1. Design of Ring-based Survivable Networks W. D. Grover TRLabs & University of Alberta © Wayne D. Grover 2002, 2003 E E 681 - Module 9

2. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 2 Given: - a two-connected (or bi-connected) graph - a set of “ring technologies” and costs. e.g OC-192 4/BLSR, OC-48 UPSR, etc...including 1+1 APS - a set of demands to be served. - a subset of node locations where demands may transit from ring-to-ring Determine: - the number, size, type and placement of all rings - the location of glass-throughs (and ADM terminals) on all rings - the end-to-end routing of each demand For minimal cost of all rings placed, including costs associated with demands transiting from ring to ring. The (static) multi-ring design problem

3. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 3 Upper bound on number of ring candidates to consider: logic: Every combination of 2, 3, 4....up to N nodes defines a prospective collection of active ADM nodes that could be grouped together to define one ring. Upper bound on the number of different multi-ring designs that exist: logic: Now, every combination of 1, 2, 3, 4....up to some pre-determined maximum number of rings can be considered for feasibility and cost as a multi-ring design solution. - in ideal case of rings with no capacity limit, can show that more than N-1 rings not needed. and... also multiply by the number of “ring technologies” being considered. On the complexity of multi-ring design

4. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 4 illustration: a 10 node network: 10 13 possible rings, 10 21 possible multi-ring networks (over 100 million years to evaluate all designs at 10 6 design evaluations / sec.) ! Question: How big is  ?

5. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 5 Concept (each follows in more detail): graph coverage: Balance Capture Span elimination Dual-ring interconnect transit sites glass-throughs....a set of rings that covers every edge of the graph. This is one class of ring network.....in a BLSR, how well are the w i quantities “balanced” ? (since the largest of them dictates the protection capacity).....to what extent does a given ring tend to serve demands that both originate and terminate in the same ring.....a multi-ring design may not “cover” all graph edges, if the working demands can take non-shortest path routes.....for the highest service availability, some demands may employ geographically redundant duplicate inter-ring transfers....not all nodes may be sites where demands can switch rings.....each ring needs ADMs where demands add / drop, but not elsewhere ( ~> Express rings etc.). Key concepts, issues, and principles in multi-ring design

6. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 6 a set of rings that uses or overlies all edges of the physical facilities graph is called a “ring cover”. “Coverage-based” design is a special (simpler) case of multi-ring design. More generally the aim is to protect all demands, not necessarily to “cover all spans.” a three ring “cover” a single ring design that may also serve all demands… Q. what is implied? example “span eliminations” “Graph coverage” and the concept of span elimination

7. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 7 how the routing of demands varies to accommodate “span eliminations” coverage to “eliminate” span (2-5) “Graph coverage” and concept of span elimination

8. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 8 problem statements “ protect every transmission span of the network by including it in a ring “ “ serve all demands in a protected manner end to end across the network “ - leads to built in presumption of coverage -type designs - working demands follow shortest paths independent of later ring choices - coverage formulations can form starting point for designs with span eliminations. coverage design with span eliminations - simpler, idealized “academic” problem - leads to solutions using only subset of available graph edges - over wide design ranges eliminations reduce # rings, reduce total cost. - However, span eliminations can be taken too far. (ring capacity requirements grow due to excessive re-routing) - more complex, but realistic planning problem. - routing policy no longer shortest paths, but coupled to ring selections and loading. (more later...algorithms for finding good span eliminations) “Graph coverage” and concept of span elimination

9. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 9 “drop-and-continue” method for BLSRs (also called a “matched nodes arrangement”- Nortel) Building 1 Concept of dual-ring interconnect (DRI)-1 Building 2

10. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 10 “drop-and-continue” method for BLSRs normal “drop”, cross-office wiring, then “adds” into r 2 Concept of dual-ring interconnect (DRI)-2 Drop Add

11. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 11 the primary gateway node has a 1+1 receive selection setup here. protected by BLSR line-loopback reaction in r1 protected by BLSR line-loopback reaction in r2 protected by 1+1 APS inter-ring setup Concept of dual-ring interconnect (DRI)-3 “drop-and-continue” method for BLSRs

12. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 12 each ADM in a UPSR already has 1+1 intra-ring receive selection setup here. just add dual geographically diverse transitions and suppress normal signal splitting in receiving ADMs for ring 2. Concept of dual-ring interconnect (DRI)-4 “drop-and-continue” method applied to interconnect UPSRs

13. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 13 Explicit dual-feeding...”df” explicit dual feeding uses up more intra-ring line capacity, but in some cases uses even less drop-and-continue capacity (inter-ring transition nodes need not be adjacent) this will be part of a later optimal routing policy using mixtures of “mn” and “df” inter-ring transitions along an end-to-end path. Concept of dual-ring interconnect (DRI)-5

14. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 14 RCG is a transformation of the graph that represents the opportunities to transition from ring to ring. example: with ring-set given, r1 is connected to r2 through only one node. For DRI routing, only the RCG edges with 2 or more parallel arcs are available for routing Concept of a Ring Connectivity Graph (RCG)

15. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 15 Routing Efficiency: a measure of how well demands are routed through the network (i.e., average hops/demand). Good (intrinsic) routingPoor (instrinsic) routing (but may increase ring balance or capture) Concepts of Balance, Capture (and routing)-1

16. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 16 Balance (Capacity) Efficiency: a measure of how evenly the working span capacities are matched in the rings (i.e., average fill). OC-12 1012 8 35 0 Good Balance Poor Balance (but could have good capture)... Concepts of Balance, Capture (and routing)-2

17. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 17 sink from source Capture Efficiency: a measure of how well the rings contain the demands that they carry, in terms ideally of delivering them from source to sink within the same ring. (i.e., relevance is to the cost of inter-ring transitions). Good CapturePoor Capture L is the number of spans on the ring, in the path of the demand T is the number of transitions on or off of the ring (excluding those at source / sinks) source to sink for demands shown: L = 2 T = 0 L = 1 T = 2 Concepts of Balance, Capture (and routing)-3

18. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 18 $ Routing Efficiency Balance Efficiency Capture Efficiency Network Topology (average nodal degree) long haul tendency $ Routing Efficiency Balance Efficiency metro area design tendency Capture Efficiency low degree or eliminations to reduce # rings higher degree to shorten average distance-related costs Effects of Routing, Balance, and Capture on design

19. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 19 SCIP = “span coverage IP” Assumes: working demands already routed -> i.e., w i values are given rings have ADMs in every node (no glass-throughs) demands can transition between rings at any node there are no costs for inter-ring transitions Let: SCIP: A formulation for idealized “pure coverage” design

20. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 20 SCIP: minimize cost of all rings placed, of each modular size decisions are to place only a whole number of rings of each modular capacity and layout ensure sum of all modules overlying any span meets or exceeds its working capacity SCIP: A formulation for idealized “pure coverage” design

21. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 21 SCIP contains several idealizations but: - is optimally solvable for small-medium sized problems. - can be used as a starting point for improvement heuristics. - identifies ring choices with very high “balance” efficiency. - can be viewed as a upper bound on expected design cost when routing, glass-throughs, span-eliminations and transition costs are also optimized. - can be used as a “surrogate” for ring network design cost in comparative studies (where relative, not absolute costs matter as the figure of merit). Class Question: Given the idealizations in SCIP, are its designs more realistic / accurate for: (a) metropolitan-scale network design (b) long-haul network design ? Answer: In the long-haul design context ADM node, glass-through, and transition costs are usually less important than transmission capacity efficiency, which correlates strongly to shortest path routing and balance-optimized ring choices. Comments on SCIP

22. Other approaches to Multi-Ring Network Design

23. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 23 Other approaches to Multi-Ring Network Design Roberts - simulated annealing ( U. Colorado Grad Seminar 1994 ) objective: minimize redundancy of an ideal ring span cover of the graph demands are shortest-path routed beforehand, cycle set enumerated beforehand (by DFS) only BLSR (ideal) rings are considered starts with an identical RingBuilder 1.0 -like greedy-iterative buildup of a ring cover based on ideal ring balance efficiency.

24. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 24 Other approaches to Multi-Ring Network Design Roberts - simulated annealing ( 1994 ) Simulated Annealing Algorithm - Initial design is represented by an ordered set of ring candidates. - At each iteration, the design is randomly “shuffled” to generate a new design. - Uses “segment reverse” and “segment move” operations randomly - The redundancy of the new design is calculated and if it lower than the redundancy of last solution, the new design is saved. - Otherwise, there is still some probability (determined by an Acceptance Criterion) that the new design will be saved. - The probability of accepting a higher redundancy designs decreases as the algorithm proceeds, i.e “cools.”

25. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 25 Other approaches to Multi-Ring Network Design Roberts - simulated annealing ( 1994 ) Accept higher redundancy? No Yes Recalculate acceptance criterion Save new design Calculate redundancy Change cycle order (r i < r i-1 ) ? Max. iterations reached? Yes End No Start No Reverse Segment 1 2 | 3 4 5 | 6 1 2 | 5 4 3 | 6 Choose and Insert 1 2 3 | 4 5 | 6 1 | 4 5 | 2 3 6..or...

26. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 26 Simulated Annealing ( partial illustration ) Methodology (cont’d) 7 7 54 2 3 9 2 Initial NetworkCycle Set = {1,2,3,4,5,6} 12 34 5 6 Apply Cycle 1 7 7 54 2 3 9 2 0 0 54 2 3 9 0 Apply Cycle 2 0 0 50 0 3 0 0 Apply Cycle 3

27. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 27 Other approaches: Gardner - Eulerian ring covers (Gardner et al., Globecom ‘94) Objective Find the min-cost set of rings that covers every span at least once. Key Assumptions & Constraints - Demand routing is determined a priori. - Cost is proportional to the working capacity on each span. - Ring capacity is infinite (i.e., “ideal rings”). Methodology: (for Unidirectional Rings): where w ij r is the working capacity on span ij in ring r and R is the set of rings in the design. - Min. cost ring cover is one which covers all spans without overlapping any span. - If an Eulerian cycle exists, the min. cost ring cover is obtained by decomposing the Eulerian cycle into rings.

28. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 28 Eulerian Ring Covers (cont’d) Methodology - Unidirectional Eulerian CycleRing CoverEulerian Graph 6 1 1 9 6 4 4 62

29. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 29 Eulerian Ring Covers (cont’d) Methodology for UPSR –When a network graph is not Eulerian, it can be converted to a Eulerian graph by adding links between nodes with odd degree. –Minimum weight matching is used to find the min. cost path(s) to add to the graph to make it a Eulerian graph. Non-Eulerian GraphRing CoverEulerian Cycle Links Added 9 7 54 3 3 6 2

30. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 30 Eulerian Ring Covers (cont’d) Methodology for BLSR: Problem is NP-complete, therefore 3 heuristic methods proposed for finding ring covers. All heuristics use a depth-first search to locate rings which are then selected iteratively to construct a ring cover. - Greedy: Selects first ring found. - Longest Feasible Ring: Selects longest ring  16 nodes - Maximally Separated Rings: Selects spans not yet included in the ring cover, if possible, to construct rings.

31. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 31 Objective –Find min-cost hierarchical SHR design that serves all demands. Key Assumptions & Constraints – where a and b are constants, l ij is the length of span ij,  is a “capacity/demand ratio” * and d ij is the demand between nodes i & j. –Ideal rings. All rings have the same, fixed, number of nodes*. –Rings are arranged in hierarchical levels for routing inter-ring demands. –All demands are served by level-1 rings. –Each ring has two adjacent supernodes which are connected to the next higher level ring. Other approaches: Shi & Fonseka - Hierarchical rings ( ICC ‘96 ) basic idea: * i.e., 1 for UPSR ~ 0.7 or 0.8 for BLSR

32. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 32 Other approaches to Multi-Ring Network Design Shi & Fonseka - Hierarchical rings Methodology (first, build the lower tier rings, then dual-homed backbone ring...) 1. Select the node pair with the minimum distance related cost minus demand related cost, i.e., 2.Add the next node k to the partial ring that minimizes the distance related cost minus the sum of the demand related costs, i.e. h k

33. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 33 Other approaches : Shi & Fonseka - Hierarchical rings Method ology (cont’d) 3.Repeat step 2 until the max. no. of nodes per ring is reached. 4.Connect the head and tail of the path to complete the ring. 5.Select 2 supernodes which are adjacent and satisfy: j i k

34. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 34 Hierarchical Rings (cont’d) Methodology (cont’d) 6.Repeat steps 1-5 until all nodes are covered by a level-1 ring. 7.Repeat the same basic process to link super-nodes together to form a level-2 ring, and so on. 8.After rings have been placed, demands are routed using shortest path routing and the capacity of each ring is determined. Level-1 SHR Level-1 SHR Level-2 SHR Level-1 SHR

35. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 35 Net Solver (Gardner, et al., Globecom ‘95) Objective –Find min-cost ring design that serves all demands. Key Assumptions & Constraints –Cost is calculated based on fixed and variable costs. –Requires an initial ring design. –Ring capacity is fixed and modular (rings not “ideal”). Methodology 1. Route demands over the initial set of rings using either (1) shortest path, (2) shortest ring transition, or (3) minimum congestion routing (user-defined). 2.Compute the total cost of the initial design. 3.Generate a set of alternative ring designs by modifying the initial ring design using three different ring operations: (1) split; (2) merge; and (3) enlargement.

36. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 36 Net Solver (cont’d) Ring Operations R R1R1 R2R2 R R R’ R1R1 R2R2 (a) Split operation (b) Merge operation (c) Enlargement operation

37. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 37 Net Solver (cont’d) Methodology (cont’d) 4.Route demands and compute the total cost for each alternative design. 5.Select the design with the lowest total cost. 6.Repeat steps 3-5 until no further improvements in cost can be obtained. Capabilities –BLSR, UPSR and mixed designs. –Accounts for fixed ring capacities. –Identifies the location of active/passive nodes and demand routing.

38. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 38 Summary Comparison of Methods

39. Comparison of Mathematical Programming Approaches to Optical Ring Network Design CCBR '99 Ottawa, Canada, November 7-9, 1999 Dave Morley and Wayne Grover TRLabs and University of Alberta selected slides from....

40. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 40 parameters and variables... - copies of candidate ring j in design. - set of spans in the network topology. - capacity of BLSR j. - working load on span s. - set of candidate rings (BLSRs). - “fixed cost” (optical line costs) of ring j. - set of routes for all demands. - set of all demands. - add/drop cost of carrying route i on ring j. - termination cost for route i. - size of demand bundle k. - flow of working route i. - flow of route i carried by ring j. costs & capacities demands and routing decision variables

41. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 41 Pure span coverage IP Span Coverage (SCIP) 1.Route demands over network topology and calculate working load w s on each span. 2.Generate a set of ring candidates (topology, ring type and capacity) and calculate ring candidate costs. IP1: SCIP,, Minimize: Subject to: (2) integer, (3) (1) “place X copies of ring candidate j”

42. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 42 “Fixed Charge and Routing” Fixed Charge and Routing (FCIP) (new for today...) 1.Generate a set of several possible routes for each demand. 2.Generate a set of ring candidates (topology and ring type) and calculate ring candidate costs. Minimize: IP2: FCRIP Subject to: (1), (2),, (3),, (4)

43. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 43 Understanding “Fixed Charge and Routing” approach O D ring three possible routes for demand pair k, I(k) (2) sum of flow F(i) to each route I(k) = d k route and flow for other demand pairs span s (4) capacity greater than sum of flows crossing span routing dependent add/ drop costs add/ drop costs (“fixed” optical line cost) (3) amongst “stacked” ring spans allocation of each ring’s portion of flow sums to total on the given route for that O-D pair Key idea: Solver is free to choose rings are routing of flows jointly, to min cost of rings plus inter-ring add/ drop transition costs

44. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 44 Study Method Net15Net20 Net32Net43 Long-haul Metro Test Networks

45. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 45 Study Method (cont’d) Modeling Assumptions –Ring types: 12- OSPR and 48- OSPR. –Cost model: 4 times capacity for twice the cost. –No restrictions on inter-ring transition locations. Experimental Procedure 1.Formulated each IP in AMPL mathematical programming language. 2.Populated AMPL data sets. 3.Generated problem instances using AMPL and solved with CPLEX. 4.Entered solutions into SONET Planner (Nortel Networks) to obtain final detailed costing.

46. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 46 Results Cost ($000s) * - time limit exceeded, best feasible solution shown.

47. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 47 Results (cont’d) Runtime* (seconds) RingBuilder SCIPFCRIP Net15 6.21.6 43,200 Net20 10.538.7 43200 Net32 8.5361 43,200 Net45 1,233 43,200 - 43,200 sec = 12 hour run-time limit