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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]
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Outline
•
•
•
•
•
•
Introduction
Multicast Problem on WDM
Multiple Multicast Problem on WDM Ring
Solution Methods
Results
Conclusion and Further Research Topics
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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
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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
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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
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Optical Components in WDM
Networking
Wavelength multiplexer & demultiplexer
1
2
1
1,2,…,n
1,2,…,n
2
n
n
Multiplexer
Demultiplexer
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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
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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
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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
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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
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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
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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
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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.
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Multiple Multicast Problem on WDM Ring
• WDM Model
– Single-hop WDM network
– All Optical Network
– Ring
– Multicast Capability (light-splitting capability)
– Static Traffic
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Problem Definition
• Ring network G(V,E)
– V: the set of nodes
– E: the set of links
– bi-directional link
– W wavelengths per link。
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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。
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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.
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Example
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Possible Assignment of Example
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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。
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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
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Solution Methods
• Heuristic Algorithms
• Genetic Algorithms
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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
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Maximal Gap Routing
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Greedy Method
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Genetic Algorithm
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Genetic Algorithm
•
•
•
•
•
•
Chromosome Encoding
Objective Function
Penalty Function
Crossover
Mutation
Selection
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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
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Example of chromosome encoding
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1
2
3
7
6
4
5
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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

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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.
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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).
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Conflict-detection Algorithm
• Construct four bipartite graph AA, AB, BA, BB,
• Node: connection
• Edge: conflict occurred
– A: clockwise direction
– B: counter-clockwise direction
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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.
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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.
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Specific n=100 (MAXM =5 or 10)
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Specific n=200 (MAXM =5 or 10)
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Specific n=300 (MAXM =5 or 10)
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Random n=100 (MAXM =5 or 10)
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Random n=200 (MAXM =5 or 10)
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Random n=300 (MAXM =5 or 10)
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More Improvement
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More Improvement
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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
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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
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