1. BROADNETS 2004 San José, California, USA October 25-29, 2004 p-Cycle Network Design with Hop Limits and Circumference Limits Adil Kodian, Anthony Sack, Wayne D. Grover Department of Electrical and Computer Engineering

2. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Presentation Overview What are p-cycles? Hop-limited p-cycle design Results Summary

3. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Presentation Overview What are p-cycles? Hop-limited p-cycle design Results Summary

4. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering What Are p -Cycles? A survivability mechanism for transport networks Physical network topology – nodes (cities) with spans (fibers) between them Working capacity layer – individual demands are routed between node pairs Spare capacity layer – p-cycles are built to protect working capacity on all spans

5. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering How Do p -Cycles Protect Against Span Failure? Sample p-Cycle loopback On-Cycle Failure Break-in Straddling Span failure

6. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Presentation Overview What are p-cycles? Hop-limited p-cycle design Results Summary

7. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Why use short protection paths ? Simplify network design. Simplify network operation. Increase service availability.

8. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Path Length Constraints in Network Design Commonly used techniques to limit path length: In mesh network design: limit the length of the longest route in the eligible route set Length <= H (Hop Limit) In p-cycle network design: limit the circumference of the longest cycle in the eligible cycle set Length <= C (Circ. Limit) Note: C = H +1 Straddling Span - Prot path length = 4 On-cycle Span - Prot path length = 7 Protection path length limit = 4

9. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Motivating Example Initial Scenario All protection path lengths should be 4 hops (or less) Working capacities to be protected are as shown 1 1 11 1 2 1 1 2 1 Solution 1 (Hamiltonian p-cycle) No hop or circumference limits Only 8 units of spare capacity But some protection paths are longer than 4 (too long) 1

10. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Solution 3 (Shorter Paths) Corresponding hop limit of 4 Only 18 units of spare capacity All protection paths are still adequate (within 4 hop limit) 1 1 1 Motivating Example Solution 2 (Smaller Cycles) Circumference limit of 5 20 units of spare capacity No protection paths are too long (all within 4 hop limit) (a) 1 1 11 1 2 1 1 2 1 1 2 1

11. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Hop-limited p -Cycle Design New parameters defined:

12. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Minimize: Total modular capacity cost (spare + working) Subject to (along with other standard design constraints): Highlights of ILP Design Model Place enough cycles, considering each side separately, to protect all working units. Number of copies of p-cycle p must be the maximum number required by any one failure, on either the L or R side of the p-cycle.

13. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Presentation Overview What are p-cycles? Hop-limited p-cycle design Results Summary

14. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Test Networks 13n23s (501 cycles) 15n26s1 (871 cycles) 12n19s (127 cycles) NSFNET (139 cycles)

15. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Results Threshold hop limit effect

16. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Results Exact comparison of mesh and p-cycle network design

17. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Results Non-joint hop and circumference limited designs p-Cycle threshold occurs about 3 or 4 hops higher than for the corresponding mesh C and H limited designs perform equally well

18. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Results Actual path lengths in hop and circumference limited designs Relatively lower number of long paths

19. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Results Bi-criteria objective function – reduces average path length Engineered for lower number of long paths

20. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Presentation Overview What are p-cycles? Hop-limited p-cycle design Results Summary

21. p-Cycle Network Design with Hop Limits and Circumference Limits – Adil Kodian, Anthony Sack, Wayne D. Grover BROADNETS 2004 – San José, California, USA – October 25-29, 2004 Department of Electrical and Computer Engineering Summary Circumference limiting is an accurate and simple surrogate for true hop-limited p-cycle designs. p-Cycles exhibit a threshold hop limit effect (like span restorable mesh) – but the threshold hop limit is higher than the corresponding mesh design. Above the threshold, p-cycle and mesh networks are equally efficient. Below the threshold, p-cycle capacity cost rises faster than in the corresponding mesh design.