On Adaptive Routing in Wavelength-Routed Networks

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

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 Wavelength conversion cost Link 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(ei) = 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 BPsd X CPsd • BPsd = Busy Factor • CPsd = Cost of links on path from s to d

10. Adaptive Routing Algorithms • Goal: Minimize value of BPsd X CPsd • BPsd = Busy Factor • CPsd = Cost of links on path from s to d *

11. Analytical Model • 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

12. Analytical Model • 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

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 Analytical Model

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

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

18. Numerical Results • Blocking probability (W=4)

19. Numerical Results • Blocking probability (W=4)

20. Numerical Results • Blocking probability (W=8)

21. Numerical Results • Blocking probability (W=8)

22. Numerical Results • Blocking probability (W=8)

23. Numerical Results • 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

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

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

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

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

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

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

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

31. Numerical Results • 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

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

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

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

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

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

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

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

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