Cc wdm network design

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Optical Core Networks

WDM Network Design

Massimo Tornatore, Politecnico di Milano, [email protected] Maier, Politecnico di Milano, [email protected]

http://www.e-photon-one.org/

http://creativecommons.org/licenses/by-nc-sa/3.0/

http://creativecommons.org/licenses/by-nc-sa/2.5/

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

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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

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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

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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

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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

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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

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• 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)

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• 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

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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

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• 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

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Outline




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• 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

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• 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

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• 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

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• 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

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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

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Outline



• References

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Approaches to WDM design

• Two basilar and well-known approaches [WaDe96],[Wi99]− FLOW FORMULATION (FF)− ROUTE FORMULATION (RF)

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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

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• 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)

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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

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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})

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Unprotected caseVWP, FF

(l,k)F

c,(l,k)x

klFWx

clslv

dlv

xx

kl

ckl

cklckl

Ak Akcc

cc

cklclk

l l

∀∀

∀⋅≤

∀

=−=

=−

∑

∑ ∑∈ ∈

integer

integer Integrity

),(Capacity

,

otherwise0

if

if

itySolenoidal

,

,,

,,,

,,,,

N.B. from now on, notation “∀l,k” implies l ≠ k

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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 ⇒

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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

Ak Akcc

cc

cklclk

l l

∀∀

∀

∀≤

∀=

∀

=−=

=−

∑∑

∑ ∑∈ ∈

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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

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• 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

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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)

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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

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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

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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 ,

,,,

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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

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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]

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Unprotected caseWP, SF

)(,,,integer

,integer

integer

,,integer

Integrity

),,(Capacity

)(,,

)(,,,

,

itySolenoidal

,,

,

,

,,,

,,,,

,,,

,,,,,,,,

,,

,,,,

lijic

is

l,kF

il,kx

klFx

liliCc

lilicxx

iCSs

isx

li

i

kl

ikl

iklikl

lili

Ak Akjiiklilk

lliii

Akiiki

l l

i

≠∀∀∀∀

∀≤

≠∀=

≠∀−=

∀==

∀=

∑∑∑ ∑∑ ∑∑

∈ ∈

∈

λλ

λ

λ

λ

λ

λ

λ

λ

λ

λλ

λλλ

λλ

λλ

• Analogous extension to FF case

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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)

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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

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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

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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.

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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

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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

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Outline




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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.

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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

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Dedicated Path Protection (DPP) Flow formulation, VWP

(l,k)F

(l,k)c,tx

klFWx

tcklxx

tclsldl

xx

kl

tckl

tckltckl

tclktckl

Ak Ak

c

c

tckltclk

l l

∀

∀

∀⋅≤

∀≤+

∀

=−=

=−

∑

∑ ∑∈ ∈

integer

),( binary Integrity

,Capacity

,,, 1disjoint-Link

;,, otherwise 0

if2 if2

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

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Dedicated Path Protection (DPP) Route formulation (RF), VWP

l,kF

ntcr

klFWr

kltcr

tcr

kl

ntc

Rrklntc

RRrntc

nntc

klntc

lkklntc

∀

∀

∀⋅≤

∀≤

∀=

∑∑∑

∈

∪∈

integer

,, binary Integrity

,Capacity

,,, 1disjoint-Link

, 2itySolenoidal

,

,,

,,,

,,

,,

,,,

,,,,

• 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)

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ILP application to WDM network design Route formulation (RF) II, VWP

l,kF

ncr

klFWr

cvr

kl

nc

Rrklnc

n

cnc

klnc

∀∀

∀⋅≤

∀=

∑∑

∈

integer

,integer 'Integrity

,'Capacity

'itySolenoidal

,

,

'',,

,

,,

• 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

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Dedicated Path Protection (DPP) Flow formulation, WP

λ

λ

λ

λ

λ

λ

λ

λ λλ

λλ

λ

λ

λλ

c,v

l,kF

l,kc,tx

klFx

tcklxx

cv

tclslvdlv

xx

c

kl

tckl

tckltckl

tclktckl

c

Ak Ak

cc

cc

tckltclk

l l

∀

∀

∀

∀≤

∀≤+

∀=

∀

=−=

=−

∑∑

∑∑ ∑∈ ∈

bynary

integer

,, binary

Integrity

,,Capacity

,,, 1disjoint-Link

2

;,,, otherwise 0

if if

itySolenoidal

,

,

,,,,

),(,,,,,

,,,,,,,,,

,

,

,

,,,,,,,,

• 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)


Dedicated Path Protection (DPP) Route formulation (RF), WP

λ

λ

λ

λ

λ

λ

λ

λλ

λλ

λλ

λ

λ

),(bynary

integer

,),,( binary

Integrity

),,(Capacity

),(),,( 1disjoint-Link

, 2

),,( itySolenoidal

,,

,

,,,

,,,,

,,,

,,

,,,,,

,,,,

,,,,,

c,tv

l,kF

ntcr

klFr

kltcr

tcv

tcvr

tc

kl

ntc

Rrklntc

RRrntc

tc

n

tcntc

klntc

lkklntc

∀∀

∀

∀≤

∀≤

∀=

∀=

∑∑ ∑

∑∑

∈

∪∈

Revision: 2/2008 50 (81)


ILP application to WDM network design Route formulation (RF) II, WP

l,kF

ncr

klFr

cvv

cvr

kl

nc

Rrklnc

cc

n

cnc

klnc

∀∀

∀≤

∀=

∀=

∑∑

∑

∈

integer

,,integer 'Integrity

,,'Capacity

, 'itySolenoidal

,

2,1,,,

2,1

'',,,

,

,

2,1,,,

21

,2,1,,

2,1

21

2,1

2,12,1

λλ

λλ

λλ

λλ

λλ

λλλλ

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)


Outline



• References

Revision: 2/2008 52 (81)


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)


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)


Link Protection

• Different protected objects− Fiber level− Wavelength channel level

FAULT EVENT(1)

(2)

Revision: 2/2008 55 (81)


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)


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)


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)


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


Revision: 2/2008 59 (81)


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)


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)


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)


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)


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)


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)


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)


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)


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)


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)


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)


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)


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)


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)


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


.

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)


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)


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


GM =MWP − MVWP

MWP

×100

Revision: 2/2008 76 (81)


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


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)


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


mH cases

, ∆

Revision: 2/2008 78 (81)


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)


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)


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


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


Tot

al f

iber

num

ber,

M

Revision: 2/2008 81 (81)


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