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This teaching material is a part of e-Photon/ONe Master study in Optical Communications and Networks
Course and module:
Author(s):
http://www.e-photon-one.orgThis tutorial is licensed under the Creative Commonshttp://creativecommons.org/licenses/by-nc-sa/3.0/
Optical Core Networks
WDM Network Design
Massimo Tornatore, Politecnico di Milano, tornator@elet.polimi.itGuido Maier, Politecnico di Milano, maier@elet.polimi.it
Revision: 2/2008 2 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 approach
Revision: 2/2008 3 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
WDM networks: basic conceptsLogical topology
• 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 traffic
Optical network access point
Electronic-layer connection request
WDM network nodes
Electronic switching node(DXC, IP router, ATM switch, etc.)
WDM network
CR1
CR2CR4
CR3
WDM LOGICAL
TOPOLOGY
Revision: 2/2008 4 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
WDM networks: basic concepts 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 phase
Wavelength converter
Optical path termination
Optical Cross Connect (OXC)
WDM optical-fiber link
WDM PHYSICAL TOPOLOGY
Revision: 2/2008 5 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
λ1λ2
Optical wavelengthchannels
LP1LP2
LP4
LP3LP1 LP2 LP3
LP4
LP = LIGHTPATH
WDM networks: basic concepts Mapping of logical over physical topology
• 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 out
λ3
Mapping is differentaccording to the factthat the network isnot (a) or is (b) providedwith wavelengthconverters
(a) (b)
CR1
CR2CR4
CR3
Revision: 2/2008 6 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 output
Revision: 2/2008 7 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Static WDM network planning Problem 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 considered
Revision: 2/2008 8 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
• 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)
Static WDM network optimization Problem definition (III)
Revision: 2/2008 9 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
• 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)
Static WDM network optimization Complexity
Revision: 2/2008 10 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Optimization problems Classification
• 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 subroutine
Revision: 2/2008 11 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
• 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− Non linear
Optimization problem solutionOptimization methods
*E.g.: traffic matrix representationcxy = 1 if a connection is required between the nodes x and y, cxy = 0 otherwise
Revision: 2/2008 12 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 approach
Revision: 2/2008 13 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
• 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 search
Optimization problem solution Mathematical programming solving
Revision: 2/2008 14 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
• 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 solution
ILP application to WDM network design Approximate methods
Revision: 2/2008 15 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
• 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]
ILP application to WDM network design ILP relaxation
Revision: 2/2008 16 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
• 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,l
Notation
l
k
Revision: 2/2008 17 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Cost functionsSome examples
• RFWA− Minimum fiber number M
• Terminal equipment cost− VWP case (cost of transponder)
− Minimum fiber mileage (cost) MC
• Line equipment [BaMu00]
• RWA− Minimum wavelength number
− Minimum wavelength mileage• [StBa99],[FuCeTaMaJa03]
− Minimum maximal wavelength number on a link
• [Mu97]
MFkl
kl minmin),(
, =∑
Ckl
klkl MFc minmin),(
,, =∑
Γ=∑ minmin),(
,kl
klλ
Ckl
klklc Γ=∑ minmin),(
,, λ
MAXklkl
Γ= min]max[min ,,
λ
Revision: 2/2008 18 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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
• References
Revision: 2/2008 19 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Approaches to WDM design
• Two basilar and well-known approaches [WaDe96],[Wi99]− FLOW FORMULATION (FF)− ROUTE FORMULATION (RF)
Revision: 2/2008 20 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Flow Formulation (FF)
• Flow variable
• Flow on link (l,k) due to a request generated by to source-destination
couple (s,d) Fixed number of variables
Unconstrained routing
dsklx ,
,
s d
1 2
3 4
dss
dss
xx
,1,
,,1
dss
dss
xx
,,3
,3,
dsds xx ,1,2
,2,1
dsds xx ,3,4
,4,3
dsd
dsd
xx
,,4
,4,
dsd
dsd
x
x,2,
,,2
ds
ds
xx
,1,3
,3,1
ds
ds
xx
,2,4
,4,2
Revision: 2/2008 21 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
• 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 equations
ILP application to WDM network designFlow Formulation (FF)
Revision: 2/2008 22 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
ILP application to WDM network designFlow formulation fundamental constraints
• Solenoidal constraint− Guarantees spatial continuity of the
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
exceed available resources(# fibers x # wavelengths)
• Wavelength continuity constraint− Required for nodes without converters
1
2
3
4
5
6
s d
Revision: 2/2008 23 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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})
Revision: 2/2008 24 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Unprotected caseVWP, FF
(l,k)F
c,(l,k)x
klFWx
clslv
dlv
xx
kl
ckl
cklckl
Ak Akcc
cc
cklclk
l l
∀∀
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∀
=−=
=−
∑
∑ ∑∈ ∈
integer
integer Integrity
),(Capacity
,
otherwise0
if
if
itySolenoidal
,
,,
,,,
,,,,
N.B. from now on, notation “∀l,k” implies l ≠ k
Revision: 2/2008 25 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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
• 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 formulations
λ,,,,, cklckl xx ⇒
Revision: 2/2008 26 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Unprotected caseWP, FF
λ
λ
λ
λ
λ
λ
λ
λλ
λ
λ
λλ
,integer
integer
,integer
Integrity
),,(Capacity
,,
otherwise0
if
if
itySolenoidal
,
,
,,,
,,,,
,
,
,
,,,,,,
cv
(l,k)F
c,(l,k)x
klFx
cvv
clslv
dlv
xx
c
kl
ckl
cklckl
cc
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cc
cklclk
l l
∀∀
∀
∀≤
∀=
∀
=−=
=−
∑∑
∑ ∑∈ ∈
Revision: 2/2008 27 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Flow (FF) vs Route (RF) Formulation
• Variable xl,s,d: flow on link i associated to source-destination couple s-d
• Variable rp,s,d: number of connections s,d routed on the admissible path p
r1,s,d
r2,s,d
r3,s,d
Fixed number of variables
Unconstrained routing Constrained routing
-k-shortest path
Sub-optimality?
FLOW ROUTEROUTE
s ds d
1 2
3 4
dss
dss
xx
,1,
,,1
dss
dss
xx
,,3
,3,
dsds xx ,1,2
,2,1
dsds xx ,3,4
,4,3
dsd
dsd
xx
,,4
,4,
dsd
dsd
x
x,2,
,,2
ds
ds
xx
,1,3
,3,1
ds
ds
xx
,2,4
,4,2
Revision: 2/2008 28 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
• 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 constrained
WDM mesh network designRoute formulation
Revision: 2/2008 29 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Unprotected caseVWP, RF
(l,k)F
n)cr
klFWr
cvr
kl
nc
Rrklnc
n
cnc
klnc
∀∀
∀⋅≤
∀=
∑∑
∈
integer
,( integer Integrity
),(Capacity
itySolenoidal
,
,
,,
,
,,
• 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)
Revision: 2/2008 30 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Unprotected caseWP, RF
λ
λ
λ
λ
λ
λ
λ
λλ
λλ
,integer
integer
,,( integer
Integrity
),,(Capacity
, itySolenoidal
,
,
,,
,,,
,
,,,
,,
cv
(l,k)F
n)cr
klFr
cvv
cvr
c
kl
nc
Rrklnc
cc
ncnc
klnc
∀∀
∀
∀≤
∀=
∀=
∑∑
∑
∈
• 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
Revision: 2/2008 31 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 routing
Revision: 2/2008 32 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
ILP source formulationSource Formulation (SF) constraints
• New flow variable − 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 lightpaths terminated in the node
∑=d
dsklskl xx ,
,,,
Revision: 2/2008 33 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
ILP source formulationAn example
• 2 connections requests− 1 to 4− 1 to 3
• Solution− X1,2,1,X1,6,1, X2,3,1,
X6,5,1,X,5,3,1,X,3,41= 1
− Otherwise X,l,k,1= 0
• 1° admissible solution− LA 1-2-3-4
− LB 1-6-5-3
• 2° admissible solution− LA 1-2-3
− LB 1-6-5-3-4
Both routing solutions arecompatible with the same SF solution
1
2 3
4
56
3
Revision: 2/2008 34 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Unprotected caseVWP, SF
(l,k)F
i,(l,k)x
klFWx
liliCxx
iCx
kl
ikl
iklikl
Ak Akliiklilk
Ak jjiiki
l l
i
∀∀
∀⋅≤
≠∀−=
∀=
∑∑ ∑
∑ ∑
∈ ∈
∈
integer
integer Integrity
),(Capacity
)(,itySolenoidal
,
,,
,,,
,,,,,
,,,
• 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]
Revision: 2/2008 35 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Unprotected caseWP, SF
)(,,,integer
,integer
integer
,,integer
Integrity
),,(Capacity
)(,,
)(,,,
,
itySolenoidal
,,
,
,
,,,
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,,
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is
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isx
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i
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∈ ∈
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λλ
λ
λ
λ
λ
λ
λ
λ
λ
λλ
λλλ
λλ
λλ
• Analogous extension to FF case
Revision: 2/2008 36 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 matrix STEP 1: Optimal dimensioning computation by exploiting SF
(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)
Revision: 2/2008 37 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
ILP source formulationComplexity comparison between SF and FF
• 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))
LWCWRCWL)C(W
L L) C(W C N C) L W(
LCSLSWSCNSLW
LRCCL
CLNCL
SLNSL
221route WP
2212flow WP
2)2()2(source WP
22route VWP
)1(22flow VWP
)1(22source VWP
variab.#const. #nFormulatio
+⋅+⋅⋅⋅++
++⋅++
++⋅++++
+⋅+
+⋅+
+⋅+
[ ] [ ][ ] [ ]NN
NN
OO WP
OOVWP
variab.# FF/SFconst. # FF/SFCase
Fully connected virtual topology
− Symbols• N nodes• L links• R number of paths• W wavelengths per fiber• C connection node-pairs• S source nodes requiring connectivity
Revision: 2/2008 38 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Case-study networksNetwork topology and parameters
• N = 14 nodes• L = 22 (bidir)links • C = 108 connected pairs
• 360 (unidir)conn. requests
NSFNET EON
Palo AltoCA
San DiegoCA
SaltLakeCity UT
BoulderCO
Houston TX
Lincoln
Champaign
Pittsburgh
Atlanta
AnnArbor
Ithaca
Princeton
CollegePk.
Seattle WA
• N = 19 nodes• L = 39 (bidir)links • C = 342 connected pairs• 1380 (unidir)conn. requests
Static traffic matrices derived from real traffic measurements Hardware: 1 GHz processor, 460 Mbyte RAM Software: CPLEX 6.5
Revision: 2/2008 39 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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.
Revision: 2/2008 40 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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
0
1 104
2 104
3 104
4 104
5 104
6 104
7 104
8 104
0 2 4 6 8 10 12 14 16
NSFNET WP
source variablesflow variablessource constraintsflow constraint
Nu
mb
er
of
va
ria
ble
s a
nd
co
nst
rain
ts
Number of wavelenghts, W
0
1 105
2 105
3 105
4 105
5 105
0 2 4 6 8 10 12 14 16
EON WP
source variablesflow variablessource constraintsflow constraints
Number of wavelengths, W
Num
ber
of v
aria
ble
s an
d co
nst
rain
ts
Revision: 2/2008 41 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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
Computational timeMemory occupation
Revision: 2/2008 42 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 approach
Revision: 2/2008 43 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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.
Revision: 2/2008 44 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 scenario
Revision: 2/2008 45 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Dedicated Path Protection (DPP) Flow formulation, VWP
(l,k)F
(l,k)c,tx
klFWx
tcklxx
tclsldl
xx
kl
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itySolenoidal
,
,,,
),(,,,,
,,,,,,
,,,,,,
• 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
Revision: 2/2008 46 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Dedicated Path Protection (DPP) Route formulation (RF), VWP
l,kF
ntcr
klFWr
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tcr
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,
,,
,,,
,,
,,
,,,
,,,,
• 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)
Revision: 2/2008 47 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
ILP application to WDM network design Route formulation (RF) II, VWP
l,kF
ncr
klFWr
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nc
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• 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
Revision: 2/2008 48 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Dedicated Path Protection (DPP) Flow formulation, WP
λ
λ
λ
λ
λ
λ
λ
λ λλ
λλ
λ
λ
λλ
c,v
l,kF
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itySolenoidal
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,,,,
),(,,,,,
,,,,,,,,,
,
,
,
,,,,,,,,
• New symbols− xl,k,c,t ,λ= number of WDM channels carried by wavelength on link λ l,k
assigned to the t-th connection between source-destination couple c − Vc,λ= traffic of connection c along wavelength λ
Revision: 2/2008 49 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Dedicated Path Protection (DPP) Route formulation (RF), WP
λ
λ
λ
λ
λ
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Revision: 2/2008 50 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
ILP application to WDM network design Route formulation (RF) II, WP
l,kF
ncr
klFr
cvv
cvr
kl
nc
Rrklnc
cc
n
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λλλλ
λλ
• 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
Revision: 2/2008 51 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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
• References
Revision: 2/2008 52 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Shared Path Protection (SPP)
• 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 fundamental
• Sharing is a way to decrease the capacity redundancy and the number of lightpaths that must be managed
Revision: 2/2008 53 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Link Protection
• 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 reduced
Connection
NormalOMS protection(link protection)
Revision: 2/2008 54 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Link Protection
• Different protected objects− Fiber level− Wavelength channel level
FAULT EVENT(1)
(2)
Revision: 2/2008 55 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 fiber
Revision: 2/2008 56 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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.
Revision: 2/2008 57 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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, Italy
Revision: 2/2008 58 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 approach
Revision: 2/2008 59 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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− Stochastic
Revision: 2/2008 60 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 conversion
Revision: 2/2008 61 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Deterministic 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 network
Revision: 2/2008 62 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Network 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 setup
Revision: 2/2008 63 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Routing 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 used
Revision: 2/2008 64 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Routing 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 nodes
Revision: 2/2008 65 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Wavelength layer graph
• Physical topology(3 wavelengths)
λ2 plane
C. Chen and S. Banerjee: 1995 and 1996I.Chlamtac, A Farago and T. Zhang: 1996
• Equivalent wavelength layer graph
λ1 plane
λ3 plane
OXC with convertersOXC without converters
Revision: 2/2008 66 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Multifiber wavelength layered graph
• Physical topology (2 fiber links, 2 wavelengths)
• Different OXC functions displayed on the layered graph
− 1 - add/drop− 2 - fiber switching− 3 - wavelength conversion− 3 - fiber switching + wavelength
conversion
3
1
2
3 2
3
1
2
3
1
2
3
1
2
λ1
Fiber 2
1
1
λ2
λ1
λ2
Fiber 1
Revision: 2/2008 67 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Multifiber wavelength layer graph
• Enables joint solution of RFWA problem
• Obtained replicating network topology as many times as WF and connecting nodes in a proper way
Revision: 2/2008 68 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Layered 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 nodesF = # of fibersW = # of wavelengths( )[ ]2O NFW
Revision: 2/2008 69 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 constraint
Revision: 2/2008 70 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Heuristic design and optimization scheme
− Connection request sorting rules
• Longest first• Most requested couples first • Balanced• Random
− Processing of an individual lightpath
• Routing, Fiber and Wavelength Assignment (RFWA) criteria
• Dijkstra’s algorithm performed on the multifiber layered graph
Sort connectionrequests
Idle network,unlimited fiber
Setup the lightpathssequentially
Prune unused fibers
Identify fibers withonly k used λs
Prune unused fibers
Attempt an alternative RFWA for the identified lightpaths
fork = 1 to W
Revision: 2/2008 71 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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 criteria
Revision: 2/2008 72 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA RFWA-criteria labels
VWP
WP
LLR
SP
C1
C2
C3
C4
C5
C6
C7
C8
mH
mL
mH
mL
mH
mL
mH
mL
LLR
SP
VWP
WP
LLR
SP
C1
C2
C3
C4
C5
C6
C7
C8
mH
mL
mH
mL
mH
mL
mH
mL
LLR
SP
Revision: 2/2008 73 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Total number of fibers
• Hop-metric minimization performs better
− Variations of M due to RFWAs and conversion in the mH case below 5%
0
100
200
300
400
500
0
100
200
300
400
500
2 4 8 16 32
404
207
109
59.
7
36.2
410
213
114
64.
5
39.4
VWPWP
Tot
al f
iber
nu
mbe
r,
M
Number of wavelengths, W
.
0
100
200
300
400
500
0
100
200
300
400
500
C3 C1 C7 C5 C4 C2 C8 C6
2481632
SP LLR SP LLR SP LLR SP LLR
VWP WP VWP WP
mH mL
• The initial sorting rule resulted almost irrelevant for the final optimized result (differences between the sorting rules below 3%)
Tot
al f
ibe
r nu
mbe
r,
M
Revision: 2/2008 74 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Fiber distribution in the network
− 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 idle
(3,4)
(5,6)
(2,2)
(6,6)
(2,2)
(2,2)
(6,5)(6,6)
(6,5)
(2,2)
(0,1)
(2,2)
(2,2)
(2,2)(2,3)
(2,2)
(2,2)
(0,0)(4,4)
(4,4)
(4,4)
(0,0)
Revision: 2/2008 75 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Wavelength conversion gain
• Wavelength converters are more effective in reducing the optimized network cost when W is high
0
2
4
6
8
10
0
2
4
6
8
10
2 4 8 16 32
1.63
3.08
4.56
7.36
8.24
M g
ain
fact
or,
GM
Number of wavelengths, W
GM =MWP − MVWP
MWP
×100
Revision: 2/2008 76 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Saturation factor
0
0.2
0.4
0.6
0.8
1
1.2
0
0.2
0.4
0.6
0.8
1
1.2
2 4 8 16 32
VWPWP
0.9
85
0.9
7
0.9
29
0.8
62
0.75
8
0.9
72
0.9
36
0.8
84
0.78
7
0.66
8
Number of wavelengths, W
Sat
ura
tion
fact
or,
ρ
..
LLR LLR LLR LLR
VWP WP
mL mH mL mH
SP SP SP SP
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
C1 C3 C2 C4 C6 C8 C5 C7
2481632
ρ
• A coarser fiber granularity allows us to save fibers but implies a smaller saturation factor
• VWP performs better than WP− Variations of ρ due to RFWAs and metrics in
the VWP case below 5%
ρ =C
W × M
C = number of used wavelength channels
Sa
tura
tion
fact
or,
Revision: 2/2008 77 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Optimization: longer lightpaths...
• Compared to the initial routing (shortest path, which is also the capacity bound) the fiber optimization algorithm increases the total wavelength-channel occupation (total lightpath length in number of hops)
− C is increased of max 10% of CSP in the worst case
∆ =C − CSP
CSP
× 100
CSP = number of used wavelength channels with SP routing and unconstrained resources (capacity bound)
0
2
4
6
8
10
12
2 4 8 16 32
2.18 2.37
3.86 4.
62
9.61
2.23
1.93
3.39
3.6
6
VWPWP
Ca
pa
city
bo
un
d p
er
cen
t de
via
tion
Number of wavelengths, W
mH cases
, ∆
Revision: 2/2008 78 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA …traded for fewer unused capacity
U = 1 −C
W × M
× 100
• Compared to the initial routing (shortest path) the fiber optimization algorithm decreases the total number of unused wavelength-channels
− U is halved in the best case
• Notes− Initial SP routing curve:
data obtained in the VWP scenario (best case)
− Optimized solution curve:averaged data comprising the WP and VWP scenarios
0
10
20
30
40
50
0 5 10 15 20 25 30 35
initial SP routingoptimized solution
% U
nu
sed
ca
pa
city
, U
Number of wavelengths, Nλ
Revision: 2/2008 79 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Convergence of the heuristic optimization
• 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 criteria
55
60
65
70
75
80
85
90
6 104
6.5 104
7 104
7.5 104
8 104
8.5 104
9 104
9.5 104
0 2 4 6 8 10 12 14 16
VWPW=16, mH, SP
M L
To
tal f
ibe
r n
um
be
r, M
To
tal fib
er le
ng
th, L
(km)
optimization counter, k
Revision: 2/2008 80 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: 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.
0
50
100
150
200
250
300
350
400
0 5 10 15 20 25 30 35
NSFNET VWP
source form.heuristic
Number of wavelengths, W
Tot
al f
iber
num
ber,
M
0
200
400
600
800
1000
1200
1400
1600
0 10 20 30 40 50 60 70
EON VWP
source form.
heuristic
Number of wavelengths, W
Tot
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Revision: 2/2008 81 (81)
Authors: Massimo Tornatore, Guido Maier Course: Optical Core NetworksModule: WDM Network Design
Heuristic static design by dynamic RFWA Concluding 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 occupancy
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