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 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, |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)

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 (s i, D i, ∆ i ) source s i destination: D i delay bound ∆ i the data transmission delay from s i to any node in D i 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.  T i (s i, D i, ∆ i ) be the routing tree for request r i (s i, D i, ∆ i )  The light signal is split at s i 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.

10. QoS requirement  The QoS requirement of routing tree T i (s i, D i, ∆ i ) is that the delay from s i to any nodes in D i should not exceed ∆ i.  Let P Ti (s i, u) denote the path in T i (s i, D i, ∆ i ) from s i to u in D i  Thus,  Assume:  where P G (s i, u) is the shortest path s i 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.  For each QoS multicast request r i (s i, D i, ∆ 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 r i. generates an edge-weight complete graph G’ where vertex-set is {s i } ∪ D i, and weight is the cost of the shortest path in G. produced an MST of G’ obtain tree t A 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 t A If node u in D i is visited the first time and the delay requirement in not met, then find the minimal delay path from s i to u on G. add the minimal delay path form s i to u to t A remove redundant edges in t A to keep it a tree structure. If t A still does not meet delay requirement then return t A = ø

17. Algorithm A for QoS routing

18. Algorithm B for Wavelength Assignment

19.  wavelengths should be assigned to k multicast trees  Obey wavelength conflict rule  Auxiliary graph G a Vertex-set: routing tree T i Edge-set: there is an edge between two vertices in G a if and only if the two routing trees share a common link in G.

20. 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.  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.  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)=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.

30. Simulated Model  QoS multicast trees are generated randomly  Delay bound is set as: Δ i = αmax{d(P G (s i,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)

31. 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)

32. Result

36. 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 ” 中山楊竹星教授

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 ” 台大郭斯彥教授

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