1. Presenter: Jonathan Murphy On Adaptive Routing in Wavelength-Routed Networks Authors: Ching-Fang Hsu Te-Lung Liu Nen-Fu Huang

2. Overview Background Information Adaptive Routing Algorithms Analytical Model Numerical Results Conclusion

3. Background Information Alternate Routing –Predefined set of paths assigned for each s-d pair –If ever s-d pair has only one path, it’s fixed routing Adaptive Routing –Routing path dynamically determined based on present state of network

4. Background Information Assumption: All wavelength routers have full wavelength conversion capabilities –Therefore, wavelength assignment is not discussed, only routing Adaptive routing is focus for this paper

5. Adaptive Routing Algorithms Shortest Path Strategy (SP) –Objective is to minimize Link cost Wavelength conversion cost * Link Cost Wavelength conversion cost

6. Adaptive Routing Algorithms Shortest Path Strategy (SP) –Advantage Minimizes use of resources –Disadvantage Does not balance link utilization –One link may be overburdened while another is not used at all

7. Adaptive Routing Algorithms Least-Loaded Path Strategy (LLP) –Objective is to balance link utilization F(e i ) = Number of free wavelengths For each possible path, find the link with the fewest number of free wavelengths Select the Path with the largest value Maximize: *

8. Adaptive Routing Algorithms Least-Loaded Path Strategy (LLP) –Advantages Balances link utilization across the network –Disadvantages May lengthen connection paths –Wasted bandwidth –Higher blocking rate *

9. Adaptive Routing Algorithms Weighted-Shortest Path Strategy (WSP) –Focus of this paper –Tries to balance utilization without cost of increased resource usage or blockage –Hybrid method of above to strategies Minimize value of B Psd X C Psd B Psd = Busy Factor C Psd = Cost of links on path from s to d

10. Adaptive Routing Algorithms –Goal: Minimize value of B Psd X C Psd B Psd = Busy Factor C Psd = Cost of links on path from s to d *

11. Exploits single-link model –Analysis of blocking probability –Extended to develop blocking performance of Weighted-Shortest Path Model Also uses overflow model –Used to obtain set of non-linear mathematical equations Final stage –Use successive substitution in iterative fashion for final solution Analytical Model

12. Assumptions –Every node is a full wavelength router –All connection calls request circuit connections –Arrival of connection requests is Poisson process with individual arrival rates. –Assume wavelength conversion cost = zero Analytical Model

13. Begin with the distribution of the number of free wavelengths on a single link –Can be done because of Poisson process of connection requests –From here can find the blocking probability of a link Now, Find the distribution of the number of free wavelength channels on a single path –Use and create a recursion function based on single link information above

14. Analytical Model Find the traffic load of a specific route –Use a cost function –Use this to determine probability that cost of current link is less than all other links Find network-wide blocking probability –Calculate blocking probability of specific route –Use this to find network-wide block probability equation, P Finally, use successive substitution of all above formulas to evaluate P

15. Numerical Results

16. Compares the three strategies (as well as the analytical model performance for blocking) Compares across the 3 network topologies as well Numerical Results

17. Blocking probability (W=4) Numerical Results Logarithmic Scale Number of connection requests per unit connection holding time Available # of wavelengths

18. Blocking probability (W=4) Numerical Results

19. Blocking probability (W=4) Numerical Results

20. Blocking probability (W=8) Numerical Results

21. Blocking probability (W=8) Numerical Results

22. Blocking probability (W=8) Numerical Results

23. Blocking probability results –Blocking probability is higher with increasing traffic load for all strategies –Both SP and WSP better than LLP LLP takes more hops thus uses more bandwidth –SP and WSP have similar performance WSP 12% less than SP when W=8 and #connections = 150 in NSFNET WSP 16% less for interconnected rings when W=8 and #connections = 50 Numerical Results

24. Overall WSP is best at higher loads Also, results of analytical model within an acceptable range –Best with mesh network though Numerical Results

25. Average Number of Hops (W=4) Numerical Results

26. Average Number of Hops (W=4) Numerical Results

27. Average Number of Hops (W=4) Numerical Results

28. Average Number of Hops (W=8) Numerical Results

29. Average Number of Hops (W=8) Numerical Results

30. Average Number of Hops (W=8) Numerical Results

31. Average # of hops results –LLP taking more hopes very obvious here SP and WSP very close Notice that average # of hops decreases as connection requests –Blocking probability increases here –Therefore, networks ability to grant longer connections (and thus more hops) decreases –Especially true when W=4 Numerical Results

32. Standard Deviation of Link Utilization (W=4) Numerical Results

33. Standard Deviation of Link Utilization (W=4) Numerical Results

34. Standard Deviation of Link Utilization (W=4) Numerical Results

35. Standard Deviation of Link Utilization (W=8) Numerical Results

36. Standard Deviation of Link Utilization (W=8) Numerical Results

37. Standard Deviation of Link Utilization (W=8) Numerical Results

38. Standard Deviation of Link Utilization results LLP performs best here!!! –But at cost previously mentioned WSP performs significantly better than SP Numerical Results

39. Conclusion Weighted-Shortest Path (WSP) adaptive routing strategy proposed –Seeks to combine best features of SP and LLP Analytical model proposed as well Results –WSP works well –Analytical model is accurate Best with mesh network