WDM Network Elements

Based on: Optical Networks a Practical Perspective (2nd Edition) –Chapter 7, by R.Ramaswami, K.N.Sivarajan

Architectural Aspects of Network Elements! Optical Line Terminals (OLT) – widely

deployed today! Optical Add-Drop Multiplexers (OADM)

– some deployment has been done! Optical Crossconnects (OXC) –

deployment just starting

WDM Network Architecture

! Optical line amplifiers are not shown (all elements may include optical amps)

WDM Network Architecture! OLTs are placed either at the end of links or

in point-to-point configurations! OADMs are used at places where some

fraction of the wavelengths need to be terminated and others need to be added and are typically in linear or ring topologies.

! OXCs enable mesh topologies and switching of wavelengths.

! Clients of these networks can be ATM, SONET, IP switches using the optical layer.

Important Features of WDM Architecture! Each link can support a number of wavelengths (physical

limitations!)! Wavelength Reuse: Multiple lightpaths can use the same

wavelength in the network as long as they do not overlap on the same link.

! Wavelength conversion: lightpaths may undergo conversion along the lightpath for better utilization/adaptation of signals.

! Transparency: optical layer is protocol insensitive.! Circuit Switching: lightpath establishment on demand. (no

packet switching at the optical layer!)! Survivability: in event of link/node failures lightpaths can be

rerouted (resiliency!)! Lightpath topology: graph representation of nodes and

links/lightpaths between them (the view of the higher layer)

Optical Line Terminals (OLTs)

Elements inside OLTs! Transponders! Wavelength multiplexers (demultiplexers)! (Optical amplifiers)

λ1 ,

IP router

SONET

SONET

O/E/O

O/E/O

Laser

Receiver

Non ITU λ

Non ITU λ

ITU λ3

ITU λ2

ITU λ1

λ1 λ2 λ3

λOSC

λOSC

Optical line terminal

Transponder Mux/demux

λ1 ,

IP router

SONET

SONET

O/E/O

O/E/O

Laser

Receiver

Non ITU λ

Non ITU λ

ITU λ3

ITU λ2

ITU λ1

λ1 λ2 λ3

λOSC

λOSC

Optical line terminal

Transponder Mux/demux

Transponders ! Adapts a signal to be transmitted in the WDM network.

My include a simple OEO conversion or optical wavelength conversion (research labs). The interface between the client and the transponder may vary (depending on: bit-rate, distance, loss, etc.)

! Most likely SONET i-face is short-reach (SR) but can be a very-short range (VSR) interface for >=10Gbps.

! The signal generated by the transponder shoguld(optimally) conform to ITU standards.

! Transponders may add networking functionality such as: overhead for management purposes or forward error correction (FEC – OEO required!).

! May Monitor BER of signal.

Need for Transponders! In some cases the clients can receive on ITU

wavelengths so transponders are only needed for transmission

! In some other (fortunate) cases the adaptation is done inside the client equipment reducing the cost of the OLT, however these interfaces are not standardized and are likely to be vendor dependent.

! The transponders create the bulk of the cost, size and power consumption of OLTs, thus the number of transponders should be kept minimal.

Optical Multiplexers! Any multiplexing technology can be

used! Optical amplifiers may be used to boost

signals in both directions (for reception as well as transmission).

Supervisory Channel in OLTs! Optical Supervisory Channel (OSC) is

carried on a separate wavelength! OSC is used to monitor the performance

of amps on the links as well as for management functions (performance, fault, configuration, security, accounting) .

Optical Line Amplifiers

Optical Line Amplifiers! Placed in the “middle” of optical fibre with a distance

of about 80-120km.! EDFA is currently the most used amp.! Typical amps cascade two or more gain blocks with

mid-stage access.! In the mid-stage compensating elements can be put

(e.g., chromatic dispersion compensators, flat gain compensators, maybe OADMs).

! Amplifiers also contain gain control and performance monitoring capabilities.

! Employment of Raman amplification has just started, where a laser pumps light in the opposite direction of the signal.

Optical Line Amplifiers! The optical supervisory channel is terminated at the

input and re-injected at the output (OEO conversion, electronic processing).

! In a system using both C and L band, bands are separated and employ separate EDFAs.

OADM

Ramanpumplaser

Receiver

λOSC Gain stage

λ1, λ2,…, λW

Gain stage

Laser

Dispersion compensator

OADM

Ramanpumplaser

Receiver

λOSC Gain stage

λ1, λ2,…, λW

Gain stage

Laser

Dispersion compensator

Optical Add/Drop Multiplexers (OADM)

OADMs! May be used in OLAs (seen previously).! Can be used as stand alone network

elements.! OADMs can save on costs significantly, by

reducing the number of point-to-point connections (terminations), thus reducing the number of OLTs (and transponders, that generate most of the cost).

! In the first of the following pictures - at node B six out of eight transponders are connected back-to-back – what a waste!

OADM vs. OLT

Note, that transponders can be skipped in the first picture, if those OLTs Are engineered in that way. (remember power levels and required SNR!)

Optical passthrough

Add/Drop

Add/Drop Transponder

OLT

OADM

Node A

Node A

Node B

Node B

Node C

Node C

(a)

(b)

Optical passthroughOptical passthrough

Add/Drop

Add/Drop Transponder

OLT

OADM

Node A

Node A

Node B

Node B

Node C

Node C

(a)

(b)

OADM Architectures! OADMs have two line ports and a number of local

ports. Attributes are:! Total number of λ-s supported! Number of λ-s that can be added/dropped

(adropped).! Any constraints on what λ-s can be adropped?! How easy to upgrade (λ-s to be adropped)?! Is it modular? Is cost proportional to the number of

λ-s to be adropped?! Complexity of its physical layer. Is the pass-through

loss, crosstalk, etc. growing with additional λ-s?! Is it reconfigurable (software control) on what λ-s

can be adropped? Today’s OADMs are rather

Parallel OADM Architecture

! No constraints on what λ-s can be adropped (minimal constraints on planning lightpaths).

! Loss is fixed (adropping additional channels is easy).! Not cost effective if adropping small number of λ-s.! Since all λ-s are always re-multiplexed, the tolerance of lasers/filters must be

stringent.

λ1, λ2,…, λWλ1, λ2,…, λW

λW

λ2

λ1

Drop Add

Demux Mux

λ1, λ2,…, λWλ1, λ2,…, λW

λW

λ2

λ1

Drop Add

Demux Mux

Modular Parallel OADM Architecture

! Implies constraints on what λ-s can be adropped.! Cost effective also if adropping small number of λ-s.! The tolerance of lasers/filters can be higher! Loss is fixed (adropping additional channels is easy).! Modular multistage approaches are also used today! Loss is not uniform for all λ-s.

λ1, λ2,…, λWλ1, λ2,…, λW

Band 4

Drop Add

Demux Mux

Band 3

Band 2

Band 1

λ1,λ2

λ1, λ2,…, λWλ1, λ2,…, λW

Band 4

Drop Add

Demux Mux

Band 3

Band 2

Band 1

λ1,λ2

Serial OADM Architecture

! A single channel is adropped (SC-OADM). To drop multiple channels, SC-OADMs can be cascaded.

! Adding additional SC-OADMs disrupts existing channels for a short while, thus planning is needed ahead of time.

! Highly modular (cost is low for less λ-s).! Loss increases with λ-s to be adropped which may require additional

OLAs.

λ1, λ2,…, λW λ1, λ2,…, λW

Drop Addλ1 λ2

λ1, λ2,…, λW λ1, λ2,…, λW

Drop Addλ1 λ2

Engineering Problems with SC-OADMs

Band-drop OADM Architecture

! Fixed group of λ-s is adropped and undergo a further level of demultiplexing.

! Adropping additional λ-s does not effect loss (if these λ-s are in the group).

! Complicates λ planning (constraints)

λ1, λ2,…, λW λ1, λ2,…, λW

Drop Add

λ1, λ2, λ3, λ4

λ1, λ2,…, λW λ1, λ2,…, λW

Drop Add

λ1, λ2, λ3, λ4

Reconfigurable OADMs! Do not only reduce maintenance cost

but enable higher flexibility.! Transponders need to be deployed

ahead (modular cost??) and tunable transponders are yet expensive.

! Reconfigurable OADMs can be viewed as OXCs.

Reconfigurable OADMs

Reconfigurable OADMs

Optical Crossconnects (OXC)

OXCs! OXCs are required to handle mesh topologies

(OADMs have only two ports making them available for ring and point-to-point only).

! OXC are also key elements for reconfigurability.

! Some ports are connected to other OXCs and some are terminated by optical layer client equipment (SONET,ATM, etc.).

! OXCs usually do not contain OLTs (separate products).

A Typical OXC

IP ATMSONETSDH

OXCOLT

IP ATMSONETSDH

OXCOLT

IP ATMSONETSDH

OXCOLT

Key Functions of OXCs! Software controlled service provisioning! Protection of lightpaths against defects! Bit rate transparency is a desirable attribute! Performance monitoring capabilities (testing,

non-intrusive troubleshooting)! Wavelength conversion may be incorporated! Multiplexing and grooming of STS signals can

be incorporated (electrical domain)

OXC Main Parts! Switch core – the switch that actually

performs the crossconnect function! Port complex – port cards or interfaces to

other equipment

! OXCs and OLTs can be interconnected in different ways: ! Opaque configurations: the signal is converted in

the E domain! All-optical: signal remains in the optical domain

Optical vs. Electrical Core! Electrical core has a total switch capacity e.g.,

2.56Tbps. This can be used to switch e.g., 1024 OC-48 or 256 OC-192 signals.

! Optical core cannot offer grooming or switching at lower signal speeds

! Optical core is bit-rate independent (and transparent) the cost is the same no matter what signal it is switching (unlike electrical ports).

! Optical core is more scalable thus future proof and may allow to switch groups of wavelengths inexpensively.

Different OXC Architectures

! The size, power consumption, cost improve down the figures.

Properties of Architectures! Electrical cores rely on the WDM signals to be demultiplexed

and fed in using e.g., SR optical interfaces (1310nm range). Wavelength conversion is easy!

! The first two architectures can easily do embedded performance monitoring, BER can be used e.g., for protection switching. In-band overhead signalling channels may be used.

! The bottom two architectures cannot do that, they need out-of-band signalling channels

! All-Optical OXCs from different vendors are unlikely to cooperate (different link-engineering).

! Migration from the second to the third architecture is relatively easy but it will require equipment from the same vendor.

Comparison of Architectures

LowMediumHighHighFootprintLowMediumHighHighPower cons.

LowMediumHighMediumCost/port

Optical PowerOptical PowerBERBERSwitchingNoYesYesYesλ conversion

HighestHighHighLowCapacityNoNoNoYesGroomingd)c)b)a)FigureOpticalOpticalOpticalElectricalSwitch-core

All-OpticalOpaqueOpaqueOpaqueAttribute

All-Optical OXCs! The bottom architecture of the last picture.! No:

! Low speed grooming! Wavelength conversion! Signal regeneration

! One solution is to combine the optical core (groups of wavelengths or entire fibres can be switched at once) with an electronic core.

! Since there is no wavelength conversion, architecture can be simplified – wavelength planes.

Combined Optical – Electrical Core

Wavelength Planes

WDM Network Design

Based on: Optical Networks a Practical Perspective (2nd Edition) –Chapter 8, by R.Ramaswami, K.N.Sivarajan

Example of a Design Problem

! Line speed: 10Gbps! 50Gbps is needed between each of the nodes.

A CB

Rou

ter

Rou

ter

Rou

ter

Rou

ter

Rou

ter••• •••

•••

•••

•••

Router

••• •••

•••

••• •••

(a)

(b)

(c)

Example of a Design Problem! 10 router ports can be saved with the

employment of an OADM. ! This may cost more but the number of router

ports (and their cost), and transponders can easily satisfy the employment of an OADM (today and in the future).

! The lightpath topology encountered by the routers is significantly different although both scenarios are valid.

! If the required bandwidth is significantly less than the line speed, then a router may be beneficial.

Formulation of Design Problems! Given: the fiber topology and the traffic matrix (traffic

requirements).! Task: designing the lightpath topology that is superposed

on the fiber topology while satisfying the traffic requirements (lightpath topology design problem).

! The routing and wavelength assignment problem (RWA) is similar to the lightpath topology problem, except that the design has to be done within the optical layer (as in the second example).

! Grooming of traffic may be necessary to come up with efficient traffic matrices.

! In general it is a good idea to separate this problem (like we did before) since solving the two problems together is quite hard.

Cost Trade-offs

Measurement of Cost1. Higher layer equipment cost is determined by

the number of ports required (e.g., IP ports).2. At the optical layer an important cost factor is

the number of transponders needed. Since every port requires a transponder (and every lightpath two), this cost can be coupled to that of 1.

3. Optical layer equipment cost is estimated by the number of wavelengths employed on links.

2-connected! There should be 2 (node-wise) disjoint routes

between every pair of nodes.! 2-connected (but arbitrary) mesh topologies

are more cost effective for large networks, but ring topologies (always 2-connected) are good for networks with less geographic spread.

! A ring topology has the minimum number of links (N) connecting N nodes that keeps a topology 2-connected, thus it has a low fiber deployment cost

Assumptions for Example! Topology is a ring.! N: number of nodes! t: is the (units of) traffic generated at each node

to be routed to remote nodes.! Destination distribution is assumed to be uniform

resulting in t/(N-1) units of traffic routed between every pair of nodes in the ring (thus there must be a way to reach each router from the others).

! The capacity of each λ is assumed to be 1 and there are no wavelength conversion capabilities.

Important Metrics! Router ports: should be kept at a

minimum! Wavelengths: should be kept at a

minimum! Hops: the maximum number of hops

taken by a lightpath! There is a trade-off between this

parameters

LTD: Point-to-point WDM Ring (PWDM)! Lightpath topology is a ring with several links (several

wavelengths)

A

D B

C

LTD: Hub Design! All routers are connected to a central hub (packet travel

over two lightpaths: source->hub and hub->destination)

C

Hub

B

A

D

LTD: Mesh topology! All-optical design: a lightpath between all pairs of routers.

C

B

A

D

RWA for PWDM Ring

! Single-hop lightpaths! W denotes the number of wavelengths on each link.

OLT 1

IP 1

OLT 2

IP 2

OLT 4

IP 4

OLT 3

IP 3λ1

λ1

λ1

λ1

λ2

λ2

λ2

λ2

Lightpaths

! Assuming N is even, and that each stream is routed on the shortest route, the traffic load (L) on each link is:

Thus:

The number of router ports required per node is: Q=2W

Hops: for a PWDM ring each lightpath is exactly one hop

RWA for PWDM Ring

tNN

L8

111−

++=

LW =

RWA for Hub Architecture

IP 1OADM

1

OADM2

IP 2

OADM4

OADM3

λ1

λ1

λ1

λ2

λ2

λ2

OADMhub

λ2

λ1 IP 4

IP 3

IPhub

! lightpaths are needed from each node to the hub for transmission and another for reception from other nodes.

! The number of router ports ! If wavelengths are reused as seen in the

picture, the number of wavelengths is

! The worst-case hop length is: H=N-1

RWA for Hub Architecture

t t

tQ 2=

tNW2

=

RWA for All-optical Design

λ3

OADM1

OADM2

IP 2

OADM4

OADM3

λ1

λ1

λ1 λ3λ2

λ2

λ1

IP 3

IP 1 IP 4

RWA for All-optical Design! Between each router

lightpaths are needed! Thus the number of router ports

! The number of wavelength depend on how the lightpaths are routed. Is is possible to find WA, so

)1/(2 −Nt

−−=

1)1(2

NtNQ

+

−=

481

2 NNN

tW

Comparing Architectures –Number of Ports! A lower bound can be calculated for the

number of ports required:! Q=2t(N-1)/N

Comparing Architectures –Number of Ports

Comparing Architectures –Number of Wavelengths! Lower bound for number of

wavelengths:! Hmin is the average number of hops

between nodes (on a minimum route), in a ring:

Average load:

)1(41

41

min −++=

NNH

nksNumberofliicTotalTraffHLavg *min=

Comparing Architectures –Number of Wavelengths

A Lightpath Topology Design Problem

LTD Assumptions! We assume that there are no constraints on the

physical layer (maximum length of lightpaths or W).! We assume that lightpaths are bi-directional (two

fibers).! At each node a maximum of ∆ ports can be used

(this constrains the number of lightpaths to N∆/2).! We assume that the cost of a lightpath does not

depend on its length (may not hold in long-haul networks).

! By designing the lightpath topology we also have to solve the routing problem.

LTD Assumptions! IP traffic is assumed, with an arrival rate of

packets between source s and destination d of λsd (packets/second).

! bi,j are (n2-n) binary variables (one for each possible lightpath; i≠j). bi,j=1 if the design has a lightpath from i to j.LTD specifies the values for {bi,j}.

! We assume that we can arbitrarily split traffic over different paths between the same pair of nodes.

! Let the fraction of traffic between s and d that is routed over (i,j) be:

! Then the traffic in (pkts/sec) for s, d over (i,j) is:

! The total traffic over (i,j) is:! Congestion parameter: ! The lambda values have to be determined!! Let’s assume a Poisson process for arrivals

and exponential distribution of transmission times with mean: 1/µ seconds.

LTD Assumptions

sdija

sdsdij

sdij a λλ =

∑=sd

sdijij λλ

ijij λλ maxmax =

LTD Problem! By modeling the traffic generation with a

Poisson process, each link can be modeled as a Markovian M/M/1 queue.

! The average queuing delay is then:

! The (max) throughput is the minimum amount of offered load, where the delay becomes infinite! (when λmax=maxi,jλ ij=µ)

! Thus the congestion has to be minimized.

ijijd

λµ −= 1

! Objective function and the constraints are linear functions of different λ-s and b-s.

! A mathematical program with these properties is called a linear program (LP) if all variables are real.

! If all variables are integers, it is an integer linear program (ILP).

! If some variables are integers and some are real it is a mixed integer linear program (MILP).

! Although LPs are P problems, ILPs and MILPshave been show to be in general NP-hard.

Hardness of LTD Problem

! Our problem is MILP and is sometimes called the LTD-MILP.

! General MILPs may be solved by heuristics (exhaustive search of variable space is too expensive).

! Heuristics can be based on LPs (LP relaxation and rounding) or other paradigms (simulated annealing, genetic algorithms, etc.)

Hardness of LTD Problem

LTD Heuristic based on LP! If we relax the bij constraint to: 0≤bij ≤ 1 then

the LTD-MILP becomes an LP.! The value of the solution of the LP is a lower

bound to LTD-MILP called the LP-relaxation bound.

! So first let us solve the LTD-LP problem and assign values to bij carefully not to violate the degree constraints.

! The with the fixed bij values rerun the now modified LTD-LP and obtain a sub-optimal solution.

Behavior of LTD-LP-relaxationFor a 14 node example:

9494946

1131131135

1421421424

1941891893

4403882482

LP roundingMILPLP-relaxDegree

Routing and Wavelength Assignment

RWA! Given a network topology and a set of lightpath

requests (which can be obtained by an LTD solution), let us determine the route and the minimum possible wavelengths.

! If no wavelength conversion is available, then lightpaths must use the same wavelength over all links (two lightpaths cannot use the same wavelength over a common link)

Wavelength conversion

Wavelength Conversion! Full wavelength conversion can be done in

opaque switches.! Fixed conversion: is fixed at the time of

deployment (a lightpath entering in port-a onλ i will always exit on port-b λj).

! Limited conversion: a signal is allowed to be converted from one λ to a limited set of other λ-s.

! The latter two can save cost on switches but not transponders (thus it is a theoretical problem when to employ them, except if the switch is all optical)

Fixed Wavelength Conversion

Limited Wavelength ConversionLimited conversion with a degree of 2

Multiple Fiber Pairs! Multiple fiber pairs may be deployed between nodes to

increase capacity.! This can be seen as having one fiber pair with limited

wavelength conversion capabilities (the two networks can be shown to be equivalent).

WA and λ conversion! Depending on the λ conversion capabilities

(NC,FC,LC,C) the WA problem changes. ! In case of C, the assignment of the

wavelengths is trivial (given the routing and LTD) and W (the required number of wavelengths) is equal to the number of wavelengths required on the link requiring the most wavelengths to be fit (L). If C is not available, the question is: how much lager Wis than L.

Graph Coloring and WA! WA relates to graph coloring:

! Graph representation of the network: G! Convert it into P(G), where each lightpath is a

vertex and vertexes are connected by edges if they share a common link in G.

! We have to assign a color to each node in P(G) so that neighboring nodes do not share the same color while minimizing the number of colors.

! The general coloring problem is NP-complete !

Dimensioning Wavelength-Routed Networks

Wavelength Dimensioning! The number (and set) of wavelength on each

WDM link have to be determined.! Today most networks are designed to support a

fixed traffic matrix that can be given in terms of lightpaths (only RWA) or higher layer traffic (LTD and RWA).

! The solution of the RWA solves the dimensioning problem (offline-RWA in the design phase).

! For a network already in operation lightpaths are added one-by-one and thus the so-called online RWA has to be solved. Today it is important to have good solutions for this problem.

Wavelength Dimensioning! Determining the number of wavelengths per

link also determines how many ports are needed to be terminated thus determines the sizes of OXCs and OLTs.

! Today a forecast is made every half a year on the required traffic matrix to be supported and networks are upgraded accordingly.

! Capacity planning can also be done by considering the statistical properties of the traffic.

Dimensioning of Wavelengths Based on Statistical Traffic Models

Two Cases for Statistical Models1. First-passage model: networks starts with

no lightpaths at all, as requests arrive (according to a statistical model), they have to be set up. Wavelengths also depart, but in average there are more arriving than terminating requests.

2. Blocking-model: lightpath requests are treated in the same way as in PSTN networks, the arrival and termination rate is assumed to be equal.

First-passage Model! Network is divergent in the long run.! The question is: when (T) will a new request

first be rejected?! Dimensioning: first rejection should happen

with high probability after T.! Today, since lightpaths are more permanent

this is a good model. Operators should not reject any requests – upgrading (dimensioning) is needed. T should be determined!

Blocking Model! Network is in equilibrium.! Request should be honored with a high

probability thus blocked with a very-low probability.

! This is for the future, when lightpaths will be provisioned on-demand.

Hardness of Problems! In general, the analysis problem is

easier to solve than the design (or dimensioning) problem.

! The easiest way to solve the design problem to iteratively solve the analysis problem.

! Thus the analysis of these networks can be a major focus.

First-Passage analysis! This is a relatively new field, and

publications just start appearing. ! The mathematical background is rather

complicated thus we will omit it.

Blocking Model analysis! Offered load: arrival rate of lightpath

requests * average duration.! Reuse factor: offered load per wavelength! If the maximum blocking probability is set,

what is the maximum offered load or reuse factor? Depends:

1. Network topology2. Traffic distribution3. RWA algorithm used4. W (number of wavelengths available)

Blocking Model analysis! The general problem is hard to solve

even analytically if routing is fixed and RWA is random.

! The problem becomes even more hard if routing is not fixed (only simulation approach), however it is possible to calculate offered load for small networks with large W.

Blocking Model - analysis! Poisson process of arrivals with exponential

holding times.! RWA: If wavelengths are numbered from 1 to

W, a new request should be assigned the first available wavelength on the shortest path over all links on this path.

! Figure shows results for a 32 node random graph with average nodal degree of 4.

Blocking Model - analysis

The Impact of Wavelength Conversion on Blocking Probability

for Lightpath Requests

Assumptions! We assume that the route for each lightpath is

specified.! With NC the network assigns arbitrary but

identical wavelength over each link on the route (if available).

! With FC the network assigns an arbitrary wavelength on each of the links on the route (if available).

! The probability that a wavelength is used on a link is π, and π is independent of the same probability of other wavelengths on the same link and other links.

Blocking Probability with NC! π: probability that a λ is used on a link! W: number of λ-s on each link.! H: a new lightpath request with H links

in its route.

( )WHNCbP )1(1, π−−=

Blocking Probability with FC! π: probability that a λ is used on a link! W: number of λ-s on each link.! H: a new lightpath request with H links

in its route.

( )HWFCbP π−−= 11,

Deriving π from Pb

( ) HWNCbNC P

/1/1

,11 −−=π

( ) WHFCbFC P /1/1

, )1(1 −−=π

HP W

NCbNC

/1,≈π

W

FCbFC H

P/1

,

≈π

Comparing NC with FC

W

NC

FC H /11−=ππ

! Comparing for the same blocking probability:

! For the NC case, the achievable link utilization is lower by a factor of the average hop of lightpaths than that of FC.

Relaxing Independency Assumption

! Lets relax the assumption that the probability that one wavelength is used over a link is independent of that of other links the following way:

! Interfering lightpath: a lightpath that has already been established and shares links with the new request.

! πl: probability that an interfering lightpath is using let’s say link-i but not link-(i+1). (departure)

! πn: probability that an interfering lightpath is not using let’s say link-i but will use link-(i+1). (arrivl.)

Relaxing Independency Assumption

! P(λ is used on link i | λ is not used on link i-1)= πn

! P(λ is used on link i | λ is used on link i-1)= (1- πl)+πnπl

! Pb,NC and Pb,FC can be derived:

! Where πi is a function of πl and πn.

( )WHnNCbP )1(1, π−−=

∏= −

−

−−−=H

iWi

Wi

Wnii

FCbP1 1

, 1)(11

πππππ

! Comparing for the same blocking probability:

! The interference length is Li=1/πl an approximation to the expected number of shared links between the new and the interfering lightpath.

! The conversion gain is more in networks where there is more mixing (dense mesh networks) (unlike ring networks).

Comparing NC with FC

llnlnW

NC

FC HH πππππππ /1 if )(/11 >>−+= −

Wavelength Assignment and Alternate Routes

Routings effect on WA! Let’s consider four different RW algorithms:1. Shortest path routing, random wavelength

assignment from available pool2. Two shortest paths, random wavelength

assignment from available pool3. Shortest path routing, assignment of wavelength

from the available pool that is the most used already in the network

4. Two shortest path routing, assignment of wavelength from the available pool that is the most used already in the network

Routings effect on WA! We look at simulation results of a 20 node

39 link network. If we fix the blocking probability to 1%, the reuse factor can be determined:

8.3Max-used-27.5Max-used-17.8Random-26.9Random-1Reuse factorRWA alg.

Maximum Load Dimensioning Models

Load Dimensioning! In an all-optical wavelength routing

network, there are very limited wavelength conversion capabilities.

! Offline case (all lightpaths are predefined), if there is FC, then W=L, otherwise W>=L.

! Online case (lightpath request keep coming in) is more difficult to determine.

Offline path request! Theorem: Given a routing of a set of

lightpaths with load L in a network G with M edges, with the maximum hops in a lightpath being D, the number of wavelengths sufficient to satisfy this request is: W≤min[(L-1)D+1,(2L-1)√M-L+2]

WA and Linear Networks

! Line networks are closely related to rings.! Algorithm for WA:

1. Number the wavelengths from 1 to L. start with the first lightpath from the left and assign it to wavelength-1.

2. Go to the next lightpath and assign the next number until all lightpaths are assigned

! In a ring there are two possible routes for each lightpath

L

λ1

λ3

λ2

(a) (b)

WA and Ring Networks! If Lmin is the routing with the minimum

possible load (there is an algorithm for that), then

! Given a set of request for lightpaths and Lmin to satisfy these requests, shortest path routing yields a load of at most 2Lmin.

RWA and NC Ring Networks! Given a set of lightpath requests and

routing on a ring with load L, WA-NC can be done with 2L-1 wavelengths

λ1

λ3

λ2

(a)

(b)

•

•

•

•Cut

RWA and NC Ring Networks! It can be shown with graph coloring,

that if no three lightpaths cover the entire ring, then W ≤ 3/2L is sufficient to perform wavelength assignment .

! Thus to support all (pathological) requests we have to employ 1/2L more wavelengths…

RWA and FC and LC Ring Networks! If FC is available, then as long as the

load is smaller then W, all requests can be accommodated (L≤W)

! It can be shown that if only one node in the ring has full wavelength conversion all all others have none, then L ≤ W still holds!

RWA and FxC and FC Ring Networks

! If a node has fixed conversion like in the picture at one node (where λ i is converted into λ(i+1)mod W), and no conversion at the other nodes, then this network can support requests with load L≤W-1

! Having two such nodes enables L≤W.

Comparison of the Impact of Conversion on Diff. Topologies

LL3/2LTree

LL3/2LStar

LLL+12L-1Ring

LLMin[(L-1)D+1,(2L-1)√M-L+2)

Arbitrary

LimitedFullFixedNone

Conversion typeNetwork

Online RWA in Rings

Online RWA in Rings! Routing of wavelengths is already given! Lightpaths arrive and depart! In this situation it is much more hard to

determine L to a given W with NC (with FC it is yet trivial)

Online Line Network Problem! If W(N,L) denotes the number of

wavelengths required to support all online lightpath requests with load L in a network of N nodes with NC. In a line network:W(N,L) ≤L+W(N/2,L) (if N is a power of 2)

Online Line Network Problem! If W(1,L)=0 thus W(2,L)=L:! In a Line network with N nodes and

online requests of a load of L, all these requests can be supported by at most L* log2N wavelengths with NC.

Online Ring Network Problem! In a Ring network with N nodes and

online requests of a load of L, all these requests can be supported by at most L* log2N+L wavelengths with NC.

Permanent Lightpaths! If the lightpath requests are permanent,

then all requests can be supported by at most 2L wavelengths with NC, and

! If there is a limited degree-d wavelength conversion, then W≤L+max(0,L-d)

Comparing RWA for Rings

LLFull conversion

L[log2N]+L0.5L[log2N]No conversion

Online model with lightpath terminations

LLFull conversion

3LLFixed conversion

3L3LNo conversion

Online model without lightpath terminations

LL≥≥≥≥2

L + 1L + 1Fixed conversion

2L – 12L – 1No conversion

Offline traffic model

Upper Bound on WLower Bound on WConversion Degree