The “Forcer” Concept & Forcer-Clipping Ring-Mesh Hybrid Networks E E Module 14 W.D. Grover TRLabs & University of Alberta © Wayne D. Grover 2002, 2003

E E Module 14 © Wayne D. Grover 2002, If AC is cut, 5 restoration paths exist on ABC and 5 on ADC. If AB is cut, 2 restoration paths exist on ACB and 5 on ADCB. – > AB ‘forces’ 7 spares on BC Similarly, Span AC is the forcer for spans AB, AD, and DC (5 spare links) Forcer threshold is the decrease needed (in the number of working links) to change a forcing span into a non-forcer (for AB that would be 3). 2 ( 10, 2) B A C D (2, 5) (2, 7 ) (3, 5) (7, 5) 5 B A C D (2, 5 ) (2, 7) (3, 5 ) (7, 5 ) 5 5 (working,spare) B A C D ( 10, 2) (2, 5) (2, 7) (3, 5) (7, 5) Why does span BC have 7 spares in this design? Introducing the “Forcer” Concept:

E E Module 14 © Wayne D. Grover 2002, The Forcer Concept (by example) Span Number Working links, Spare links, Forcer Magnitude Forcer Span “Forcer Skeleton” Network 1 - “Bellcore” (NJ LATA) - with published demand data - 11 nodes - 23 spans - Average degree = 4.2 Notes: Forcers are red Forcer magnitudes are the amount of w i by which the given span is above the threshold of being a forcer. Non-forcers has a negative forcer magnitude indicating how many w i additions are possible without requiring any increase in total network spare capacity. “ All non-forcer spans could have w i =0 and the total spare capacity for 100% span restorability would not be any lower.” The forcer skeleton alone accounts for all the spare capacity required in the optimal design.

E E Module 14 © Wayne D. Grover 2002, Formal Statements Preamble: –In general, for any span j, there will always be some other span i, which will require a number of spare links on j, that is equal to or greater than that required by any other failure span. –When this relationship is true, we say that span i is the forcer (or a co-forcer) of span j. re: co-forcer: more than one span may require the same number of spares on span j, so the forcer relationships may be many-to-one. Definition: A forcer span is any span for which an increase in network total sparing is required to maintain restorability if the span's working capacity is increased. –Conversely, a non-forcer is a span on which at least one working link may be added without requiring any additional spare capacity for the network to remain 100% restorable. “Super-restorability”

E E Module 14 © Wayne D. Grover 2002, Algorithms for forcer analysis 1. Iterate the mesh spare capacity optimal solution: –idea is to observe change in as w i values are reduced. solve an initial mesh spare capacity placement (scp) problem - for given set of w i - record scp 0 = for every span - j:=0; spare_tot(j) := scp 0 repeat w i := w i -1 ; j:=j+1 ; re-solve scp ; spare_tot(j) < spare_tot(j-1) ? if no, span i is a (now) a non-forcer; done_loop := true if yes, span i is a (still) a forcer until done_loop (and exit with j-1 as the “forcer strength” of span i)

E E Module 14 © Wayne D. Grover 2002, Use a routing model of the restoration process: –idea is to discover which failures fully require the s i values found on other spans. solve an initial mesh spare capacity placement (scp) problem for every span x (taken as a failure span) - run “ksp” as a simulation of the restoration process - for every span i in the ksp pathset for failure x: - record s i (x) - the number of spares on span i used upon failure of span x. - if (s i (x) = s i ) then span x is a forcer of span i. - else (if s i (x) < s i then span x is not a forcer of span i.) until {done all spans, x} (and exit with the matrix of s i (x) values ) Algorithms for forcer analysis

E E Module 14 © Wayne D. Grover 2002, Information encoded in the s i (x) results A. the logical forcer structure: for span i, every other span x such that (s i (x) = s i )… is a (co-) forcer of span i. for every span i, there must be at least one such other span x Class: (or else what...?) non-forcers are spans x such that s i (x) = s i is false for every i B. measures of forcer magnitude:.... (next slide) when span x fails..... how much spare does it use on span i ? s i (x) table (x,i) where s i (x) = s i

E E Module 14 © Wayne D. Grover 2002, x = a particular span, considered in its role as a possible forcer span i, j = other spans of the network. s i (x) = amount of spare capacity used on span i, by restoration of span x. Forcing Strength of span x on a specific other span i : Measures of Global Forcer Strength of span x: Or... Logical Forcer status of a span x “ latent forcer ” Measures of Forcer Magnitude encoded in the s i (x)...

E E Module 14 © Wayne D. Grover 2002, Understanding the forcer magnitude and “latent forcer” relationships Span x Span j Span i Forces 14 spares for its restoration Requires 10 spares on span i for its restoration Span j Span k... All other spans require < 10 spare on span i i.e. span j is the next latent forcer. Aside from x itself, no other span requires as much spare on i as does span j. This D is the “forcer magnitude” of x on i.

E E Module 14 © Wayne D. Grover 2002, Motivation: –Hybrid designs may be lower in cost than pure ring or pure mesh. Pure ring designs typically contain some very inefficient individual rings Efficiency of pure mesh designs may be limited by dominant forcer effects ( demand-topology interactions, to be explained). reference paper: W.D. Grover, R.G. Martens, “Forcer-Clipping: A Principle for Economic Design of Ring-Mesh Hybrid Transport Networks”, accepted (July 2000) for publication in Information Technology and Management, Special Issue on Design of Communication Networks. An approach to ring - mesh hybrids based on the forcer analysis of mesh networks

E E Module 14 © Wayne D. Grover 2002, DCS / OCX mesh Termination costs  Network redundancy  Protection - only dropped traffic needs terminations ADM / OADM rings Termination costs  Network redundancy  W S1S1 S3S3 S2S2 W1W1 W2W2 W DCS DCS/OXC based $ RING MESH  ADM/OADM based $$  Sparing high $$    Sparing low $  W3W3 S Why hybrids?: Comparing ADM-based rings and X- connect based mesh

E E Module 14 © Wayne D. Grover 2002, Physical Topology Logical Demand Ring-2 Ring-1 Selected “Forcer clipping” Rings “ Residual Mesh” ADM Glassthrough X-connect hybrid transport network A first view of the hybrid concept being considered...

E E Module 14 © Wayne D. Grover 2002, This is not a “multi-layer scheme” in the sense of involving fault escalation. Every demand is protected on each segment of its route either in a ring- or a mesh-survivability domain. Both ring and mesh components act simultaneously and independently to protect demand segments in their domains An important clarification…

E E Module 14 © Wayne D. Grover 2002, The “forcer-clipping” hypothesis Preamble: –Measures such as F*(x) let us pinpoint which spans most drive the spare capacity requirements of the surrounding restorable mesh network design. –F*(x) reflects the total 'height' by which span x's working link quantity is above the point at which it would no longer be a forcer (i.e., other spans would become forcers, halting the relief of spare capacity) Main idea: –if the strongest forcers were removed or lowered, the complete mesh network would become more efficient –maybe rings could be used to “clip off” these worst forcers.... –hypothesis: a ring might be placed on the mesh network to 'clip the tops' off of one or more of the forcer spans, thereby more than proportionally reducing its total working and spare capacity cost. Net cost reductions would arise if the cost of the forcer-clipping ring is less than the net savings in the underlying mesh layer after its working capacity is adjusted and its spare capacity plan is re-optimized.

E E Module 14 © Wayne D. Grover 2002, Self-contained BLSR “clips” off strong forcers Reduces & levels underlying mesh Residual mesh forcer landscape and “forcer-clipping” rings Forcer span spare capacity Forcer span ‘hidden’ forcer “forcer” landscape of a pure- mesh network For certain ring placements, economies may arise from: 1) enhancement of the residual mesh capacity efficiency, due to forcer clipping 2) creation of a well-loaded ring, displacing w i quantities from the mesh, lowering relative termination costs. The “Forcer Clipping” Hypothesis Rings could “clip the tops off ” strong forcers in the mesh, resulting in net savings, exceeding the cost of the rings.

E E Module 14 © Wayne D. Grover 2002, A F G Z E C B (9,10) (7,14) (16,14) (10,10) (16,0) (9,10) (14,20) (29,16) (30,15) Pure mesh: Redundancy = 129 / 154 = 0.84 (9,9) (7,8) (16,8) (10,9) (16,3) (9,10) (2,9) (17,10) (18,9) Test ring 1: Revised mesh: Redundancy = 84 / 106 = 0.79 Capacity return ratio = (129-84) + ( ) 4 x 12 x 2 = just to see the nature of how ring and mesh interact in a capacity-design sense - not yet guided by forcing clipping principle, but quantitatively exact mesh network redesigns following each ring trial placement Example uses a 12 unit-capacity ring Example of some actual ring-placement trials “Capacity return ratio” = total (mesh working + re-designed sparing) reduction total (w + s) capacity represented by ring placement High CRR --> good economics

E E Module 14 © Wayne D. Grover 2002, A F G Z E C B (9,10) (7,14) (16,14) (10,10) (16,0) (9,10) (14,20) (29,16) (30,15) Pure mesh: Redundancy = 129 / 154 = 0.84 (9,10) (0,13) (4,3) (10,10) (16,0) (9,10) (14,20) (17,17) (30,14) Test ring 2: Revised mesh: Redundancy = 117 / 123 = 0.95 Capacity return ratio = ( ) + ( ) 4 x 12 x 2 = just to see the nature of how ring and mesh interact in a capacity-design sense - not yet guided by forcing clipping principle, but quantitatively exact mesh network redesigns following each ring trial placement “Capacity return ratio” = total (mesh working + re-designed sparing) reduction total (w + s) capacity represented by ring placement High CRR --> good economics Example uses a 12 unit-capacity ring Example of some actual ring-placement trials

E E Module 14 © Wayne D. Grover 2002, Heuristic 1: sums the global forcer magnitudes F*(x) of spans in the cycle - Heuristic 2: looks at the fraction of logical forcers in the cycle, i.e. Forcer analysis of initial mesh Find all cycles of network graph Use forcer assessments to build ranked “short-list” of ring placements Place a “short-list” ring Residual mesh re-design Assess total economic impact Callable CPLEX Place max-payback ring and permanently alter the residual mesh design Repeat until no further rings prove-in no further gain from any ring at least one ring proves in Heuristic Algorithms based on “Forcer Clipping”

E E Module 14 © Wayne D. Grover 2002, Heuristic Algorithms: Details

E E Module 14 © Wayne D. Grover 2002, Step 1: Forcer Analysis Stage Pure Mesh Reference Spare Capacity: 625 Working Capacity: 1252 Total Capacity: 1877 Very weak forcers (F*(x)=1) are ignored here Example

E E Module 14 © Wayne D. Grover 2002, Spare Capacity: 625  323 Working Capacity: 1252  730 Total Cost: 1877  1705 After 3 ring placement iterations OC-48 BLSR (x3) Ring Cost Factor = 0.8 Net Cost Reduction: 172 (9%) Example (cont’d)

E E Module 14 © Wayne D. Grover 2002, Residual Mesh Resultant - lower spare capacities - increased mesh efficiency Example (cont’d)

E E Module 14 © Wayne D. Grover 2002, (for assessment of heuristic performance) Minimize: cost of spare and working in mesh, plus costs of rings placed. Subject To: 1) The mesh must be restorable: Y i = set of eligible rest routes for span i x ip = restoration flow assigned to p th elig. route for restoration of span i. 2) The mesh working capacity is reduced by rings: R = set of all cycles of graph 3) Restoration sparing for the residual mesh: Z i j = { Y i : route contains span j } 4) Ring capacity is modular (M modularities): b q is the working capacity offered by the q th modular ring size. An Optimal Formulation Reference: W. Grover, R. Martens, "Optimized design of ring-mesh hybrid networks,” Proc. DRCN 2000.

E E Module 14 © Wayne D. Grover 2002, Ü 12, 24, 48-unit module ring capacities Ü {2  cost  4  capacity} economy-of-scale model for rings Ü 4-fibre BLSR ring capacity model Ü ADM-ring cost / unit installed capacity = mesh * cost 24 - unit modular capacity (see next slide) Ü ‘gravity type’ point-to-point demand patterns Other Data for Results:

E E Module 14 © Wayne D. Grover 2002, “Cost factor” is defined as relative cost per physical unit capacity to average DCS-terminated unit capacity in mesh for OC-24 ring relative cost scale: ring / mesh Mesh (per unit capacity) Rings (modular at sizes 12, 24, 48) OC-12 OC-24 OC-48 May apply economy of scale rule, e.g., 4 times capacity for 2 times cost Example: Cost factor = 0.8 implies that an OC-24 ring span (actually representing 48 units of capacity) is cost -equivalent to 0.8 (48) = 38.4 units of capacity on a mesh span Ring relative cost then scales up or down according to the economy of scale model employed Ring-Mesh Relative Costing Model

E E Module 14 © Wayne D. Grover 2002, Ring cost factor = 0.8 Objective function values, (% savings), execution time, number of rings “Cost savings” are relative to objective function value for “pure-mesh” * * result obtained with MIPGAP = 200 Some Results ( … where optimal and heuristic can be compared)

E E Module 14 © Wayne D. Grover 2002, Ring cost factor = 0.6 Objection function values (total cost), execution times, and number of rings placed * result from optimal formulation after 24 hours Some Results ( … where optimal and heuristic can be compared)

E E Module 14 © Wayne D. Grover 2002, Heuristic #2 % savings over optimal pure mesh Number of rings placed CPU time Net #4 19 nodes 39 spans Net #5 16 nodes 29 spans Net #6 27 nodes 48 spans 23.8% 8 rings 11.9 hrs 38.6% 12 rings 1.0 hr 39.5% 11 rings 2.3 hrs Other Results (where only the heuristic can go):

E E Module 14 © Wayne D. Grover 2002, But if rings are less costly, won’t the solution just slide to an all-rings design ? No: There is a true Cross-Architectural Optimum design point Network #1, Heuristic #2 Ring Cost Factor = 0.8 Test case where heuristic was compelled to place one more ring (4) than it wanted. Question

E E Module 14 © Wayne D. Grover 2002, Insights - understanding hybrid and why it “works” A good forcer clipping ring pays for itself by: (1) attaining good utilization for itself, while displacing mesh capacity (2) enhancing the mesh efficiency through forcer-levelling. But even when ring transport is up to 40% cheaper than mesh, architectural aspects lead to a hybrid - not a pure ring outcome. - why? Pure ring or pure mesh now seen to arise only as limiting cases: –(1) “rings must be rings” …closing the circle limits ring efficiency. –(2) mesh residual become more and more efficient (because it becomes more forcer leveled) and eventually no ring addition can pay off anymore Why is the prediction of “forcer levelling” in the residual meshes not more evident in the results than actually seen? When rings are placed they scour out mesh capacity to their full depth, not just the forcer peaks they were placed to ‘clip’.

E E Module 14 © Wayne D. Grover 2002, The “forcer-clipping” hypothesis is suggested as an effective principle in ring-mesh hybrid network design. Advent of DCS with integrated ADM shelf functionality motivates / enables this type of true hybrid. Heuristics observed to be within ~ 5% of optimal for test cases –This is taken as confirming the basic validation of the forcer-clipping insight. Heuristic #2 seems superior, and executes in reasonable time for large problems –Heuristic 2 thought to be “selecting in” more co-forcer and latent-forcer combinations which the economic trial placements then discover and exploit This work suggests that in general even mesh networks should be examined for “express ring” opportunities. Summary of Main Findings