Presented by: Douglas L. Potts CEG 790 Summer 2003

1. Algorithms for Allocating Wavelength Converters in All-Optical NetworksAuthors: Goaxi Xiao and Yiu-Wing Leung Presented by: Douglas L. Potts CEG 790 Summer 2003 From IEEE/ACM Transactions on Networking, Vol. , No. 4, Aug. 1999 Authors: Goaxi Xiao and Yiu-Wing Leung

2. Overview: • Wavelength Converters: background • Converter Placement: a study, a algorithm proposal • Simulations to determine worth • Conclusions

3. Wavelength Converters: background • What are they? • Distinction in terminology • Why?

4. Wavelength Converters: background – What are they? • In Wavelength Division Multiplexing (WDM) divides bandwidth across multiple wavelength channels • On multiple hop lightpaths, it is difficult to reserve a single wavelength for all hops (Wavelength Continuity Constraint) • For high network load, need a way to get around the Wavelength Continuity Constraint • Mechanism for converting one fiber optic signal’s light wavelength to another light wavelength

5. Wavelength Converters: background – Distinction in Terminology • Full Range Wavelength Converter (FWC) • Converts incoming wavelength to any outgoing wavelength • Limited Range Wavelength Converter • Converts incoming wavelength to a subset of outgoing wavelengths

6. Wavelength Converters: background – Distinction in Terminology • Complete Wavelength Conversion • When number of FWC’s in a node is equal to total number of outgoing wavelength channels of this node • Partial Wavelength Conversion • As Complete Wavelength Conversion has a high cost using fewer FWC’s per node.

7. Wavelength Converters: background – Why use them? • To resolve wavelength conflicts on a particular hop… • Which reduces blocking probability.

8. Wavelength Converters: background – Why not? • Costly (in terms of $ cost, but also in time delay for conversion and signal degradation) • Introduces complexity in Route-Wavelength Allocation (RWA)

9. Converter Placement – converters for all • Previous studies looked at putting a FWC at each node • Results were that blocking probability is drastically reduced, but at great cost (and an unrealistic assumption)

10. Converter Placement – example node

11. Converter Placement – Choosy allocation • Paper looks at a method for optimizing FWC placement to reduce total number of wavelength converters • Goals for allocation • Reduce overall blocking probability (better mean quality of service) • Maximum of the blocking probabilities experienced at all the source nodes (better fairness)

12. Converter Placement – Choosy allocation • Want to minimize blocking probability • Blocking probability is available via: • Analysis • Simulation

13. Converter Placement – Choosy allocation • Blocking probability by analysis is only available by making some simplifying assumptions • specific traffic models or • specific routing and wavelength assignment methods • Therefore simulation approach chosen

14. Converter Placement – Choosy allocation • Main Idea – Simulate a complete wavelength conversion network and analyze the utilization matrix of the node’s FWC’s, optimize converter allocation based on this utilization matrix • Optimized allocation does alter utilization matrix for the network, but authors claim that the estimated utilization (i.e. that based on complete conversion) is good because for a “well-engineered network” the traffic load handled by each node should not approach or exceed its capacity.

15. Converter Placement – Choosy allocation • It is because of the only slight change to the utilization matrix when fewer FWC’s are used that network performance is maintained.

16. Converter Placement – RWA Algorithm • Previous work based on two extremes of wavelength conversion • No Wavelength Conversion • Complete Wavelength Conversion • Authors needed to come up with a new allocation algorithm

17. Converter Placement – RWA Algorithm • Critical problem that algorithm needs to solve: when a certain no. of FWC’s have been allocated to each node, how should the tuning nodes (i.e. nodes with wavelength converters) be selected

18. Converter Placement – RWA Algorithm • Main ideas for solving the problem: • Once a request arrives, select the set of tuning nodes such that required number of FWC’s is minimized • When more than one choice, select the one that maximizes the min. no. of free FWC’s in each tuning node of src. to dest. path • When more than one choice, select one that has max. no. of FWC’s installed on the critical node

19. Converter Placement – RWA Algorithm • Resulting algorithm: • Check if there is at least one clear channel on source-to-destination path. If one exists, assign this clear channel to the transmission request; if there is more than one channel, select one of them on a first-fit basis; if there is none, go to step 2. • If there is at least one free wavelength channel (at any wavelength) on every hop of the source-to-destination path, execute: • Construct a directed graph in a manner similar to that in the Conflict Resolution Algorithm. For each free wavelength channel on every hop, the weight of the corresponding edge is M. On every intermediate node l, the weight of the edge between the node vi(λi, l) and node vo(λo, l) is: c(λi, λo, l)={ M + S, if λi ≠ λo or 0, if λi = λo} where: S={M/(Nt(l) – Na(l)) + (1 – Na(l)/Nt(l)), if Nt(l) > Na(l) or ∞, if Nt(l) = Na(l)}

20. Converter Placement – RWA Algorithm

21. Converter Placement – RWA Algorithm • Resulting algorithm (cont.): Apply in the Conflict Resolution Algorithm to find the shortest path from the source to the destination • Determine the set of tuning nodes and increment Na(l) of each tuning node by 1. Otherwise, the transmission request is blocked.

22. Numerical Results • Simulations used to evaluate performance of the proposed allocation method, with the steps: • Conduct simulation for any given network with complete wavelength conversion and any given traffic load and pattern. During simulation, record utilization matrix. • Based on recorded utilization matrix, execute Optimization Algorithm to optimize allocation of FWC’s. • Conduct another simulation for the same network with the FWC allocation being that determined by the Optimization Algorithm. During simulation, execute the RWA Algorithm to perform routing and wavelength assignment and record blocking probability.

23. Numerical Results • “Extensive” Simulations conducted on regular and irregular networks, considering both uniform and non-uniform traffic • Regular network: 11x11 torus mesh network with 121 nodes • Irregular network: generated randomly, starting from a 10x10 mesh network with 100 nodes and 180 bi-directional links • Randomly delete 20 links, while ensuring that resulting network is not disconnected • Randomly add 30 links to the network: for the j1th node on the i1th row and j2th node on the i2th row, define the distance as: d(i1,j1),(i2,j2) =sqrt((i1-i2)2+(j1+j2)2)

24. Simulations – Results • Fig. 7a, 7b, 8a, and 8b

25. Simulations – Results • Fig. 9a, 9b, 10a, and 10b

26. Simulations – Results • Fig 11a, 11b, 12a, and 12b

27. Summary: • Wavelength Converters: why and why not • Converter Placement: all nodes, select nodes • Simulations indicate Proposed allocation matching Complete wavelength conversion within a small margin

28. Conclusions • Utilizing Wavelength Converters in a Optical WDM Network drastically reduces blocking probability • Wavelength Converters are expensive, so ideal situation is to use small number of converters while maintaining performance • By using a simulation-based optimization approach, it is possible to collect utilization statistics, upon which converter allocation is based • It is possible to use the optimized converter allocation to significantly reduce the number of converters required, and achieve blocking probabilities which are roughly those of Complete Wavelength Conversion