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Cc wdm network design Cc wdm network design Presentation Transcript

  • This teaching material is a part of e-Photon/ONe Master study in Optical Communications and Networks Course and module: Optical Core Networks WDM Network Design Author(s): Massimo Tornatore, Politecnico di Milano, tornator@elet.polimi.it Guido Maier, Politecnico di Milano, maier@elet.polimi.itThis tutorial is licensed under the Creative Commons http://www.e-photon-one.orghttp://creativecommons.org/licenses/by-nc-sa/3.0/
  • Outline • Introduction to WDM network design and optimization • Integer Linear Programming approach • Physical Topology Design − Unprotected case − Dedicated path protection case − Shared path & link protection cases • Heuristic approachAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 2 (81)Module: WDM Network Design
  • WDM networks: basic conceptsLogical topology CR1 Electronic-layer connection request Electronic switching node CR3 (DXC, IP router, ATM switch, etc.) CR2 Optical network access point CR4 WDM WDM network LOGICALTOPOLOGY WDM network nodes • Logical topology (LT): each link represent a lightpath that could be (or has been) established to accommodate traffic • A lightpath is a “logical link” between two nodes • Full mesh Logical topology: a lightpath is established between any node pairs • LT Design (LTD): choose, minimizing a given cost function, the lightpaths to support a given trafficAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 3 (81)Module: WDM Network Design
  • WDM networks: basic conceptsPhysical topology WDM optical-fiber link Optical path termination Optical Cross Connect (OXC) Wavelength converter WDM PHYSICAL TOPOLOGY • Physical topology: set of WDM links and switching-nodes • Some or all the nodes may be equipped with wavelength converters • The capacity of each link is dimensioned in the design phaseAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 4 (81)Module: WDM Network Design
  • WDM networks: basic conceptsMapping of logical over physical topologyMapping is different CR1 CR3according to the factthat the network isnot (a) or is (b) provided CR2 CR4with wavelengthconverters LP1 LP1 LP2 LP3 LP2 LP3 LP = LIGHTPATH (a) (b) λ1 λ2 λ3 LP4 LP4 Optical wavelength channels • Solving the resource-allocation problem is equivalent to perform a mapping of the logical over the physical topology − Also called Routing Fiber and Wavelength Assignment (RFWA) • Physical-network dimensioning is jointly carried outAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 5 (81)Module: WDM Network Design
  • Static WDM network planningProblem definition • Input parameters, given a priori − Physical topology (OXC nodes and WDM links) − Traffic requirement (virtual topology) • Connections can be mono or bidirectional • Each connection corresponds to one lightpath than must be setup between the nodes • Each connection requires the full capacity of a wavelength channel (no traffic grooming) • Parameters which can be specified or can be part of the problem − Network resources: two cases • Fiber-constrained: the number of fibers per link is a preassigned global parameter (typically, in mono-fiber networks), while the number of wavelengths per fiber required to setup all the lightpaths is an output • Wavelength-constrained: the number of wavelengths per fiber is a preassigned global parameter (typically, in multi-fiber networks) and the number of fibers per link required to setup all the lightpaths is an outputAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 6 (81)Module: WDM Network Design
  • Static WDM network planningProblem definition (II) • Physical constraints − Wavelength conversion capability • Absent (wavelength path, WP) • Full (virtual wavelength path, VWP) • Partial (partial virtual wavelength path, PVWP) − Propagation impairments • The length of lightpaths is limited by propagation phenomena (physical-length constraint) • The number of hops of lightpaths is limited by signal degradation due to the switching nodes − Connectivity constraints • Node connectivity is constrained; nodes may be blocking • Links and/or nodes can be associated to weights − Typically, link physical length is consideredAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 7 (81)Module: WDM Network Design
  • Static WDM network optimizationProblem definition (III) • Routing can be − Constrained: only some possible paths between source and destination (e.g. the K shortest paths) are admissible • Great problem simplification − Unconstrained: all the possible paths are admissible • Higher efficiency in network-resource utilization • Cost function to be optimized (optimization objectives) − Route all the lightpaths using the minimum number of wavelengths (physical- topology optimization) − Route all the lightpaths using the minimum number of fibers (physical-topology optimization) − Route all the lightpaths minimizing the total network cost, taking into account also switching systems (physical-topology optimization)Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 8 (81)Module: WDM Network Design
  • Static WDM network optimizationComplexity • Routing and Wavelength Assignment (RWA) [OzBe03] − The capacity of each link is given − It has been proven to be a NP-complete problem [ChGaKa92] − Two possible approaches • Maximal capacity given ⇒ maximize routed traffic (throughput) • Offered traffic given ⇒ minimize wavelength requirement • Routing Fiber and Wavelength Assignment (RFWA) − The capacity of each link is a problem variable − Further term of complexity ⇒ Capacitated network − The problem contains multicommodity flow (routing), graph coloring (wavelength) and localization (fiber) problems − It has been proven to be a NP-hard problem (contains RWA)Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 9 (81)Module: WDM Network Design
  • Optimization problemsClassification • Optimization problem – optimization version − Find the minimum-cost solution • Optimization problem – decision version (answer is yes or no) − Given a specific bound k, tell me if a solution x exists such that x<k • Polynomial problem − The problem in its optimization version is solvable in a polynomial time • NP problem − Class of decision problems that, under reasonable encoding schemes, can be solved by polynomial time non-deterministic algorithms • NP-complete problem − A NP problem such that any other NP problem can be transformed into it in a polynomial time − The problem is very likely not to be in P − In practice, the optimization-problem solution complexity is exponential • NP-hard problem − The problem in its decision version is not solvable in a polynomial time (is NP-complete) ⇒ the optimization problem is harder than an NP-problem − Contains an NP-complete problem as a subroutineAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 10 (81)Module: WDM Network Design
  • Optimization problem solutionOptimization methods • WDM network optimal design is a very complex problem. Various approaches proposed − Graph coloring • Mainly for WP networks (with no converters) − Ring techniques • In certain cases it can be extended to arbitrary physical topology − Integer linear programming (ILP) • The most general exact method − Heuristic methods • A very good alternative to ILP for realistic dimension problems • According to the cost function, the problem is − Linear *E.g.: traffic matrix representation cxy = 1 if a connection is required between the − Non linear nodes x and y, cxy = 0 otherwiseAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 11 (81)Module: WDM Network Design
  • Outline • Introduction to WDM network design and optimization • Integer Linear Programming approach • Physical Topology Design − Unprotected case − Dedicated path protection case − Shared path & link protection cases • Heuristic approachAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 12 (81)Module: WDM Network Design
  • Optimization problem solutionMathematical programming solving • WDM-network static-design problem can be solved with the mathematical programming techniques − In most cases the cost function is linear ⇒ linear programming − Variables can assume integer values ⇒ integer linear programming − NP-complete/hard problems ⇒ computational complexity grows faster than any polynomial function of the size of the problem − Matches very well with algebraic network modeling • LP solution − Variables defined in the real domain − The well-known computationally-efficient Simplex algorithm is employed • Exponential complexity, but high efficiency • ILP solution − Variables defined in the integer domain − The optimal integer solution found by exploring all integer admissible solutions • Branch and bound: admissible integer solutions are explored in a tree-like searchAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 13 (81)Module: WDM Network Design
  • ILP application to WDM network designApproximate methods • A arduous challenge − NP-completeness/hardness coupled with a huge number of variables − In many cases the problem has a very high number of solutions (different virtual-topology mappings leading to the same cost-function value) − Practically tractable for small networks • Simplifications − RFWA problem decomposition: first routing and then f/w assignment − Route formulation with constrained routing − Relaxed solutions • ILP, when solved with approximate methods, loses one of its main features: the possibility of finding a guaranteed minimum solutionAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 14 (81)Module: WDM Network Design
  • ILP application to WDM network designILP relaxation • Simplification can be achieved by removing the integer constraint − Connections are treated as fluid flows (multicommodity flow problem) • Can be interpreted as the limit case when the number of channels and connection requests increases indefinitely, while their granularity becomes indefinitely small • Fractional flows have no physical meaning as they would imply bifurcation of lightpaths on many paths − LP solution is found • In some cases the closest upper integer to the LP cost function can be taken as a lower bound to the optimal solution • Not always it works… • See [BaMu96]Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 15 (81)Module: WDM Network Design
  • Notation k l • l,k: link identifiers (source and destination nodes) • Fl,k: number of fibers on the link l,k ∀ λl,k: number of wavelengths on the link l,k • cl,k: weight of link l,k (es. length, administrative weight, etc.) − Usually equal to ck,lAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 16 (81)Module: WDM Network Design
  • Cost functionsSome examples • RFWA − Minimum fiber number M • Terminal equipment cost min ∑F (l ,k ) l ,k = min M − VWP case (cost of transponder) − Minimum fiber mileage (cost) MC • Line equipment [BaMu00] min ∑c (l ,k ) l ,k Fl ,k = min M C • RWA − Minimum wavelength number min ∑λ = min Γ (l ,k ) l ,k − Minimum wavelength mileage min ∑c λ = min Γ l ,k l ,k C • [StBa99],[FuCeTaMaJa03] (l ,k ) − Minimum maximal wavelength min [max λl ,k ] = min ΓMAX l ,k number on a link • [Mu97]Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 17 (81)Module: WDM Network Design
  • Outline • Introduction to WDM network design and optimization • Integer Linear Programming approach • Physical Topology Design − Unprotected case − Dedicated path protection case − Shared path & link protection cases • ReferencesAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 18 (81)Module: WDM Network Design
  • Approaches to WDM design • Two basilar and well-known approaches [WaDe96],[Wi99] − FLOW FORMULATION (FF) − ROUTE FORMULATION (RF)Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 19 (81)Module: WDM Network Design
  • Flow Formulation (FF) • Flow variable xls,,kd • Flow on link (l,k) due to a request generated by to source-destination couple (s,d)  Fixed number of variables  Unconstrained routing x1s,,2d x2,,1 s d x1s,,sd 1 2 x2,,d s d s ,d xs ,1 s ,d s ,d xd ,,d s x1,3 x2 , 4 2 s x3,,1d s x4,,2 s d d xss,,3 d xd ,,d s 4 x3, s 3 s ,d 4 s ,d x s ,d x s ,d x4 , d 3, 4 4,3Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 20 (81)Module: WDM Network Design
  • ILP application to WDM network designFlow Formulation (FF) • Variables represent the amount of traffic (flow) of a given traffic relation (source-destination pair) that occupies a given channel (link, wavelength) • Lightpath-related constraints − Flow conservation at each node for each lightpath (solenoidal constraint) − Capacity constraint for each link − (Wavelength continuity constraint) − Integrity constraint for all the flow variables (lightpath granularity) • Allows to solve the RFWA problems with unconstrained routing • A very large number of variables and constraint equationsAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 21 (81)Module: WDM Network Design
  • ILP application to WDM network designFlow formulation fundamental constraints• Solenoidal constraint − Guarantees spatial continuity of the s d lightpaths (flow conservation) − For each connection request, the neat flow (tot. input flow – tot. output flow) must be: • zero in transit nodes • the total offered traffic (with appropriate sign) in s and d• Capacity constraint − On each link, the total flow must not 2 4 exceed available resources (# fibers x # wavelengths) 1 6• Wavelength continuity constraint − Required for nodes without converters 3 5 Authors: Massimo Tornatore, Guido Maier Course: Optical Core Networks Revision: 2/2008 22 (81) Module: WDM Network Design
  • Notation • c: node pair (source sc and destination dc) having requested one or more connections • xl,k,c: number of WDM channels carried by link (l,k) assigned to a connection requested by the pair c • Al: set of all the nodes adjacent to node i • vc: number of connection requests having sc as source node and dc as destination node • W: number of wavelengths per fiber • λ: wavelength index (λ={1, 2 … W})Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 23 (81)Module: WDM Network Design
  • Unprotected caseVWP, FF  vc if l = d c  Solenoidality ∑x k ,l , c − ∑ xl ,k ,c = − vc if l = sc ∀ l, c k∈Al k∈Al  0 otherwise  Capacity ∑ xl ,k ,c ≤ W ⋅ Fl ,k ∀(l , k ) c xl ,k ,c integer ∀c,(l,k) Integrity Fl ,k integer ∀(l,k) N.B. from now on, notation “∀l,k” implies l ≠ kAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 24 (81)Module: WDM Network Design
  • Extension to WP case • In absence of wavelength converters, each lightpath has to preserve its wavelength along its path • This constraint is referred to as wavelength continuity constraint • In order to enforce it, let us introduce a new index in the flow variable to analyze each wavelength plane xl ,k ,c ⇒ xl ,k ,c ,λ • The structure of the formulation does not change. The problem is simply split on different planes (one for each wavelength) • The vc traffic is split on distinct wavelengths ⇒ vc,λ • The same approach will be applied for no-flow based formulationsAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 25 (81)Module: WDM Network Design
  • Unprotected caseWP, FF  vc ,λ if l = d c  ∑x k ,l , c , λ − ∑ xl ,k ,c ,λ = − vc ,λ if l = sc ∀ l , c, λ Solenoidality k∈Al k∈Al  0  otherwise ∑vc,λ = vc λ ∀c Capacity ∑x c l , k ,c ,λ ≤ Fl , k ∀(l , k ), λ xl , k ,c ,λ integer ∀c,(l,k), λ Integrity Fl , k integer ∀(l,k) vc ,λ integer ∀c, λAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 26 (81)Module: WDM Network Design
  • Flow (FF) vs Route (RF) Formulation FLOW ROUTE s ,d x1s,,2d x2,,1 sd x1, s 1 s ,d 2 x2 , d r 1,s,d s ,d x s ,1 x s ,d s r 3,s,d d x1s,,3d x2 ,,4 sd d ,2 s x3,,1d s x4 ,,2 sd d s ,d x s ,3 xd ,,d s 4 x3,,sd 3 s s ,d s ,d 4 x s ,d r 2,s,d x 3, 4 x 4,3 4,d • Variable xl,s,d: flow on link i • Variable rp,s,d: number of associated to source-destination couple s-d connections s,d routed on the admissible path p  Fixed number of variables  Constrained routing  Unconstrained routing -k-shortest path  Sub-optimality?Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 27 (81)Module: WDM Network Design
  • WDM mesh network designRoute formulation• All the possible paths between each sd-pair are evaluated a priori• Variables represent which path is used for a given connection − rpsd: path p is used by rpsd connections between s and d• Path-related constraints − Routing can be easily constrained (e.g. using the K-shortest paths) − Useful to represent path-interference • Physical topology represented in terms of interference (crossing) between paths (e.g. ipr = 1 (0) if path p has a link in common with path r)• Number of variables and constraints − Very large in the unconstrained case, − Simpler than flow formulation when routing is constrainedAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 28 (81)Module: WDM Network Design
  • Unprotected case VWP, RF• New symbols − rc,n: number of connections routed on the n-th admissible path between source destination nodes of the node-couple c − R(l,k): set of all admissible paths passing through link (l,k) Solenoidality ∑r n c ,n = vc ∀c Capacity ∑r rc ,n∈Rl ,k c ,n ≤ W ⋅ Fl ,k ∀(l , k ) rc ,n integer ∀ (c, n) Integrity Fl ,k integer ∀(l,k) Authors: Massimo Tornatore, Guido Maier Course: Optical Core Networks Revision: 2/2008 29 (81) Module: WDM Network Design
  • Unprotected case WP, RF• Analogous extension to FF case − rc,n,λ = number of connection routed on the n-th admissible connection between node couple c (source-destination) on wavelength λ ∑r λ = v λ c ,n, c, ∀ c, λ Solenoidality n ∑v λ = v λ c, c ∀c Capacity ∑r λ ≤ F c ,n, rc , n∈Rl , k l ,k ∀(l , k ), λ rc ,n ,λ integer ∀ (c, n), λ Integrity Fl ,k integer ∀(l,k) vc ,λ integer ∀c, λ Authors: Massimo Tornatore, Guido Maier Course: Optical Core Networks Revision: 2/2008 30 (81) Module: WDM Network Design
  • ILP source formulationNew formulation derived from FF  Reduced number of variables and constraints compared to the flow formulation  Allows to evaluate the absolute optimal solution without any approximation and with unconstrained routing  Can not be employed in case path protection is adopted as WDM protection technique − Does not support link-disjoint routingAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 31 (81)Module: WDM Network Design
  • ILP source formulationSource Formulation (SF) constraints • New flow variable xl ,k , s = ∑d xls,,kd − Flow carried by link l and having node s as source − Flow variables do not depend on destinations anymore • Solenoidality − Source node • the sum of xl,k,s variables is equal to the total number of requests originating in the node − Transit node • the incoming traffic has to be equal to the outgoing traffic minus the nr. of lightpathsAuthors: Massimo Tornatore, Guido Maier in the node terminatedCourse: Optical Core Networks Revision: 2/2008 32 (81)Module: WDM Network Design
  • ILP source formulationAn example • 2 connections requests − Both routing solutions are 1 to 4 compatible with the same SF solution − 1 to 3 2 • Solution 3 − X1,2,1,X1,6,1, X2,3,1, 1 X6,5,1,X,5,3,1,X,3,41= 1 4 − Otherwise X,l,k,1= 0 6 5 • 1° admissible solution − LA 1-2-3-4 3 − LB 1-6-5-3 • 2° admissible solution − LA 1-2-3 − LB 1-6-5-3-4Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 33 (81)Module: WDM Network Design
  • Unprotected caseVWP, SF• New symbols − xl,k,i : number of WDM channels carried by link l, k assigned connections originating at node i − Ci, j: number of connection requests from node i to node j• See [ToMaPa02] ∑x i , k ,i = ∑ Ci , j j ∀i k∈Ai Solenoidality ∑x k ,l ,i = ∑x l , k ,i − Ci ,l ∀i, l (i ≠ l ) k∈Al k∈Al Capacity ∑x i l , k ,i ≤ W ⋅ Fl ,k ∀(l , k ) xl ,k ,i integer ∀i,(l,k) Integrity Fl ,k integer ∀(l,k) Authors: Massimo Tornatore, Guido Maier Course: Optical Core Networks Revision: 2/2008 34 (81) Module: WDM Network Design
  • Unprotected case WP, SF• Analogous extension to FF case ∑x λ = s λ i , k ,i , i, ∀i, λ k∈Ai ∑ s λ = S = ∑C λ i, i i ,l ∀i Solenoidality l ∑x λ = ∑x λ −c k ,l ,i , l , k ,i , i , j ,λ ∀i, l , λ, (i ≠ l ) k∈Al k∈Al ∑c λ = C λ i ,l , i ,l ∀i, l , (i ≠ l ) Capacity ∑x λ ≤ F i l , k ,i , l ,k ∀(l , k , λ ) xl , k ,i ,λ integer ∀l,k , i, λ Fl ,k integer ∀l,k Integrity si ,λ integer ∀i, λ ci ,l ,λ integer ∀i, j , λ, (i ≠ l ) Authors: Massimo Tornatore, Guido Maier Course: Optical Core Networks Revision: 2/2008 35 (81) Module: WDM Network Design
  • ILP source formulationTwo-step solution of optimization problem• The source formulation variables xl,k,s and Fl,k − Do not give a detailed description of RWFA of each single lightpath − Describe each tree connecting a source to all the connected destination nodes (a subset of the other nodes) − Define the optimal capacity assignment (dimensioning of each link in terms of fibers per link) to support the given traffic STEP 1: Optimal dimensioning computation by exploiting SF matrix (identification problem, high computational complexity) STEP 2: RFWA computation after having assigned the number of fibers of each link evaluated in step 1 (multicommodity flow problem, negligible computational complexity) Authors: Massimo Tornatore, Guido Maier Course: Optical Core Networks Revision: 2/2008 36 (81) Module: WDM Network Design
  • ILP source formulationComplexity comparison between SF and FF Formulation # const. # variab. VWP source 2L + S ⋅ N 2 L(1 + S ) VWP flow 2L + C ⋅ N 2 L(1 + C ) VWP route 2L + C C ⋅ R + 2L − Symbols WP source W ( 2 L + NS ) + C + S W (S + 2L ⋅ S + C ) + 2L • N nodes WP flow W( 2 L + N C) + C W ⋅ C( 1 + 2 L) + 2 L • L links WP route C(W + 1 ) + 2 L ⋅W C ⋅ R ⋅W + C ⋅W + 2 L • R number of paths Fully connected virtual topology • W wavelengths per fiber Case FF/SF # const. FF/SF # variab. • C connection node-pairs VWP O[ N ] O[ N ] • WP O[ N ] O[ N ] S source nodes requiring connectivity• The second step has a negligible impact on the SF computational time − Fl,k are no longer variables but known terms• Fully-connected virtual topology: C = N (N-1), S=N − Worst case (assuming L << N (N-1)) Authors: Massimo Tornatore, Guido Maier Course: Optical Core Networks Revision: 2/2008 37 (81) Module: WDM Network Design
  • Case-study networksNetwork topology and parameters NSFNET EON • N = 14 nodes • N = 19 nodes • L = 22 (bidir)links • L = 39 (bidir)links • C = 108 connected pairs • C = 342 connected pairs • 360 (unidir)conn. requests • 1380 (unidir)conn. requests Seattle WA Salt Ithaca Palo Alto Ann CA Lake Arbor Princeton City UT Lincoln Pittsburgh College Boulder Champaign Pk. San Diego CO CA Atlanta Houston TX Static traffic matrices derived from real traffic measurements Hardware: 1 GHz processor, 460 Mbyte RAM Software: CPLEX 6.5 Authors: Massimo Tornatore, Guido Maier Course: Optical Core Networks Revision: 2/2008 38 (81) Module: WDM Network Design
  • Case-study networksSF vs. FF: variables and constraints (VWP) • The number of constraints decreases by a factor − 9 for the NSFNet − 26 for the EON • The number of variables decreases by a factor − 8.5 for the NSFNet − 34 for the EON • These simplifications affect computation time and memory occupation, achieving relevant savings of computational resources Network/Formulation # const. # variab.Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 39 (81)Module: WDM Network Design
  • Case-study networksSF vs. FF: variables and constraints (WP) • In the WP case − The number of variables and constraints linearly increases with W − The gaps in the number of variables and constraints between FF and SF increase with W • The advantage of source formulation is even more relevant in the WP case Number of variables and constraints EON WP Number of variables and constraints NSFNET WP 5 8 10 4 5 10 source variables source variables 7 104 flow variables source constraints 4 105 flow variables 6 104 flow constraint source constraints flow constraints 5 104 3 105 4 104 3 104 2 105 2 104 4 1 105 1 10 0 0 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 Number of wavelenghts, W Number of wavelengths, WAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 40 (81)Module: WDM Network Design
  • Case-study networksSF vs. FF: time, memory and convergence• The values of the cost function Msource obtained by SF are always equal or better (lower) than the corresponding FF results (Mflow)• Coincident values are obtained if both the formulations converge to the optimal solution − Validation of SF by induction• Memory exhaustion (Out-Of-Memory, O.O.M) prevents the convergence to the optimal solution. This event happens more frequently with FF than with SF Memory occupation Computational timeAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 41 (81)Module: WDM Network Design
  • Outline • Introduction to WDM network design and optimization • Integer Linear Programming approach • Physical Topology Design − Unprotected case − Dedicated path protection case − Shared path & link protection cases • Heuristic approachAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 42 (81)Module: WDM Network Design
  • Protection in WDM NetworksMotivations • Today WDM transmission systems allow the multiplexing on a single fiber of up to 160 distinct optical channels − recent experimental systems support up to 256 channels: • A single WDM channel carries from 2.5 to 40 Gb/s (ITU-T G.709) • The loss of a high-speed connection operating at such bit rates, even for few seconds, means huge waste of data !! • The increase in WDM capacity associated with the tremendous bandwidth carried by each fiber and the evolution from ring to mesh architectures brought the need for suitable protection strategies into foreground.Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 43 (81)Module: WDM Network Design
  • Dedicated Path Protection (DPP) • 1+1 or 1:1 dedicated protection (>50% capacity for protection) − Both solutions are possible − Each connection-request is satisfied by setting-up a lightpath pair of a working + a protection lightpaths − RFWA must be performed in such a way that working and protection lightpaths are link disjoint − Additional constraints must be considered in network planning and optimization • Transit OXCs must not be reconfigured in case of failure • The source model can not be applied to this scenarioAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 44 (81)Module: WDM Network Design
  • Dedicated Path Protection (DPP)Flow formulation, VWP • New symbols − xl,k,c,t = number of WDM channels carried by link (l,k) assigned to the t-th connection between source-destination couple c • Rationale: for each connection request, route a link-disjoint connection ⇒ route two connection and enforce link-disjoint constraint 2 if l = dc  Solenoidality ∑x k ,l , c ,t − ∑ xl ,k ,c ,t = − 2 if l = sc ∀ l , c, t ; k∈Al k∈Al 0  otherwise Link - disjoint xl ,k ,c ,t + xk ,l ,c ,t ≤ 1 ∀ l , k , c, t Capacity ∑x ( c ,t ) l , k , c ,t ≤ W ⋅ Fl ,k ∀l , k xl ,k ,c ,t binary ∀ (c,t ), (l,k) Integrity Fl ,k integer ∀(l,k)Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 45 (81)Module: WDM Network Design
  • Dedicated Path Protection (DPP) Route formulation (RF), VWP• New symbols − rc,n,t = 1 if the t-th connection between source destination node couple c is routed on the n-th admissible path − R(l,k) = set of all admissible paths passing through link (l,k) Solenoidality ∑r n c ,t , n =2 ∀ c, t Link - disjoint ∑r c ,t , n rc , t , n∈Rl , k ∪Rk , l ≤1 ∀ c, t , l , k Capacity ∑r c ,t , n rc , t , n∈Rl , k ≤ W ⋅ Fl ,k ∀l , k rc ,t ,n binary ∀ c, t , n Integrity Fl ,k integer ∀l,k Authors: Massimo Tornatore, Guido Maier Course: Optical Core Networks Revision: 2/2008 46 (81) Module: WDM Network Design
  • ILP application to WDM network designRoute formulation (RF) II, VWP • Substitute the single path variable rc,n by a protected route variable r’c,n (~ a cycle) • No need for representation in terms of interference (crossing) between paths • Identical formulation to unprotected case Solenoidality ∑r = v n c ,n c ∀c Capacity ∑r ≤ W ⋅ F r c , n∈R l , k c ,n l ,k ∀l , k r c ,n integer ∀c, n Integrity Fl ,k integer ∀l,kAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 47 (81)Module: WDM Network Design
  • Dedicated Path Protection (DPP)Flow formulation, WP • New symbols − xl,k,c,t ,λ= number of WDM channels carried by wavelength λ on link l,k assigned to the t-th connection between source-destination couple c − Vc,λ= traffic of connection c along wavelength λ vc , λ if l = dc  ∑ xk ,l ,c,t ,λ − ∑ xl ,k ,c,t ,λ = − vc, λ if l = sc ∀ l , c, t , λ; Solenoidality k∈Al k∈Al 0  otherwise ∑vc, λ = 2λ ∀c Link - disjoint ∑λ x λ + x λ ≤ 1 ∀ l , k , c, t l , k , c ,t , k ,l , c , t ,, Capacity ∑x λ ≤ F ( c ,t ) ∀l , k , λ l , k , c ,t , l ,k xl ,k ,c ,t ,λ binary ∀ c,t , l,k , λ Integrity Fl , k integer ∀l,k vc , λ bynary ∀c,λAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 48 (81)Module: WDM Network Design
  • Dedicated Path Protection (DPP)Route formulation (RF), WP ∑ r λ = v λ ∀ (c, t ), λ c ,t , n , c, t , Solenoidality n ∑ v λ = 2 ∀ c, t λ c ,t ,Link - disjoint ∑ ∑ r λ ≤ 1 ∀ (c, t ), (l , k ) λ c ,t , n , rc , t , n , λ∈Rl , k ∪ Rk , l Capacity ∑ r λ ≤ F ∀(l , k ), λ c ,t , n , rc , t , n , λ∈Rl , k l ,k rc ,t ,n ,λ binary ∀ (c, t ), n, λ Integrity Fl ,k integer ∀l,k vc ,t ,λ bynary ∀(c,t ), λAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 49 (81)Module: WDM Network Design
  • ILP application to WDM network designRoute formulation (RF) II, WP • rc,n,λ = number of connections between source-destination couple c routed on the n-th admissible couple of disjoint paths having one path over wavelength λ1and the other over λ2 ∑r c , n , λ 1, λ 2 = vc , λ1, λ 2 ∀ c, λ1, λ 2 Solenoidality n ∑v λ λ 1, 2 c , λ 1, λ 2 = vc ∀c Capacity ∑r c , n , λ 1, λ 2 r c , n , λ 1, λ 2∈R l , k ≤ Fl ,k ∀l , k , λ1, λ 2 r c ,n ,λ1,λ 2 integer ∀c, n, λ1, λ 2 Integrity Fl ,k integer ∀l,kAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 50 (81)Module: WDM Network Design
  • Outline • Introduction to WDM network design and optimization • Integer Linear Programming approach • Physical Topology Design − Unprotected case − Dedicated path protection case − Shared path & link protection cases • ReferencesAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 51 (81)Module: WDM Network Design
  • Shared Path Protection (SPP) • Sharing is a way to decrease the capacity redundancy and the number of lightpaths that must be managed • Protection-resources sharing − Protection lightpaths of different channels share some wavelength channels − Based on the assumption of single point of failure − Working lightpaths must be link (node) disjoint • Very complex control issues − Also transit OXCs must be reconfigured in case of failure • Signaling involves also transit OXCs • Lightpath identification and tracing becomes fundamentalAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 52 (81)Module: WDM Network Design
  • Link Protection OMS protection Normal (link protection) Connection • Link protection (≥50% capacity for protection) − Each link is protected by providing an alternative routing for all the WDM channels in all the fibers − Protection switching can be performed by fiber switches (fiber cross-connects) or wavelength switches − Signaling is local; transit OXCs of the protection route can be pre-configured − Fast reaction to faults − Some network fibers are reserved for protection • Link-shared protection (LSP) − Protection fibers may be used for protection of more than one link (assuming single-point of failure) − The capacity reserved for protection is greatly reducedAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 53 (81)Module: WDM Network Design
  • Link Protection • Different protected objects − Fiber level − Wavelength channel level FAULT EVENT (1) (2)Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 54 (81)Module: WDM Network Design
  • Link ProtectionSummary results • Comparison between different protection technique on fiber needed to support the same amount of traffic • Switching protection objects at fiber or wavelength level does ot sensibly affects the amount of fibers. − This difference increases with the number of wavelength per fiberAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 55 (81)Module: WDM Network Design
  • References • Articles − [WaDe96] N. Wauters and P. M. Deemester, Design of the optical path layer in multiwavelength cross-connected networks, Journal on selected areas on communications,1996, Vol. 14, pages 881-891, June − [CaPaTuDe98] B. V. Caenegem, W. V. Parys, F. D. Turck, and P. M. Deemester, Dimensioning of survivable WDM networks, IEEE Journal on Selected Areas in Communications, pp. 1146–1157, sept 1998. − [ToMaPa02] M. Tornatore, G. Maier, and A. Pattavina, WDM Network Optimization by ILP Based on Source Formulation, Proceedings, IEEE INFOCOM ’02, June 2002. − [CoMaPaTo03] A.Concaro, G. Maier, M.Martinelli, A. Pattavina, and M.Tornatore, “QoS Provision in Optical Networks by Shared Protection: An Exact Approach,” in Quality of service in multiservice IP Networks, ser. Lectures Notes on Computer Sciences, 2601, 2003, pp. 419–432. − [ZhOuMu03] H. Zang, C. Ou, and B. Mukherjee, “Path-protection routing and wavelength assignment (RWA) in WDM mesh networks under duct-layer constraints,” IEEE/ACM Transactions on Networking, vol. 11, no. 2, pp.248–258, april 2003. − [BaBaGiKo99] S. Baroni, P. Bayvel, R. J. Gibbens, and S. K. Korotky, “Analysis and design of resilient multifiber wavelength-routed optical transport networks,” Journal of Lightwave Technology, vol. 17, pp. 743–758, may 1999. − [ChGaKa92] I. Chamtlac, A. Ganz, and G. Karmi, “Lightpath communications: an approach to high-bandwidth optical WAN’s,” IEEE/ACM Transactionson Networking, vol. 40, no. 7, pp. 1172–1182, july 1992. − [RaMu99] S. Ramamurthy and B. Mukherjee, “Survivable WDM mesh networks, part i - protection,” Proceedings, IEEE INFOCOM ’99, vol. 2, pp. 744–751, March 1999. − [MiSa99] Y. Miyao and H. Saito, “Optimal design and evaluation of survivable WDM transport networks,” IEEE Journal on Selected Areas in Communications, vol. 16, pp. 1190–1198, sept 1999.Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 56 (81)Module: WDM Network Design
  • References − [BaMu00] D. Banerjee and B. Mukherjee, “Wavelength-routed optical networks: linear formulation, resource budgeting tradeoffs and a reconfiguration study,” IEEE/ACM Transactions on Networking, pp. 598–607, oct 2000. − [BiGu95] D. Bienstock and O. Gunluk, “Computational experience with a difficult mixed integer multicommodity flow problem,” Mathematical Programming, vol. 68, pp. 213–237, 1995. − [RaSi96] R. Ramaswami and K. N. Sivarajan, Design of logical topologies for wavelength-routed optical networks, IEEE Journal on Selected Areas in Communications, vol. 14, pp. 840{851, June 1996. − [BaMu96] D. Banerjee and B. Mukherjee, A practical approach for routing and wavelength assignment in large wavelength-routed optical networks, IEEE Journal on Selected Areas in Communications, pp. 903-908,June 1996. − [OzBe03] A. E. Ozdaglar and D. P. Bertsekas, Routing and wavelength assignment in optical networks, IEEE/ACM Transactions on Networking, vol. 11, no. 2, pp. 259-272, Apr 2003. − [KrSi01] Rajesh M. Krishnaswamy and Kumar N. Sivarajan, Design of logical topologies: A linear formulation for wavelength-routed optical networks with no wavelength changers, IEEE/ACM Transactions on Networking, vol. 9, no. 2, pp. 186-198, Apr 2001. − [FuCeTaMaJa99] A. Fumagalli, I. Cerutti, M. Tacca, F. Masetti, R. Jagannathan, and S. Alagar, Survivable networks based on optimal routing and WDM self-heling rings, Proceedings, IEEE INFOCOM 99, vol. 2, pp. 726-733,1999. − [ToMaPa04] M. Tornatore and G. Maier and A. Pattavina, Variable Aggregation in the ILP Design of WDM Networks with dedicated Protection , TANGO project, Workshop di metà progetto , Jan, 2004, Madonna di Campiglio, ItalyAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 57 (81)Module: WDM Network Design
  • Outline • Introduction to WDM network design and optimization • Integer Linear Programming approach to the problem • Physical Topology Design − Unprotected case − Dedicated path protection case − Shared path protection case − Link protection • Heuristic approachAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 58 (81)Module: WDM Network Design
  • WDM mesh network designHeuristic approaches • Heuristic: method based on reasonable choices in RFWA that lead to a sub-optimal solution • Solution of the static network design exploiting a dynamic model • Connections are routed one-by-one • Strategies can be: − Deterministic − StochasticAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 59 (81)Module: WDM Network Design
  • Static WDM mesh networksOptimization problem definition and solution • Design variables − Number of fibers per link − Routing, fiber and wavelength assignment for each lightpath • Cost function: total number of fibers / total fiber length • With or without protection • With or without wavelength conversionAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 60 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWADeterministic approach for fiber minimization • Optimal design of WDM networks under static traffic • A deterministic heuristic method based on dynamic RFWA is applied to multifiber mesh networks, with or without wavelength converters: − RFWA for all the lightpaths separately and in sequence (greedy phase) − Improvement by lightpath rerouting • It allows to setup lightpaths so to minimize the amount of fiber deployed in the networkAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 61 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWANetwork and traffic model specification • Pre-assigned physical topology graph (OXCs and WDM links) − WDM multifiber links • Composed of multiple unidirectional fibers • Pre-assigned number of WDM channels per fiber (global network variable W) − OXCs • Strictly non-blocking space-switching architectures • Wavelength conversion capacity: 2 scenarios − No conversion: Wavelength Path (WP) − Full-capability conversion in all the OXCs: Virtual Wavelength Path (VWP) • Pre-assigned static virtual topology − Set of requests for optical connections • OXCs are the sources and destinations (add-drop function) • Multiple connections can be demanded between an OXC pair • Each connection requires a unidirectional lightpath to be setupAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 62 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWARouting Fiber Wavelength Assignment-RFWA • Routing criteria − Shortest path (SP) -- Distance metrics! • Number of hops (mH) • Physical link length in km (mL) − Least loaded routing (LLR) − Least loaded node (LLN) • Fiber assignment criteria − First fit, random, most used, least used • Wavelength assignment criteria − First fit, random, most used, least usedAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 63 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWARouting Fiber Wavelength Assignment-RFWA • Wavelength assignment algorithms − Pack → the most used wavelength is chosen first − Spread → the least used wavelength is chosen first − Random → random choice − First Fit → wavelengths are preordered • Routing algorithms − Shortest Path (SP) → selects the shortest source- destination path (# of crossed links) − Least Loaded Routing (LLR) → avoids the busiest links − Least Loaded Node (LLN) → avoids the busiest nodesAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 64 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWAWavelength layer graph • Physical topology • Equivalent wavelength (3 wavelengths) layer graph λ1 plane λ2 plane λ3 plane OXC without converters OXC with converters C. Chen and S. Banerjee: 1995 and 1996 I.Chlamtac, A Farago and T. Zhang: 1996Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 65 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWAMultifiber wavelength layered graph • Physical topology (2 fiber links, 2 3 2 λ1 Fiber 1 wavelengths) 3 2 1 3 2 λ2 1 1 1 • Different OXC functions displayed on the layered graph 3 2 λ1 − 1 - add/drop − 2 - fiber switching 1 − 3 - wavelength conversion 3 2 − 3 - fiber switching + wavelength λ2 conversion Fiber 2 1Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 66 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWAMultifiber wavelength layer graph • Enables joint solution of RFWA problem • Obtained replicating network topology as many times as WF and connecting nodes in a proper wayAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 67 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWALayered graph utilization • The layered graph is “monochromatic” • Routing, fiber and wavelength assignment are resolved together • Links and nodes are weighted according to the routing, fiber and wavelength assignment algorithms • The Dijkstra Algorithm is finally applied to the layered weighted graph • Worst case complexity N = # of nodes [ O (W F N ) 2 ] F = # of fibers W = # of wavelengthsAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 68 (81)Module: WDM Network Design
  • Path-protected WDM mesh networksOptimization tool for dedicated path-protec. • Optimal design of WDM networks under static traffic with dedicated path-protection (1+1 or 1:1) • The heuristic optimization method can be applied to multifiber mesh networks, with or without wavelength converters • It allows to setup protected lightpaths so to minimize the amount of fiber deployed in the network • Each connection request is satisfied by setting up a working- protection (W-P) lightpath pair under the link-disjoint constraintAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 69 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWAHeuristic design and optimization scheme Sort connection − Connection request sorting requests rules Setup the lightpaths sequentially • Longest first Idle network, • Most requested couples first unlimited fiber • Balanced Prune unused fibers • Random Identify fibers with − Processing of an individual only k used λs for lightpath k = 1 to W • Routing, Fiber and Wavelength Assignment Prune unused fibers (RFWA) criteria • Dijkstra’s algorithm performed Attempt an alternative on the multifiber layered RFWA for the identified lightpaths graphAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 70 (81)Module: WDM Network Design
  • Path-protected WDM mesh networksCase-study • National Science Foundation Network (NSFNET): USA backbone • Physical Topology − 14 nodes − 44 unidirectional links • Design options − W: 2, 4, 8, 16, 32 − 8 RFWA criteriaAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 71 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWARFWA-criteria labels mH C1 LLR mL C2 VWP C3 mH SP mL C4 mH C5 LLR mL C6 WP mH C7 SP mL C8Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 72 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWATotal number of fibers • The initial sorting rule • Hop-metric minimization performs resulted almost irrelevant for better the final optimized result . − Variations of M due to RFWAs and (differences between the conversion in the mH case below sorting rules below 3%) 5% mH mL VWP VWP WP VWP WP WP SP LLR SP LLR SP LLR SP LLR 500 500 500 500 410 404 2 400 400 400 400 4 Total fiber number, M Total fiber number, M 8 16 300 300 300 300 32 213 207 200 200 200 200 114 109 64.5 59.7 100 100 100 100 39.4 36.2 0 0 0 0 2 4 8 16 32 C3 C1 C7 C5 C4 C2 C8 C6 Number of wavelengths, WAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 73 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWAFiber distribution in the network (6,5) (0,1) (4,4) (0,0) (4,4) (2,2) (0,0) (2,2) (2,2) (5,6) (6,6) (6,6) (4,4) (6,5) (3,4) (2,2) (2,2) (2,2) (2,3) (2,2) (2,2) (2,2) − NSFNet with W = 16 wavelengths per fiber, mL SP RFWA criteria − The two numbers indicate the number of fibers in the VWP and WP network scenarios − Some links are idleAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 74 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWAWavelength conversion gain 10 10 8.24 7.36 8 8 M M gain factor, G 6 4.56 6 MWP − MVWP GM = ×100 MWP 3.08 4 4 1.63 2 2 0 0 2 4 8 16 32 Number of wavelengths, W • Wavelength converters are more effective in reducing the optimized network cost when W is highAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 75 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWASaturation factor C • A coarser fiber granularity allows us to save ρ= fibers but implies a smaller saturation factor W×M • VWP performs better than WP .. C = number of used − Variations of ρ due to RFWAs and metrics in wavelength channels the VWP case below 5% VWP V WP WP WP mL mH mL mH 1.2 1.2 LLR SP LLR SP LLR SP LLR SP 0.985 1 1 0.972 0.936 0.97 0.929 0.884 2 0.862 1 1 0.95 0.95 4 0.787 0.758 Saturation factor, ρ 0.9 0.9 8 0.668 0.8 Saturation factor, ρ 0.8 16 0.85 0.85 32 0.6 0.6 0.8 0.8 0.4 0.4 0.75 0.75 0.2 0.7 0.7 0.2 0.65 0.65 0 0 2 4 8 16 32 0.6 0.6 Number of wavelengths, W C1 C3 C2 C4 C6 C8 C5 C7Authors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 76 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWAOptimization: longer lightpaths... C − CSP • Compared to the initial ∆= × 100 routing (shortest path, CSP which is also the capacity CSP = number of used wavelength channels with SP routing and unconstrained resources (capacity bound) bound) the fiber optimization algorithm VWP WP mH cases increases the total wavelength-channel Capacity bound per cent deviation ∆ 12 , occupation (total lightpath 9.61 10 length in number of hops) 8 − C is increased of max 10% of CSP in the worst 6 6 4.62 3.86 case 3.39 3.6 4 2.37 2.18 2.23 1.93 2 0 2 4 8 16 32 Number of wavelengths, WAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 77 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWA…traded for fewer unused capacity  • Compared to the initial routing C  U = 1 −  × 100 (shortest path) the fiber  W × M optimization algorithm decreases the total number of unused wavelength-channels 50 − U is halved in the best case initial SP routing 40 optimized solution % Unused capacity, U 30 • Notes − Initial SP routing curve: 20 data obtained in the VWP 10 scenario (best case) − Optimized solution curve: 0 averaged data comprising 0 5 10 15 20 25 30 35 Number of wavelengths, Nλ the WP and VWP scenariosAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 78 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWAConvergence of the heuristic optimization M VWP L W=16, mH, SP 90 9.5 104 9 104 Total fiber length, L (km) 85 Total fiber number, M 80 8.5 104 75 8 104 70 7.5 104 65 7 104 60 6.5 104 55 6 104 0 2 4 6 8 10 12 14 16 optimization counter, k • The algorithm appears to converge well before the last iteration  Improvements of the computation time are possible • Notes: − Convergence is rather insensitive to initial sorting rule and to RFWA criteriaAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 79 (81)Module: WDM Network Design
  • Case-study networksComparison SF vs heuristic optim. (VWP) • ILP by SF is a useful benchmark to verify heuristic dimensioning results − Approximate methods do not share this property . NSFNET VWP EON VWP 400 1600 source form. 1400 source form. 350 heuristic 1200 heuristicTotal fiber number, M 300 Total fiber number, M 250 1000 200 800 150 600 100 400 50 200 0 0 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 Number of wavelengths, W Number of wavelengths, WAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 80 (81)Module: WDM Network Design
  • Heuristic static design by dynamic RFWAConcluding remarks • A heuristic method for multifiber WDM network optimization under static traffic has been proposed and applied to various physical network scenarios • Good sub-optimal solutions in terms of total network fiber resources can be achieved with a reasonable computational effort • The method allows to inspect various aspects such as RFWA performance comparison and wavelength converter effectiveness • Future possible developments − Upgrade to include also lightpath protection in the WDM layer − Improvement of the computation time / memory occupancyAuthors: Massimo Tornatore, Guido MaierCourse: Optical Core Networks Revision: 2/2008 81 (81)Module: WDM Network Design