1. Exploiting Forcer Structure to Serve Uncertain Demands and Minimize Redundancy of p-Cycle Networks Gangxiang Shen & Wayne D. Grover TRLabs and University of Alberta TRLabs and University of Alberta Edmonton, AB, Canada web site for related research group: web site for related research group: http://www.ece.ualberta.ca/~grover OptiComm 2003, October 13-17, Dallas, Texas

2. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 2 Outline Conventional survivable network design What is a forcer and what is the meaning of a forcer in a p-cycle network? Exploitation of forcer structure for a p-cycle network Experiments and results Conclusion

3. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 3 Conventional Survivable Network Design 12 345 6 1 2 3 4 5 6 Node index Demand matrix 31223 2232 113 33 3 2 3 4 6 1 Network topology 5 2 3 4 6 1 Network with working capacity 5 w=9 6 6 2 6 5 4 5 3 2 3 4 6 1 Network with protection capacity 5 s=6 9 4 5 4 5 0 1 5 Survivable network design methods, e.g., span restoration, path restoration, p-cycle, SBPP, flow p-cycle, path-segment restoration… Here span restoration method was employed ? Who forces this span to require 5-unit spare capacity?

4. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 4 What is a Forcer? “A forcer is any span for which an increase in network total spare capacity is required (to retain restorability) if the span’s working capacity is increased.” Have a look at the previous example again 2 3 4 6 1 Network with working capacity 5 w=9 6 6 2 6 5 4 5 3 2 3 4 6 1 Network with protection capacity 5 s=6 9 4 5 4 5 0 1 5 2 3 4 6 1 Network forcers 5 forcers 3 6 4 2 non-forcers

5. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 5 Forcer in p-Cycle Networks 0 11 3 7 6 9 12 10 1 2 4 5 8 Straddling span On-cycle span p-cycle Forcer span A p-cycle with 3-unit spare capacity 6 0 w=6 3 2 1 3 1 5 4 1 2 “A forcer is any span for which an increase in p-cycle spare capacity (corresponding to total network spare capacity) is required (to retain restorability) if the span’s working capacity is increased.” A p-cycle with 3-unit spare capacity 6 3 w=6 3 3 3 3 3 6 6 3 3 p-cycle protected envelope

6. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 6 Forcing Chain in p-Cycle Networks Span working capacity p-cycle protected envelope Protected working capacity envelope Span working capacity Span protection capacity How should we deal with this gap? p-cycle 3 p-cycle 1 p-cycle 2 p-cycle 4 p-cycle N p-cycle spare capacity

7. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 7 How to Exploit the Gaps? Forcer Filling: adding working capacity to non-forcers to make them forcers; the added capacity can be used to serve future uncertain demands. … the basic idea of this paper Protected working capacity envelope Span working capacity Protected working capacity envelope Span working capacity after forcer filling Extra protected span working capacity for future uncertain demands Just use it! No need to pay for anything for protection !

8. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 8 Forcer Maximized Design and its Relation to Conventional Design Regular design Working demand pattern Network topology Minimize required spare capacity for restorability Forcer maximized design Span spare capacity budget Maximize extra servable protected working channels Network topology Total network spare capacity budget

9. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 9 Three ILP Models Common ground of the three models --Objective: Maximize total servable protected working channels --Conditions: 1. Ensure the restorability of working capacity 2. Ensure spare capacity shall be within budgets Forcer analyzer (FA) model Maximize extra servable working channels, but disallowing to touch the existing working channels Forcer maximization-1 (FM-1) Maximize servable working channels given span spare capacity budgets, but allowing to change the existing working channels Forcer maximization-2 (FM-2) Maximize servable working channels given total network spare capacity budgets, but allowing to change the existing working channels

10. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 10 Test Methods and Network Topologies 1.Two metrics: hop-based and physical distance-based 2.Dijkstra’s shortest path algorithm is used to find the route for a working path 3.Demand matrixes are randomly generated within the range [1-20] for each node pair NSFNET ARPA-2 SmallNet COST239

11. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 11 Test Methods and Network Topologies (cont’) Level-3 network

12. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 12 Results of the FA Model for p-Cycle Networks Percentages of extra working channels that can be served in p-cycle networks without any increase in span spare capacity budget

13. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 13 Redundancy Comparison between Various Survivable Schemes 1: Conventional design 2: Forcer analyzer (FA) 3: Forcer maximization-1 (FM-1) 4: Forcer Maximization-2 (FM-2)

14. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 14 Concluding Discussion A simple but efficient forcer analyzer is developed Two forcer maximization design models are proposed Experiments show that there is a rich “protected working capacity bank” under the forcer structure formed in the conventional survivable network design The direct use of protected capacity in the “bank” to serve future uncertain demands ……”Just use it! No need to pay any extra spare capacity for protection! (Its already protected)” Neighbouring concept to this study is to use “protected working capacity envelope (PWCE)” to serve dynamic protected demands for efficiency and simplicity Thanks!

15. Gangxiang Shen and Wayne D. Grover OptiComm ‘03 Dallas 15 How to Deal with the Gaps? --Clipping and Filling Forcer Clipping: clipping forcers to make non-forcers become forcers as well and to improve network spare capacity efficiency Protected working capacity envelope Span working capacity Protected working capacity envelope Remaining span working capacity Clipped span working capacity Ring covering