Advances in Optical Network Design with p -Cycles:

1. Advances in Optical Network Design with p-Cycles: Joint optimization and pre-selection of candidate p-cycles (work in progress) Wayne D. Grover, John Doucette grover@trlabs.ca, doucette@trlabs.ca TRLabs and University of Alberta Edmonton, AB, Canada Related papers available at: www.ee.ualberta.ca/~grover IEEE LEOS Summer Topicals 2002 Mont Tremblant, Quebec, Canada July 2002

2. Outline • What are p- Cycles ? • Why do we say they offer “mesh-efficiency with ring-speed ?” • Optimal design with p-Cycles • non-joint or “spare capacity only design” • jointly optimized design • What makes a “good” p-Cycle ? • The idea of Preselection • Preselection by Topological Score, by A Priori Efficiency (AE) • Application of Preselection to Joint and non-joint p_cycle Design Problems

3. Important Features of p-Cycles • Working paths go via shortest routes over the graph • p-Cycles are formed only in the spare capacity • Can be either OXC-based or on ADM-like nodal devices • a unit-capacityp-cycle protects: • one unit of working capacity for “on cycle” failures • two units of working capacity for “straddling” span failures • Straddling spans: • there may be up to N(N-1)/2 -N straddling span relationships • straddling spans each bear two working channels and zero spare • Only two nodes do any real-time switching for restoration • protection capacity is fully preconnected • switching actions are known prior to failure

4. The Unique Position p-Cycles Occupy • p -cycles: • BLSR speed • mesh efficiency Path rest, SBPP Speed Span (link)rest. 200 ms BLSR “50 ms” 50 % 100 % 200 % Redundancy

5. Backgrounder: p-Cycles Ring network: p-Cycle: Spare Capacity x2 protection coverage on each“straddling” span Protection Coverage Able to restore 9 working wavelength channels Able to restore 29 working wavelength channels (on 19 spans)

6. 1 spare 2 spares 2 spares 2 spares 1 spare 1 spare route length = 2 route length = 2+ε 2 spares 1 spare 2 spares 1 spare 2 spares 1 spare 2 λ 2 λ Motivation for Joint Optimization • In “joint” optimization the working route assignments are chosen in conjunction with survivability considerations: • example of the effect this can have: 2 working channel-hops 12 spares in total TOTAL Capacity = 14 2+ε working 6 spares in total TOTAL Capacity = 8+ ε

7. Approaches to p-Cycle Network Design (non-joint) (joint) Route all lightpath requirementsvia shortest-paths enumerateeligible working routes enumerategraph cycles enumerategraph cycles I.L.P. solution forp-cycle formation Heuristic algorithm(s) forp-cycle formation “all in one” I.L.P. solution working routes &working capacity working routes &working capacity p-cycles& spare capacity p-cycles& spare capacity

8. Integer Linear Programming (I.L.P) Formulation (for the joint problem) • Objective Function: • Minimize { total cost of working and spare capacity } • Subject To: • A. All lightpath requirements are routed. • B. Enough WDM channels are provisioned to accommodate the routing of lighpaths in A. • C.The selected set of p-cycles give 100% span protection. • D. Enough spare channels are provisioned to create the p-cycles needed in C. • E. Integer p-cycles decision variables, integer capacity

9. Comments : Approaches to p-Cycle Network Design • Non-joint problem: • several heuristic algorithms under development • however, optimal solution is quite fast too • no real difficulties here • Joint design problem: • I.L.P more complex to solve (coupled integer decision variables and constraint systems) • Idea: use I.L.P. but with reduced number of “preselected” candidate cycles • need some a priori view as to what makes a candidate cycle a promising as p-cycle

10. Preselection Criteria: (1) Topological Score (TS) TS Credit rules: +1 for an “on-cycle”protection relationship +2 for a “straddling span”protection relationship Examples 6 spans, all on-cycle(equiv. To a ring) TS= 6 7 spans on-cycle 2 straddlers TS = 7 + 2*2 = 11 “on-cycle” “straddlers” By itself TS tends to like large cycles (Hamiltonian maximizes TS):no regard to corresponding cost of the cycle

11. Preselection Criteria: (2) a Priori Efficiency (AE) Examples AE AE is defined as: TS j-------------- Cost of cyclej TS= 6 Cost = 6 hops --> AE = 1 Note: all rings have AE = 1 TS= 11 Cost = 7 hops --> AE = 1.57 • Preselection hypothesis: • choose a “small” number of elite cycle candidates based on AE • Let I.L.P. formulation assemble final design

12. COST239 European Study Network • Pan European optical core network • planning model defined by COST 239 study group for optical networks • 11 nodes, 26 spans • Average nodal degree = 4.7 • Demand matrix • Distributed pattern • 1 to 11 lightpaths per node (average = 3.2) Copenhagen London Berlin Amsterdam Brussels Luxembourg Prague Zurich Paris Vienna Milan

13. Results(1): Benefits of Preselection by AE Metric (non-joint design) COST239 non-joint designs: Solution quality vs. No. candidate p-cycles in designc 500 cycles 2000 cycles

14. Results(2): Benefits of AE Metric Pre-Selection (Joint Design) COST239 joint designs: Solution quality vs. No. candidate p-cycles in designc 200 cycles 2000 cycles

15. Benefits of AE Metric Pre-Selection (Joint Design) Additional Test Network:20 nodes, 40 spans, 190 demand pairs 2000 cycles 18,000 cycles mipgap

16. Where the Preselection Heuristic Can Really Help... Exponential Nature of Cycle Enumeration Illustrated for 40 nodes and a varying # of spans (hence connectivity) The preselection strategy will help us keep the problem sizes manageable, i.e., in thisrange, avoiding the “combinatorial explosion” that happens over here.

17. How Much Does Joint Design Improve Efficiency? COST-239Joint design uses 5% more working capacity, and 43% less spare capacity for total network capacity reduction of 13%. Network redundancy = 39% working spare (4 p-cycles) (7 p-cycles) joint non-joint

18. Summary : Main Findings • “Jointly optimized” p-cycle protected OTNs can be extremely efficient: • as little as 39% redundancy observed (for 100% span protection) • Joint design is a more complex problem, however: • Solution time reduced by preselection of a small number of elite cycle candidates based on AE Further Work and Applications: Other test networks Incremental application to dynamic demands Strategies for wavelength conversion Design heuristics