Optimization of Wavelength Assignment for QoS Multicast in WDM Networks

1
Optimization of Wavelength Assignment for
QoSMulticast 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
2
Outline

• Introduction
• Preliminaries
• Rerouting Algorithm
• Simulations
• Conclusion
• Further Research Problem

3
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 system
• a 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.

4
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.

5
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.

6
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.

7
System Models

• WDM network
• Connected and undirected graph G(V, E, c, d)
• V vertex-set, Vn
• E edge-set, Em
• 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)

8
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

9
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.

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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.

11
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.

12
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.

13
Algorithm A for QoS routing
14
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).

15
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.

16
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

17
Algorithm A for QoS routing
18
Algorithm B for Wavelength Assignment
19
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.

21
Algorithm B for Wavelength Assignment
22
Algorithm C Optimization through Load Balancing
23
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.

24
Algorithm C Optimization through Load Balancing
25
Algorithm D Optimization through Wavelength
Reassignment
26
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.

27
Algorithm D Optimization through Wavelength
Reassignment
28
Simulations

• Four different combinations of algorithms A, B,
  C, D
• nonoptimization AB,
• load balancing optimization ABC,
• wavelength assignment optimization ABD,
• combined optimization ABCD

29
Simulation Model

• Network topology random generated
• 100 nodes are distributed randomly over a
  rectangular coordinate
• A link between two nodes u and v is added by
  using the probability function P(u,v)?exp(-p(u,v)
  /?d), where
• p(u,v) is the distance between u and v,
• d is the maximum distance between any two nodes,
• 0 lt ?, ??1
• c and d on link (u,v) are the distance between
  nodes u and v on the rectangular.

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Simulated Model

• QoS multicast trees are generated randomly
• Delay bound is set as ?i amaxd(PG(si,u))u in
  Di
• The lower bound is defined as the maximal link
  load in the system which is obtained running
  algorithm AC (without considering wavelength
  assignment)

31
Analysis of Simulation Results

• simulate the number of wavelengths against three
  parameters
• delay ratio a (1.1-2.0)
• number of multicast destinations 10
• the number of multicast requests (5, 10, 20)

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Result
33
Result
34
Result
35
Result
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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)

37
Further Research

• GA
• Heuristic GA
• Heuristic SA
• Include sparse MC nodes
• Consider delay variations

38
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
  ???????

39
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 ???????

40
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