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![Page 1: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/1.jpg)
Optimization of Wavelength Assignment for QoS
Multicast in WDM Networks
Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu,
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 2, FEBRUARY 2001 pp.341-350
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Outline
Introduction Preliminaries Rerouting Algorithm Simulations Conclusion Further Research Problem
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Introduction
There are two types of architectures of WDM optical networks: single-hop systems and multi-hop systems [2]. Single-hop system
a communication channel should use the same wavelength throughout the route of the channel
Multi-hop systema channel can consist of multiple light-paths and wavelength conversion
is allowed at the joint nodes of two light-paths in the channel. (with wavelength conversion)
In this paper, we consider single-hop systems, since all-optical wavelength conversion is still an immature and expensive technology.
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Introduction
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.
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Introduction
Each fork node of the tree is a multicast-capable (MC) optical switch, where a power splitter is used to split an input optical signal into multiple signals which are then forwarded to output ports without electrical conversions.
End-to-end delay is an important quality-of-service (QoS) parameter in data communications.
QoS multicast requires that the delay of messages from the source to any destination be within a bound.
![Page 6: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/6.jpg)
Introduction
The problem is formalized as follows: given a set of QoS multicast requests in a WDM network system, compute a set of QoS routing trees and assign wavelengths to them.
The objective is to minimize the number of distinct wavelengths to be used under the following constraints on each routing tree: the delay from the source to any destination along the
tree does not exceed a given bound; the total cost of the tree is suboptimal.
![Page 7: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/7.jpg)
System Models
WDM network Connected and undirected graph G(V, E, c, d) V: vertex-set, |V|=n E: edge-set, |E|=m Each edge e in E is associated with two weight functions
c(e): communication cost d(e): the delay of e ( include switch and propagation delays)
![Page 8: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/8.jpg)
System Models
Cost of path P(u,v):
Delay of path P(u,v):
k bidirectional QoS multicast requests in the system are given, denoted by
multicast request r i (si, Di, ∆i) source si destination: Di delay bound ∆i the data transmission delay from si to any node in Di should be within
bound ∆i
),(
)()),((vuPe
edvuPd
),(
)()),((vuPe
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},...,2,1|),,({ kiDsr iiii
![Page 9: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/9.jpg)
System Models
This paper assumes an optical signal can be split into an arbitrary number of optical signals at a switch. Thus, there is no restriction on node degree in a routing tree.
Ti (si, Di, ∆i) be the routing tree for request r i (si, Di, ∆i)
The light signal is split at si and forwarded to the output ports leading to its children, which then transmit the signal to their children until all nodes in the tree receive it.
![Page 10: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/10.jpg)
QoS requirement
The QoS requirement of routing tree Ti (si, Di, ∆i) is that the delay from si to any nodes in Di should not exceed ∆i.
Let PTi(si, u) denote the path in Ti (si, Di, ∆i) from si to u in Di
Thus,
Assume:
where PG(si, u) is the shortest path si to u in G.
iiusiPe
iT DedusPdiT
i
u )(),((),(
iiGi DusPd u ),,((
![Page 11: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/11.jpg)
Objective
The cost of the tree
One objective of the multicast routing is to construct a routing tree which has the minimal cost.
The problem is regarded as the minimum Steiner tree problem, which was proved to be NP-hard.
Another objective is to minimize the number of wavelengths used in the system.
In a single-hop WDM system, two channels must use different wavelengths if their routes share a common link, which is the wavelength conflict rule.
)()),,((),,(
iiii DsTe
iiii ecDsTc
![Page 12: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/12.jpg)
Rerouting Algorithms
Four algorithms A: QoS routing algorithm B: wavelength assignment problem C and D aiming at minimizing the number of
wavelengths over the results produced by algorithms A and B. C: reroutes some of the routing trees to reduce the maximal link
load by avoiding use of the links whose load is the maximum. D: reroutes the trees whose wavelengths are the least used,
which tries to free out the least used wavelengths.
![Page 13: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/13.jpg)
Algorithm A for QoS routing
![Page 14: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/14.jpg)
Algorithm A for QoS routing
For each QoS multicast request r i (si, Di, ∆i), algorithm A constructs a suboptimal QoS routing tree.
Generate a low cost routing tree by applying a heuristic for the Steiner tree problem.
Modifies this tree into the one which meets the QoS requirements (delay requirement).
![Page 15: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/15.jpg)
Algorithm A for QoS routing
Step 1. Using an MST-based heuristic to generate a routing tree for request ri. generates an edge-weight complete graph G’ where
vertex-set is {si}∪ Di , and weight is the cost of the shortest path in G.
produced an MST of G’ obtain tree tA in G by substituting each edge of the
MST in G with the corresponding path in G.
![Page 16: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/16.jpg)
Algorithm A for QoS routing
Step 2. Use DFS search method to traverse tA If node u in Di is visited the first time and the delay
requirement in not met, then find the minimal delay path from si to u on G.
add the minimal delay path form si to u to tA
remove redundant edges in tA to keep it a tree structure.
If tA still does not meet delay requirement then return tA = ø
![Page 17: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/17.jpg)
Algorithm A for QoS routing
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Algorithm B for Wavelength Assignment
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Algorithm B for Wavelength Assignment
wavelengths should be assigned to k multicast trees
Obey wavelength conflict rule Auxiliary graph Ga
Vertex-set: routing tree Ti
Edge-set: there is an edge between two vertices in Ga if and only if the two routing trees share a common link in G.
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Algorithm B for Wavelength Assignment
Wavelength assignment problem is transformed to the coloring problem
How to color all vertices in Ga such that no two adjacent vertices receive the same color and minimize the use of colors.
NP-complete problem. Heuristic Algorithm
chooses a vertex which has the least degree finds a maximal set of vertices that are not adjacent to the selected
vertex and there is no edge between any pair of vertices in the set assigns a wavelength to the vertices in this set and remove from the
graph repeats this process until all vertices are colored and removed.
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Algorithm B for Wavelength Assignment
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Algorithm C: Optimization through Load Balancing
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Algorithm C: Optimization through Load Balancing
Given a set of routing trees, algorithm C minimizes the number of wavelengths by reducing the maximal link load in the system. calculate the load on each link choose a tree which contains the links having the
maximum load. reroute it by running algorithm A on the sub-graph
of G after removing the links having the maximum load.
The routing operation is repeated until the maximum link load cannot be reduced any further.
![Page 24: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/24.jpg)
Algorithm C: Optimization through Load Balancing
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Algorithm D: Optimization through Wavelength Reassignment
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Algorithm D: Optimization through Wavelength Reassignment
For a set of routing trees assigned with wavelengths, algorithms D reduces the number of wavelengths by assigning some of the trees in such a way that some of the wavelengths they are currently using can be freed.
For each wavelength, calculate the set of routing trees it is assigned to
reroute the trees which are assigned with the least used wavelength, so that they can be assigned to with other wavelength
The rerouting operation is repeated until the number of wavelength used cannot be reduced an further.
![Page 27: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/27.jpg)
Algorithm D: Optimization through Wavelength Reassignment
![Page 28: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/28.jpg)
Simulations
Four different combinations of algorithms A, B, C, D
nonoptimization AB, load balancing optimization ABC, wavelength assignment optimization ABD, combined optimization ABCD
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Simulation Model
Network topology: random generated 100 nodes are distributed randomly over a rectangular coord
inate A link between two nodes u and v is added by using the pro
bability function P(u,v)=λexp(-p(u,v)/γδ), where p(u,v) is the distance between u and v, δ is the maximum distance between any two nodes, 0 < λ, γ≦1
c and d on link (u,v) are the distance between nodes u and v on the rectangular.
![Page 30: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/30.jpg)
Simulated Model
QoS multicast trees are generated randomly Delay bound is set as: Δi = αmax{d(PG(si,u))|u in D
i}
The lower bound is defined as the maximal link load in the system which is obtained running algorithm AC (without considering wavelength assignment)
![Page 31: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/31.jpg)
Analysis of Simulation Results
simulate the number of wavelengths against three parameters delay ratio α (1.1-2.0) number of multicast destinations 10 the number of multicast requests (5, 10, 20)
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Result
![Page 33: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/33.jpg)
Result
![Page 34: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/34.jpg)
Result
![Page 35: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/35.jpg)
Result
![Page 36: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/36.jpg)
Conclusion
The proposed algorithms can significantly reduce the number of wavelengths over the cases where no optimization is done (AB).
D (wavelength reassignment) is better than C (load balancing)
![Page 37: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/37.jpg)
Further Research
GA Heuristic +GA Heuristic + SA Include sparse MC nodes Consider delay variations
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Possible issues
GA for “constrained multicast routing in WDM networks with sparse light splitting” J. of Lightwave Tech. 18 (12) Dec. 2000, p1917-1927.
GA for “Multicast routing with power consideration in sparse splitting WDM networks” 中山楊竹星教授
![Page 39: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/39.jpg)
•Possible issues
GA for “Virtual source based multicast routing in WDM networks with sparse light splitting”
GA for “All-optical multicasting on wavelength-routed WDM networks with partial replication” 台大郭斯彥教授
![Page 40: Optimization of Wavelength Assignment for QoS Multicast in WDM Networks Xiao-Hua Jia, Ding-Zhu Du, Xiao-Dong Hu, Man-Kei Lee, and Jun Gu, IEEE TRANSACTIONS.](https://reader030.fdocuments.us/reader030/viewer/2022033101/56649ebb5503460f94bc4290/html5/thumbnails/40.jpg)
Possible issues
Assignment of k-tree of previous problem Placement problem
MC nodes placement problem with budget constraints
Virtual nodes placement problem with budget constraints