Optimization Models for the Design of Bi-directional Self-healing Ring Based Networks

1. Optimization Models for the Design of Bi-directional Self-healing Ring Based Networks Dr. Meir Herzberg Dr. Felix Shleifer Network Planning and Engineering, Transport Networks SBU

2. Outline • Introduction (basic self-healing ring terms) • Mesh-type network modeling • Relationship between mesh-type and BLSR network modeling • The process derived for BLSR network design • Numerical results • Concluding remarks

3. Rings & Add Drop Multiplexers (ADMs) ADM - Central element of ring setting • Unidirectional Path Switched Ring (UPSR) • Bi-Directional Line Switched Ring (BLSR) • 2 Fibers (TSI) , 4 Fibers (TSA) • Advanced ADM types and special features • Bi-Directional Path Switched Ring (BPSR) • ADMs with Xconnect and Protection Flexibility • Data-centric ADMs

4. 17 7 15 11 19 18 3 8 7 38 25 22 29 4 16 10 10 12 36 23 2 2 39 26 12 28 27 24 1 19 18 6 14 1 13 20 9 11 17 5 31 20 37 3 30 13 35 21 9 4 6 14 5 33 32 8 16 15 34 Mesh-type Modeling Glass (pass) through Transmission Systems (TSs) Point-to-point TSs

5. Mesh-type Modeling • Objectives • Minimal (weighted) number of point-to-point Transmission Systems (TSs) assigned - Primary • Minimal consumption of resources - Secondary • Integer decision variables for TSs • Constrains • Satisfying end-to-end demand through predefined possible routes (subject to TS setting, may be large) • Predetermined usage level of resources available (parameter value =< Modularity value of the TSs)

6. Mesh-type vs Ring - Design Relationship • Is there a clear relationship? (literature wasn’t promising) • Is Mesh-type network modeling closer to BLSR than to UPSR? • If yes, how can we benefit from it? • Are performance measures valid?

7. n3 TM TM TM TM P-t-P P-t-P n2 n1 0.5 ADM 0.5 ADM 0.5 ADM 0.5 ADM n3 BLSR section BLSR section n2 n1 BLSR Network Modeling • Minimal (weighted) Number of ADMs, Terminal Multiplexers (TM) are now replaced by 0.5 ADM, P-t-P links are now BLSR sections

8. BLSR Network Modeling - Node Constraints • Even number of ring arms per node (as a single ADM at node sites is associated with two arms) • Lower bound for number or rings (ADMs) per node • Rn >= Rounding up integer of the term [Tn:U], where Tn - Total terminating capacity at node n, U - Max ADM load per node (significant for 4-Fiber BLSR) Odd number of BLSR Sections at a network node does not yield a ring solution n

9. BLSR Network Modeling • Stage 1: “Set BLSR sections to satisfy e-t-e demand” or Capacity Placement Efficiency (CPEF) to minimize weighted number of ADMs (Mesh-type network modeling with node constraints - Euler network) • Stage 2: “Find ring cover and flow assignment” or Traffic Capture Efficiency (TCEF) to maximize intra-ring traffic, using the terms TCEF(r) and TCEF(f) for ring cover and flow assignment, respectively.

10. Start Find Optimal CPEF, set TCEF(r) = TCEF(f)=0 Stage 1 Y Stage 2 TCEF(r) < TCEF(f) N Maximize TCEF(f) Stop Maximize TCEF(r) N Y TCEF(r) > TCEF(f) BLSR Network Modeling

11. 18 11 8 7 3 19 10 12 2 9 1 20 13 17 4 14 6 5 16 15 Numerical Results Solution found after Stage 1 (Euler property network)

12. Numerical Results

13. Concluding Remarks • A tied relationship between mesh-type and BLSR network modeling is found and elaborated • A practical two-stage process for optimal BLSR network design is derived • Solutions of real-size networks can be found with commercial software (CPLEX/AMPL) and conventional computer resources • Numerical results obtained are of high quality