Download Wavelength Converter

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts
no text concepts found
Transcript
The Optimal Multiple Multicast
Problem on WDM Ring
演講者:丁德榮
弘光科技大學 資訊管理系助理教授
兼電算中心主任
Mail: [email protected]
1
Outline
•
•
•
•
•
•
Introduction
Multicast Problem on WDM
Multiple Multicast Problem on WDM Ring
Solution Methods
Results
Conclusion and Further Research Topics
2
What is WDM
• Wavelength Division Multiplexing (WDM)
– Each wavelength is an independent communication
channel
– Multiple wavelengths channels can be multiplexed
into one fiber
wavlength 
wavlength 
wavlength n
Opitcal Fiber
3
Why WDM?
• Provide huge bandwidth using fiber
– Fiber has about 50 terabits per second
– Multiple WDM channels provide huge aggregate
bandwidth in a single fiber
• Avoid the bottleneck of increasing baud rate
– Current peak rate is about only 10 Gbps
– Implementation of higher bit rate using fiber for longdistance transmission is more difficult
– Multiple WDM channels with peak rate can achieve
huge capacity
• Upgrade network capacity without fiber redeployment
4
Optical Components in WDM
Networking
• Optical Transmitter
– Tunable transmitter
– Fixed transmitter
• Transmit at a fixed wavelength
• Optical Receivers (Filters)
– Tunable receiver
– Fixed receiver
• Filter out one or multiple wavelengths from
5
Optical Components in WDM
Networking
Wavelength multiplexer & demultiplexer
1
2
1
1,2,…,n
1,2,…,n
2
n
n
Multiplexer
Demultiplexer
6
Optical Components in WDM
Networking
• Wavelength router
Wavelength
Demux.
 1,.., N

Wavelength Mux.
 1,.., N
Optical
Switch

 1,.., N
 1,.., N
Optical
Switch

 1,.., N
 1,.., N
Optical
Switch
Arrayed WDM
Receiver
Arrayed WDM
Trans mitter
Arrayed WDM
Receiver
Arrayed WDM
Trans mitter
Arrayed WDM
Receiver
Arrayed WDM
Trans mitter
Local source and sink
7
Optical Components in WDM
Networking
• Wavelength converter
– Main function: convert the input wavelength from one
to another
– Used to raise wavelength utilization and reduce call
blocking rate
c
s
Wavelength
Converter
s = 1,2,…,N
c = 1,2,…,N
8
Two Kinds of WDM-based LAN
• Single-hop systems
– The source node’s transmitter and the destination node’s receiver
always tune to the same wavelength.
– Direct transmission without store-and-forward by intermediate
nodes.
– Transmission coordination is necessary to avoid channel collision
and receiver collision
.
• Multi-hop systems
– Only some pair of nodes have direct transmission.
– Traffic between two nodes may be stored-and-forwarded via
intermediate nodes.
– Wavelength converter is need
9
Wavelength-Routed Network
• Light-path: the all-optical communication
channel between two nodes.
Wavelength Router
d
g
2

3
a
b
h
1



i
4
6

5

c
e
j
f
10
Wavelength-Routed Network
• Constraints
– Wavelength continuity
• A light-path is required to be on the same
wavelength throughout its path.
• Wavelength converter can be used to change the
wavelength in one light-path.
– Different light-paths traversing the same fiber must be
on different wavelengths
11
Research Problems
•
•
•
•
Virtual topology embedding
Topological optimization
Virtual topology reconfiguration
Routing and wavelength assignment
(RWA)
• Optimization problems due to using
wavelength converters
• Multicast problem
• Placement Problem
12
Multicast Problem on WDM
• Multicast is a point to multipoint communication,
by which a source node sends messages to
multiple destination nodes.
• A light-tree, as a point to multipoint extension of
a light-path, is a tree in the physical topology
and occupies the same wavelength in all fiber
links in the tree.
• Definition: given an multicast request in a
WDM network system, compute a set of
routing trees and assign wavelengths to
them such the cost is minimized.
13
Multiple Multicast Problem on WDM Ring
• WDM Model
– Single-hop WDM network
– All Optical Network
– Ring
– Multicast Capability (light-splitting capability)
– Static Traffic
14
Problem Definition
• Ring network G(V,E)
– V: the set of nodes
– E: the set of links
– bi-directional link
– W wavelengths per link。
15
Problem Definition
• r groups of multicasts,
–
–
–
–
Mi={si, Di},i=1, 2, …, r, 1≦ki≦n;where
Di={d1i, d2i, …, dkii } be the destination
si :source
For each multicast Mi={si, Di},a multicast tree MTi is
need
– Construct a multicast forest MF=Ui=1,2,…r MTi。
– Construct MF with wavelength continuity constraint,
such the number of used wavelengths is minimized。
16
OMMP
• Optimal multiple multicast problem, OMMP
• 給定一個WDM網路與r個多點傳送的需求所成的
集合M={Mi={si, Di},i=1, 2, …, r, 1≦ki≦n},建
立一個多點傳送樹林,並決定每一個多點傳送樹
之波長通道指派,使的所需求的波長通道為最少。
• OMMP is a NP-hard problem
• Since RWA(NP-hard) is a special case of OMMP
• RWA on Ring is a NP-hard problem.
17
Example
18
Possible Assignment of Example
19
Observation
• Each MTi can be constructed by:
– 建立一個順時針方向的路徑:Pc(si, dl-1i)
– 建立一個逆時針方向的路徑:Pr(si, dl+1i)
– 建立兩個路徑,一個順時針與逆時針之路徑
Pr(si, dl’i) 與Pc(si, dl’i),對某一個l’D。
20
Model
Objective : Min
y
wW
w
s.t.
k
c
x

1
,

e

P
 wc
k
wW
k
r
x

1
,

e

P
 wr
k
wW

wM ec
k
xwc

k
x
 wr  yw , w  W , e  E
wM er
k
k
xwc
, xwr
 {0,1}, c  M
y w  {0,1}, w  W
21
Solution Methods
• Heuristic Algorithms
• Genetic Algorithms
22
Heuristic Algorithms
• Two phases
– Routing Phase:
• R1: Maximal-gap Routing
• R2: Minimal Load Routing
– Assignment Phase:
• A1: Greedy Method
• A2: Approximation Method: 7/4-approximation
algorithm
23
Maximal Gap Routing
24
Greedy Method
25
Genetic Algorithm
26
Genetic Algorithm
•
•
•
•
•
•
Chromosome Encoding
Objective Function
Penalty Function
Crossover
Mutation
Selection
27
Chromosome Encoding
• routing gene
• MGi={mgik, i=1,...,r; k=1,2} AGi={agik, i=1,...,r; k=1,2}
• r: number of connections. r=4
mg11 mg12 mg 12 mg 22
7 1 2 7 ...
...
1
2
mg1r mg r2 ag1 ag1
ag 12 ag 22
3 8 1 2 2 2
...
ag 1r ag r2
3 4
28
Example of chromosome encoding
8
1
2
3
7
6
4
5
29
Wavelength gene
 if (there is one element ag ik , such ag ik  j ) and (mgik  si );
1
y j   for i  1,2,..., r; k  1,2)
0
otherwise

30
Objective Function
• Objective function
W
Objective function   y j
j 1
• The assignment represented by the connection
may not constraint-satisfy, thus, a penalty
function should be included in objective function.
31
Penalty Function
• Assume both connections c1=(1,2) and
c2=(1,4) are assigned to wavelength 1 with
clockwise direction, then conflict occurred.
• Penalty should be defined.
• How to detect the conflict in a connection
gene?
• A conflict-detection algorithm should be
developed.
• O(M2) pairs of connections should be
examined.
• The conflict between two connections can be
detected in constant time O(1).
32
Conflict-detection Algorithm
• Construct four bipartite graph AA, AB, BA, BB,
• Node: connection
• Edge: conflict occurred
– A: clockwise direction
– B: counter-clockwise direction
33
Experiments
• Run on PC with a Pentium III 1GHz CPU
and 512MB RAM.
• For nodes n=100, 200, 300
• Two sets of multicast requests are
randomly generated.
– Specific
– Random
• MAXM={5, 10} : the maximal number
destinations in D.
34
Specific Set
• Ranges Ai = { j | n*(i-1)/5+1 ≦ j ≦ n*i/5 }
• The source and destination nodes of
multicast Mi, i=1,2,...,r are randomly
selected from nodes in Ai and two of which
are n*(i-1)/5+1 and n*i/5.
• The lower bound of the minimal used
wavelengths of the set Mspecific is n/5.
35
Specific n=100 (MAXM =5 or 10)
36
Specific n=200 (MAXM =5 or 10)
37
Specific n=300 (MAXM =5 or 10)
38
39
Random n=100 (MAXM =5 or 10)
40
Random n=200 (MAXM =5 or 10)
41
Random n=300 (MAXM =5 or 10)
42
43
More Improvement
44
More Improvement
45
Conclusion and Further Research
• Proposed
– Mathematic Model for multiple multicast problem on
WDM ring
– Several Heuristic Algorithms
– Genetic Algorithms
• Further Research in the problem
– Lower bound proof
– CPLEX package to found optimal solution
– Other Soft-computing method
• Simulated Annealing, Tabu search, Ant algorithm, Scatter
search
46
Further Extension
• Dynamic traffic case: minimize blocking
probability
• Allow dynamic joining and leaving multicast
group
• Different WDM Model
– Multi-hop WDM
– Partial Multicast Capacity
– Different Network Topology: Mesh, General Network
• Other research problem
– Group Communication Problem
47