue lengths at all logical buffers.
Model Formulation
• Consider J data streams, each associated with a source-destination pair of edge routers, Qos class, a route and wavelength assignment sequence from the source to the destination, and other external classifications.
• So there are J logical buffers.
Model Formulation
• Normalized lightpath arrival rates
• Normalized lightpath transmission rates K
• Circuit switching decision epoch n
{ ,1 }jA j J
Model Formulation• The queue length in logical buffer j at epoch n
• The system state at epoch n
• A binary vector indicating which of the logical buffers are allocated circuits at state
( )jX n
1 2( ) ( ( ), ( ), , ( ))Jn X n X n X nX
1 2( ) ( ( ), ( ), , ( ))R R R RJx x x x δ
( )nX
Mathematical Model
• The process is a Markov chain.
• But each is not a Markov chain.
• Let be the probability that algorithm R allocates a circuit to buffer j with length i at epoch n.
( ( ), 0)n n X
( )jX n
( 1) [ ( ) ( ( )) ]Rj j j jX n X n A n K X
( , )j i n
[ ] , with probability ( , );( 1)
, with probability 1 ( , );
j jj
j j
i A K i nX n
i A i n
Simulation
• Discrete Event Simulation Model.
• OCS and OBS extension on NS.
Discrete Event Simulation Model
N
INIT()Initialize System1. simulation timer2. system status3. event list4. performance statistics
TIMING()Timing control1. Schedule events accordingto the event list, return thenext event to happen2. Modify timer
EVENT()Handle differentevents from TIMING()1. Modify system status2. Modify performance statistics3. Get the time of the nextevent and add it into event list
Simulation Over
Y
1. Obtain performance statistics2. Print results
Event handling• Accept
Execute RWA for connection requests;Modify the number of arriving requests, the number of successfully established working path;Modify the information of network resource. Create the next event according to assumed distribution and append it into event list.
• Service OverRelease the resource of working channel which is not alive.
Basic Modules• Phy-Topo : Generate physical topology, such as TORUS, NSFNet.• Routing : Implement known routing algorithms, such as Dijkstra’s
Algorithm, Floyd-based SPF, K-Shortest-With-Loop-Path.• Graph Theory Algorithm : provide basic graph theory algorithms,
such as MaxFlow, MinCost-Flow.• Survival : provides protection and restoration schemes.• Resource : Different policies, such as routing, wavelength
assignment, control management, survivability schemes, will lead to different efficiency in resource usage.
• Wave-Assign : Combined with routing Module, it completes the RWA function in WDM networks.
• V-Topo : This module controls the virtual topology in IP layer. • Traffic : It contains Poisson, Gaussian, Self-Similar traffic module. It
is used to generate the random sequence of connection requests.• Pseudo-Random Number : Generate random number in (0, 1)
uniformly.• DES : discrete event simulation module. • Performance Metrics Statistic : In each DES process, track
interested statistics variables. After simulation is over, prints out the values of performance metrics.
Basic Modules
Wave-AssignVirtual
TopologyGraph Theory
Traffic Arrive Routing
Pseudo-RandomNumber
Link-Failure-Occur
PhysicalTopology
TimingLink-Failure-
OverSurvival
PerformanceMetricsStatistic
Server Over Resource
OBS extension on NS• OBS-ns (UMBC)
Use centralized structure to assign resource;
Add new classes for new types;
Ignore the architecture of NS.
• OBS-extension
Keep to the distributed architecture of NS;
Add new component in existing composite classes for new features.
OBS-extension Task
• WDM link extension
No multi-channel link model in NS;
To add a multi-server queue in normal link model.
• Assembly Module in Ingress Nodes of OBS Networks
• Signaling, Qos and contention resolution
Normal Link Model
enqT_ revT_ttlT_linkT_queueT_ deqT_
drophead_ drpT_
Link
head_
head_ The entry of a link
queue_ The queue reference of a link
link_ The reference of a link with delay and bandwidth property
ttl_ The reference of TTL management
drophead_ The reference of the head of the drop queue
WDM link extension
WvAssign
queueT_
Wavelength classifier
WvAssign : Queue
WaveClassifier : Classifier
Wavelength ClassifierReceive packet
Process packet head
Get Wavelengthnumber
Support Wavelengthconversion
Execute WAalgorithm
Y
N
Wavelength available
Any port available
Modify packet headreturn wavelength
number
return wavelengthnumber
Y
return -1
return -1
N
N
Y
WDM link extension
enqT_ revT_ttlT_linkT_deqT_
drophead_ drpT_
Link
head_
WvAssign
queueT_
#Create WDM link $ns duplex-link $n3 $n4 1Mb 20ms WvAssign 4 FirstFit 1
OBS extension
• Redirector
Redirecting table and redirecting buffer. Similar to route table and cache in traditional router.
• Assembly Agent
Set assembly scheme, parameters and signaling .
OBS extension
UDP
CBR
IP router
Ingress
Assembly
core
NULL
egress
Disssembly
Packet flow
Burst flow
WDM
OBS
Assembly agent
Addressclassifier
Portclassifier
Assembly
Redirector
Packet flow
Burst flow
WDM link WDM link
OBS ingress node
Test
Reference• Steven K. Korotky, “Network Global Expectation
Model: A Statistical Formalism for Quickly Quantifying Network Needs and Costs”, Journal of Lightwave Technology Preprint, 2004.
• Zvi Rosberg, “Packet Delay in Optical Circuit-Switched Networks”, 2004.
• Zvi Rosberg, “Analysis of OBS Networks with Limited Wavelength Conversion”, 2004.
• Jean-Francois Labourdette, “Fast Approximate Dimensioning and Performance Analysis of Mesh Optical Networks”, Design of Reliable Communication Networks 2003, 428-438.
• Damon J. Wischik, “Mathematical Modeling of Optical Burst-Switched (OBS) Networks”, 2004.