Presentation Overview

2. Presentation Overview • What are p-cycles? • Hop-limited p-cycle design • Results • Summary

3. Presentation Overview • What are p-cycles? • Hop-limited p-cycle design • Results • Summary

4. Spare capacity layer –p-cycles are built to protect working capacity on all spans Working capacity layer – individual demands are routed between node pairs Physical network topology – nodes (cities) with spans (fibers) between them What Are p-Cycles? • A survivability mechanism for transport networks

5. loopback Break-in loopback Break-in How Do p-Cycles Protect Against Span Failure? Sample p-Cycle Straddling Span failure On-Cycle Failure

6. Presentation Overview • What are p-cycles? • Hop-limited p-cycle design • Results • Summary

7. Why use short protection paths ? • Simplify network design. • Simplify network operation. • Increase service availability.

8. Protection path length limit = 4 On-cycle Span - Prot path length = 7 Path Length Constraints in Network Design • Commonly used techniques to limit path length: 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 In mesh network design: limit the length of the longest route in the eligible route set Length <= H (Hop Limit) Straddling Span - Prot path length = 4

9. 1 1 1 1 1 2 Initial Scenario • All protection path lengths should be 4 hops (or less) • Working capacities to be protected are as shown 1 2 1 1 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) Motivating Example

10. 1 1 1 1 (a) 2 Solution 2 (Smaller Cycles) • Circumference limit of 5 • 20 units of spare capacity • No protection paths are too long (all within 4 hop limit) 1 2 1 1 1 1 1 2 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

11. Hop-limited p-Cycle Design • New parameters defined:

12. 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. Highlights of ILP Design Model • Minimize: Total modular capacity cost (spare + working) • Subject to (along with other standard design constraints): Place enough cycles, considering each side separately, to protect all working units.

13. Presentation Overview • What are p-cycles? • Hop-limited p-cycle design • Results • Summary

14. Test Networks 13n23s (501 cycles) 15n26s1 (871 cycles) 12n19s (127 cycles) NSFNET (139 cycles)

15. Results • Threshold hop limit effect

16. Results • Exact comparison of mesh and p-cycle network design

17. p-Cycle threshold occurs about 3 or 4 hops higher than for the corresponding mesh C and H limited designs perform equally well Results • Non-joint hop and circumference limited designs

18. Results • Actual path lengths in hop and circumference limited designs Relatively lower number of long paths

19. Results • Bi-criteria objective function – reduces average path length Engineered for lower number of long paths

20. Presentation Overview • What are p-cycles? • Hop-limited p-cycle design • Results • Summary

21. 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.