metro network design - university of pittsburghdtipper/2110/slides9.pdf · – graph theory based...

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Metro Network Design Metro Network Design

David TipperGraduate Telecommunications and Networking

ProgramUniversity of PittsburghTelcom 2110 Slides 9Telcom 2110 Slides 9

Taxonomy

• The various network design classifications can be combined

Network DesignSize

Metro AccessWAN

Wired

Size

Wired Wireless. . . . . . . . . .

Technology

Stage

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VPN. . . . . . . . . .

greenfield greenfield incremental

Stage

For example may have a wireless incremental access network design problemThe techniques used to design the network will depend on the classification

2

Access, Metro and Long-Haul Transport

WAN Long-haul network

Access network

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Metro networkSource: J. Doucette, Ph.D. Thesis, UofA, 2004

• Metropolitan Area Networks (MANs) : provide connectivity across a geographical area the size of a city

Metropolitan Area Networks

Telcos/ISPs

OC 192size of a city • Typically a backbone network type

of architecture– For private networks similar to

campus backbone design– In Telcos and ISPs has a distribution

and aggregation function – reliability a bigger factor

Technolog

OC 48

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• Technology– SONET/SDH technology– GigEthernet, Carrier Ethernet

deployments, Fiber Channel– WDM and MPLS– Emergence of wireless alternatives

(e.g., WiMAX, 802.11 based Mesh)

Private

3

• Cost and Reliability are a bigger factor than access network

• Typically seek to minimize cost • Subject to Constraints for example

Basic MAN Backbone Network Design

• Subject to Constraints … for example– Average Packet Delay must be < maximum– Reliability requirements– Throughput, etc.

• Approaches are a bit different for private/campus network and service provider

• Many algorithms in the literature

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Many algorithms in the literature – Graph theory based (e.g., MENTOR,

MENTOUR)– Optimization based, (e.g., SONET Toolkit

from Telcordia - used by many LECs to plan MANs)

– Heuristics – routing based (will see some with WANs)

Mentor (MEsh Network Topological Optimization and Routing) Algorithm Builds backbone and access network together – good for

Mesh Network Design Algorithms

Builds backbone and access network together good for campus type design

1. Backbone selection (classify backbone/edge sites) Threshold clustering

2. Creation of the initial topology Prim-Dijkstra tree or Backbone tour

3. Link addition

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Utilization based

4. Access topology Star , Esau-William, MSLA, etc.

Low complexity – reasonable quality – in some design tools

4

• Divide sites into backbone sites and edge sites • Backbone sites are traffic aggregation points and node in the

routing mesh

Mentor Algorithm Step 1

routing mesh• Inputs are nodes Ni and their locations and node weights

(i.e., sum of all traffic demand at a node) W(Ni)• Initially assume a single link type with capacity C• Highly parameterized procedure – can produce many

alternative backbone node groups – by changing parameter settings in Mentor algorithm

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g g• Parameters are

– Radius (RPARM)– Weight Limit (WPARM)

• Use threshold clustering assign nodes to groups

• Choose backbone sites. (Threshold Cluster Algorithm)• Calculate the normalized weight NW(Ni)=W(Ni)/C

• In NW(Ni) > WPARM select Ni as a backbone node


• In NW(Ni) > WPARM, select Ni as a backbone node,

• Group end sites Nj around a backbone site, Ni, based onCost(Nj, Ni)/MAXCOST < RPARM.

• Where MAXCOST=Max i,j Cost(Nj, Ni)

The middle stage of clustering

Big squares are backbone nodes

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Big squares are backbone nodes

Nodes on or within circles are edges associated with that backbone node

What to do with nodes not assigned to backbone or edge status?

5

Merit function – gives equal value to proximity to center of network and weight merit(n)= 0.5(MaxDistCtr-distCtrn)/MaxDistCtr + 0.5(Wn/W_Max)Here 22 )()( yctryxctrxDistCtr nnn nn Weightx

Mentor Algorithm Step 1 Merit Functions

and

Center of Mass (xctr, yctr) defined by

• Sort the merit functions. The node with largest merit get picked as backbone node. Group end node around it. Repeat until all nodes are covered in groups.

22 )()(max yctryxctrxMaxDistCtr nnNn

Nnn

Nnnn

Weight

gxctr

Nnn

Nnnn

Weight

Weightyyctr

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Based on merit(), three more backbone nodes are picked.

The final clustering


• Pick a backbone node to be center of the network (called median node)( )

• Median determined by computing the moment for each backbone node – smallest moment is selected

nWeightnndistnMoment ),()(

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Nn

6

• Build a tree rooted at median connecting all nodes – Try to restrict interior tree nodes to backbone nodes

• Tree can be build using MST or SPT but Prim-Dijkstra is


• Tree can be build using MST or SPT , but Prim-Dijkstra is often recommended, recall link cost in Prim-Dijkstra:

)),(),((min nodeneighbordistneighborrootdistneighbors 10

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•Sequencing node pairs to prepare adding additional direct links to the tree. Use the tree to list node pair in “sequence”.The node pair with longer path will be listed first – OUTSIDE IN ORDERING For Example


p

Note sequence is not unique

It obeys an outside-in ordering:

Do not sequence the pair (N1, N2) until we sequence all pairs (N3, N4) such that N1 and N2 lie on the path between N3 and N4.

If n nodes in network have

n

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pairs in sequence

2

7

• For each nonadjacent node pair in the tree (Ni,Nj), select a home node H

• In (Ni,Nj) are two hops apart, home node is node between them

Mentor Algorithm Step 5 Homing

• If more than two hops apart, there are multiple candidates for home node H. For example consider (N1,N2) separated by N3 and N4.

• Where N3 is first node in path from N1 to N2 and N4 is the first node in path from N2 to N1if Cost(N1, N3) + Cost(N3,N2) <= Cost(N1, N4) + Cost(N4,N3) then

N3 is the home otherwise N4

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N3 is the home otherwise N4

•In general pick H that gives minimum costCost(Ni, H) + Cost(H,Nj) <= Cost(Ni, Nx) + Cost(Nx,Nj).

- H and Nx are intermediate nodes along the path.

• Decide which node pairs deserve direct links.• Start with the top node pair (N1,N2) in the sequence.

C l l t th b f b i li k d d


• Calculate the number of basic links needed

n=ceil(Traf(N1,N2)/C).• Compute resulting link utlization u=Traf(N1,N2)/(n*C)

• If u > utilmin, add direct link between N1 and N2.

• If u < utilmin, do not add direct link, but instead direct traffic 1 hop through the tree,

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• Add Traf(N1,N2) to Traf(N1,H) and Traf(H,N2). Here H is the home of (N1,N2).

• Remove (N1,N2) from the sequence and repeat Step 6 again until all node pairs are processed.

• Idea is to aggregate traffic to justify links connecting sites several hops apart in tree

8

• The three basic steps: backbone selection, tree building, and direct link addition are all O(n2) where n is the number of nodes.

Complexity of Mentor Algorithm

• It can be executed pretty fast.• Typically we will generate a set of designs based on the

same threshold parameter WPARM, RPARM,– Use vary in the restricted Prim-Dijkstra tree and/or vary utilmin . Prim-Dijkstra tree is parameterized by

)),(),((min nodeneighbordistneighborrootdisti hb 10

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The smaller the value of utilmin, the easier it is to add direct links.

• We then pick the best design from the set

)),(),((min nodeneighbordistneighborrootdistneighbors

15 sites, 5 backbone nodes N2, N4, N8, N9 and N13.

Cost= $ 269,785/month utilmin= 0.9

Generated with file mux1 inp as input to Delite program

Example of Mentor Algorithm

Generated with file mux1.inp as input to Delite program

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9

Same 5 backbone nodes, with lower utilmin=0.7

Cost= $221,590/month,


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Same 5 backbone nodes but with =0.1, utilmin=0.9

Cost = $209,220/month.


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10

=0.1 and 1-utilmin=0.1 is the best value.

Effect of varying alpha and utilmin

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Cost vs. Size of Backbone

• Varying WPARM, RPARM changes number of backbone nodes – leaving other parameters fixed

Ni d i i• Nine nodes give min cost

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11

Reliability Issues

Given a network of nodes and links, one measure of reliability of the network is the probability that the working nodes are connectedconnected.

So far the cost-optimized networks that we have studied are often tree like. Tree designs have low reliability in many cases.

One measure of reliability is the connectedness of the network – a network is K –connected if it can loose K links and a path still exist between every source-destination pair.

Many real backbone networks are 2 or more connected

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y• If using MENTOR algorithm, one can simply change the

parameters WPRAM, RPARM, , utilmin to make the network more dense (at a greater cost )

• Alternative is MENTour algorithm

Remember steps in Mentor Algorithm 1. Backbone selection (classify backbone/edge sites)

Threshold clustering

MENTour

Threshold clustering

2. Creation of the initial topology Prim-Dijkstra tree

3. Link addition Utilization Based

4. Access topology Star , Esau-William, MSLA, etc.

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MENTour modifies Step 2 replacing tree rooted at median node with a Ring (tour) using nearest neighbor algorithm As in MENTOR should generate many designs by varying parameter

settings

12

45 Node Example

The initial topology for MENTour Mentor Design

Example

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A final design by MENTour has lower cost

Example

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MAN Design

• Majority of MANs in use by Telcos and ISPs are based on rings in order to provide fault tolerance

• SONET/SDH is currently the bulk of implementationsSONET/SDH is currently the bulk of implementations• Can implement rings in other technology though (GigE),

wireless, etc.

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MAN Design

• MANs for Telcos typically have a distribution/collector structure with increasing channel rate as approach long haul networkhaul network

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14

Typical LEC Network Topology

HUB

Core Network

Collector Ring

HUBCO

CO CO

Metro Network

COHUBCO

HUBCO

OBusiness

Inter-Office Facilities

CO

VIP VIP

ISPISPCO = Central OfficeDLC = Digital Loop CarrierDSLAM = DSL Access MultiplexerISP = Internet Service ProviderONU = Optical Network Unit

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NU

xDSL

xDSL

LAN

IP, GbE

BusinessAccessRing

Access

DSLAM

DLCDLC

POS

ONT ONT•••PON

ADM

ONT = Optical Network TerminationPOS = Passive Optical SplitterPON = Passive Optical NetworkVIP = Video Information Provider

Synchronous Optical Network (SONET)

• The ANSI standard for synchronous data transmission on optical media.

• Provide end-to-end circuit-switched connectionsProvide end to end circuit switched connections• Provide efficient mechanism for multiplexing low-

speed connections into higher-speed connections– Define a base rate of 51.84 Mbps and a set of multiples

of the base rate known as "Optical Carrier levels (OCx)"

• Provide efficient way to extract low-speed streams from a high-speed stream at intermediate nodes

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• High availability (99.99% to 99.999%)– Rings have rapid service restoration in the

event of failures

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SONET

Basic SONET RatesOC-1 = 51.84 MbpsOC-3 = 155 52 Mbps

• SONET Components• Terminal multiplexers (TMs): nodes at

the ends of point-to-point links OC 3 155.52 MbpsOC-12 = 622.08 MbpsOC-24 = 1.244 GbpsOC-48 = 2.488 GbpsOC-192 = 9.953 GbpsOC-768 = 39.814 Gbps

the ends of point to point links, multiplex and demultiplex traffic streams

• Add/drop multiplexers (ADMs):drop/add one or more low-speed streams from/to a high-speed stream, allow the remaining traffic to pass throughDi it l t (DCS ) l

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• Digital crossconnects (DCSs): large number of ports, extract and switch lower-speed streams (44.736Mbps and 1.544Mbps), interconnect SONET rings

Self-healing Rings (SHRs)

• SHR is a topology connecting a set of nodes by one (or more) rings.

• Two types of SHRs :Two types of SHRs :– Uni-directional ring (USHR)

• Nodes are connected to two rings forwarding traffic in opposite direction.

– Bi-directional ring (BSHR)• Four rings are used as two working and two standby routes. • An extension of 1:1 Automatic Protection Switching

A D MA D M

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1 :1 B i-d ire c t io n a l s e lf-h e a lin g r in g(B S H R )

A D M A D M

A D M

1 :1 U n i-d ire c t io n a l s e lf -h e a lin g r in g(U S H R )

A D M A D M

A D M

16

USHR also called Unidirectional Path-switched Ring ...

USHR

Unidirectional - because in normal operation all working demand flows in one direction only. i.e., A sends to B clockwise,

B also sends to A clockwise

Path-switched - because in restoration each receiver l t lt t d t d th

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selects an alternate end-to-end paththrough ring, regardless of where actual break occurred.

Source: W. D. Grover, ECE 681, UofA, Fall 2004

USHR Animation

Protection fibre

Working fibre 1

2

3

4

5

Tail-end Switch

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17

• Consider a bi-directional demand quantity between nodes A, B: dA,B.- A to B may go on the short route

A

E B

A -> B

USHR Capacity Requirement

- A to B may go on the short route- then B to A must go around the longer route

• Thus, every (bi-directional) demand paircircumnavigates the entire ring.

• Hence in any cross section of the ring,we would find one unidirectional instanceof every demand flow between nodes of the ring.

• Therefore the line capacity of the UPSR

D C

B -> A

“ The UPSR must have a line rate

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• Therefore, the line capacity of the UPSRmust be:

UPSR iji j

c d

(capacity) greater (or equal to)the sum of all the (bi-directional)demand quantities between nodes of the ring. “


BSHR

Cable cut

Loop Back

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(a) Normal Operation (before failure) (b) Protection Operation (after failure)

18

Bi-directional - because in normal operation working demand flows travel in opposite directions over the same

BSHR

(a) Normal Operation (before failure) (b) Protection Operation (after failure)

Cable cut

Loop Back

opposite directions over the sameroute through the ring

Also called Bi-directional Line-switched Ring (BLSR)

Line-switched - because in restoration the compositeoptical line transmission signal is switched to the other direction around the ring (on the other fibre pair)“ The BLSR must have a line rate

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g ( p )specifically around the failed section.

Note implication: Protection fibre capacity must equal the largest-working capacitycross-section of any span on the ring.

The BLSR must have a line rate (capacity) greater (or equal to)the largest sum of demands routedover any one span of the ring. “

BSHR

Protection fibres

Working fibres

Loop-back

1

2

34

5

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Loop-back


19

•The Capacity required depends on the routing of demands

•A heuristic algorithm for BLSR ring loading (Wu ‘92)....

1. Rank all demands in descending order

BLSR Capacity

1. Rank all demands in descending order

2. Map any adjacent-node demands onto the ring (and remove from list)

3. Repeat In descending order:

- map next largest demand into ring over its shortest route

- map the same demand into the ring over the complementary route

- choose the route that produces:min max i

i

w

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where wi is the accumulation of demands crossing span i.

- if each route produces the same {max wi } choose the shorter route- if both routes are equal, alternate this route choice with that at the next

similar “tie”.

Until all demands are served

i

• Example of the heuristic BLSR loading algorithm....

Demands(sorted in decreasing order):

AC 10

AB

C

Example

AC 10

EB 8

EA 6 *

ED 6 *

DB 5

DC 4 *

EC 4

AB

step 1 : Place adjacent-node demands:

wi = 6 wi = 3

wi = 2

D

CE

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BC 3 *

AB 2 * D

CE

* denotes demand between adjacent nodes

wi = 6 wi = 4

20

Remaining demands(sorted):

AC 10

EB 8

AB

step 2 : Consider routing of the AC demand:

6

wi = 2+ 10 = 12

Example

min max iw

EB 8

DB 5

EC 4

D

CE

wi = 6

wi = 6 wi = 4

wi = 13

AB

wi = 16 wi = 3

wi = 2

i

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D

CE

wi = 16 wi = 14 shorter route is preferred:

map AC via route A-B-C (max wi = 13)


EB 8

AB

step 3 : Consider routing of the EB demand:

14

wi = 20

Example

EB 8

DB 5

EC 4

D

CE

wi = 14

wi = 6 wi = 4

wi = 13

AB

wi = 6 wi = 21

wi = 12

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D

CE

wi = 14 wi = 12 shorter route is again preferred:

map EB via route E-A-B

(max wi = 20)

21


AB

step 4 : Consider routing of the DB demand:

14

wi = 20

Example

DB 5

EC 4

D

CE

wi = 14

wi = 6 wi = 9

wi = 18

AB

wi = 19 wi = 13

wi = 25

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shorter route is again preferred: map DB via route D-C-B

(max wi = 20)

D

CE

wi = 11 wi = 4


AB

step 5 : Consider routing of the EC demand:

18

wi = 24

Example

EC 4

D

CE

wi = 18

wi = 6 wi = 9

wi = 22

AB

wi = 14 wi = 18

wi = 20

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shorter route is again preferred: map EC via route E-D-C

(max wi = 20)

D

CE

wi = 10 wi = 13

22

Resultant ring loading and sizing plan:

Demand pair routeAC 10 ABC

Resulting in these net span loadings:

and thus requiring (in practise) an

Example

D

AB

CE

wi = 14

wi = 10 wi = 13

wi = 18

wi = 20AC 10 ABC

EB 8 EAB

EA 6 * direct

ED 6 * direct

DB 5 DCB

DC 4 * direct

EC 4 EDC

(in practise) an

OC-24 4-fiber BLSR

or

OC-48 2-fiber BLSR

oran “ideal” 4-fiber

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EC 4 EDC

BC 3 * direct

AB 2 * direct

an ideal 4 fiberOC-20 BLSR

• consider the ring just designed... One measure of BLSR efficiency is:

ii

w ~ capacity usefullyserving demands

BLSR Capacity efficiency

D

AB

CE

wi = 14

wi = 10 wi = 13

wi = 18

wi = 20 max{ }iN w ~ redundant protectioncapacity required

20 14 10 13 1875%

max{ } 5 20

ii

i

w

N w

here...

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or conversely the redundancy is ... 133 %

si required to be 20 everywhere

23

• to serve the same set of demands, the UPSR would require the ring line rate to be :

1 0 8 6 6 5 4 4 3 2 4 8U P S R iji j

c d

• but the amount of demand-serving capacity of the BLSR loading still applies as the

Compare to UPSR ...

AB

CE

wi = 14 wi = 18

wi = 20

but the amount of demand-serving capacity of the BLSR loading still applies as the measure of useful service or utility:

20 14 10 13 18 75ii

w

• Therefore, the redundancy measure (“spare to working” ratio) for the UPSR can be formed as:

total capacity - working capacity

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Dwi = 10 wi = 13

total capacity working capacity

working capacity

2 5 48 2 75220 %

2 75redundancy

• From preceding it is evident that BLSR demand-serving ability depends in general on the demand pattern.

• Some of the recognized tendencies in real demand patterns are:

Effect of some “generic” demand patterns on BLSR

HubDemand

Node-to-Adjacent Node Double HubSingle HubUniform

or “mesh”

ideal case for BLSRf t b

this is thegeneral tendency in this is a fairly exact

same basic “access” demand pattern but dual hubs employed

for access survivability

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perfect bw re-use

BLSR much moreefficient than UPSR

no optimization required

general tendency in inter-city backbone

network

optimization of ring loading

ymodel for access ring applications

BLSR efficiency = UPSR

24

SHRs Restoration Capability

• USHR– 100% restoration for a single link failure but no g

protection against a node failure.

• BSHR– 100% restoration for a single link or ADM failure.

– Fully automatic for a fast restoration.

– Spare capacity of each link can be shared between

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p p ytwo working paths.

– More expensive but usually less than twice as expensive

• SONET rings operate at OC-n line rates and the STS-1 tributaries are the “channels”

• The nodes of a ring are equipment called “Add-Drop Multiplexers” (ADMs)

• SONET rings typically have a maximum of 16 active nodes, plus “glass-through” sites

Rings

SONET rings typically have a maximum of 16 active nodes, plus glass through sites

• “Glass-throughs” are just nodes transited by the ring, but where no ADM is present

• “Glass-throughs” may be simply fiber splices or a regenerator point (“pass throughs”)

• Demand splitting refers to whether or not the total demand exchanged between two nodes has to be kept together on the same route of a ring or can be ‘split’

• Time slot interchange (TSI) refers to whether the ADMs have the ability to cross-connect timeslot contents (assign a new time slot to a demand on the next span)

• More recent Optical rings have a DWDM optical line signal and add / drop single

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p g p g p gwavelengths or wave-bands

- the logical “channel” is a wavelength () or waveband- UPSR < - > OPPR (Optical Path Protection Ring)- BLSR < - > OSPR (Optical Shared Protection Ring)- ADM < - > OADM- TSI (Time slot interchange) < - > conversion

25

SHRs Interconnection Architecture

• Due to geographical/bandwidth limitations, multiple, interconnected rings are deployed.p , g p y

• Multi-Ring network design

• Capacity assignment at all links on the ring can needs to be minimum.

• For traffic restoration, a larger logical self-

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For traffic restoration, a larger logical selfhealing ring can be formed from an interconnection of two or more rings.

Two possible Ring Interconnections

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26

C

Dual-ring Interconnect

When connecting two rings at a transit node want to have redundancy – several methods

Below is drop-and-continue method for BSHRs

1A

2A

3A

4A

(primary)

(secondary)

r1 r

2

C3

C4

C1

C2

C5

the primary gateway node has a 1+1 receive

selection setup here.

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protected byBLSR line-loopback

reaction in r1

protected byBLSR line-loopback

reaction in r2

protected by1+1 APS inter-ring

setup

• Given:

- a two-connected (or bi-connected) graph

- a set of “ring technologies” and costs. e g OC 192 4/BLSR OC 48 UPSR etc

Multi-ring Design Problem

e.g OC-192 4/BLSR, OC-48 UPSR, etc.

- a set of demands to be served.

- a subset of node locations where demands may transit from ring-to-ring

• Determine:

- the number, size, type and placement of all rings

- the location of glass-throughs (and ADM terminals) on all rings

- the end-to-end routing of each demand

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That results in minimal cost of all rings placed, including costs associated with demands transiting from ring to ring.

•Solution

• Can use simple divide and conquer heuristic with nearest neighbor

• NetSolver Heuristic

• Optimization based approaches

27

• Upper bound on number of ring candidates to consider:

logic: Every combination of 2, 3, 4....up to N nodes defines a prospective collectionof active ADM nodes that could be grouped together to define one ring.

On the complexity of multi-ring design

2

2 1N

N

i

NQ N

i

• Upper bound on the number of different multi-ring designs that exist:

logic: Now, every combination of 1, 2, 3, 4....up to some pre-determined maximumnumber of rings can be considered for feasibility and cost as a multi-ring design solution.

- in ideal case of rings with no capacity limit

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in ideal case of rings with no capacity limit,can show that more than N-1 rings not needed.

1

1

N

j

Q

j

and ... also multiply by the number of “ring technologies”

being considered.

60

7010

Question: How big is ?

10

20

30

40

50

60

No

. of

Po

ss

ible

De

sig

ns

10

10

10

10

10

10

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0

3 4 5 6 7 8 9 10 11 12 13 14 15 16

No. of Node s

10

illustration: a 10 node network: 1013 possible rings, 1021 possible multi-ring networks

(over 100 million years to evaluate all designs at 10 6 design evaluations / sec.) !

28

Concept

• graph coverage: ....a set of rings that covers every edge of the graph. This is one class of ring network.

in a BLSR how well are the w quantities “balanced” ? (since

Key concepts in multi-ring design

• Balance

• Capture

• Span elimination

• Dual-ring interconnect

....in a BLSR, how well are the wi quantities balanced ? (sincethe largest of them dictates the protection capacity).

....to what extent does a given ring tend to serve demands that both originate and terminate in the same ring.

....a multi-ring design may not “cover” all graph edges, if the working demands can take non-shortest path routes.

....for the highest service availability, some demands may employ geographically redundant duplicate inter-ring transfers

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• transit sites

•glass-throughs

geographically redundant duplicate inter ring transfers

....not all nodes may be sites where demands can switch rings.

....each ring needs ADMs where demands add / drop, but not elsewhere ( ~> Express rings etc.).

• a set of rings that uses or overlies all edges of the physical facilities graph is called a “ring cover”.

• “Coverage-based” design is a special (simpler) case of multi-ring design.

M ll th i i t t t ll d d t il t “ ll

Graph coverage

• More generally the aim is to protect all demands, not necessarily to “cover all spans.” “span eliminations”

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a three ring “cover”a single ring design

that may also serve alldemands…

Q. what is implied?

example


29

Net Solver (Gardner, et al., Globecom ‘95)

• Objective– Find min-cost ring design that serves all demands.

• Key Assumptions & Constraintsy p & C– Cost is calculated based on fixed and variable costs.

– Requires an initial ring design.

– Ring capacity is fixed and modular (rings not “ideal”).

• Methodology1. Route demands over the initial set of rings using either (1) shortest path, (2)

shortest ring transition, or (3) minimum congestion routing (user-defined).

2. Compute the total cost of the initial design.

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3. Generate a set of alternative ring designs by modifying the initial ring design using three different ring operations:(1) split; (2) merge; and (3) enlargement.

Net Solver

• Ring Operations

R R1

R2

R

R1

R2

(a) Split operation

(b) Merge operation

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R R’

(c) Enlargement operation

30

Net Solver (cont’d)

• Methodology (cont’d)4. Route demands and compute the total cost for each alternative

designdesign.

5. Select the design with the lowest total cost.

6. Repeat steps 3-5 until no further improvements in cost can be obtained.

• Capabilities– BLSR, UPSR and mixed designs.

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– Accounts for fixed ring capacities.

– Identifies the location of active/passive nodes and demand routing.

Optimization Formulation Notation

S - set of spans in the network topology.

J - set of candidate rings (BLSRs). K - set of all demands.

d size of demand bundle k

demands and routing

swjm - capacity of BLSR j.

- working load on span s.

jc - “fixed cost” (optical line costs) of ring j.

I - set of routes for all demands.

ijb - add/drop cost of carrying route i on ring j.

ie - termination cost for route i.

kd - size of demand bundle k.

iF - flow of working route i.

ijG - flow of route i carried by ring j.

costs & capacities

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jX - copies of candidate ring j in design.

decision variables

31

Pure span coverage IP

• Span Coverage (SCIP)1. Route demands over network topology and calculate working load

ws on each span.

2 Generate a set of ring candidates (topology ring type and capacity)2. Generate a set of ring candidates (topology, ring type and capacity) and calculate ring candidate costs.

SCIPMinimize:

Subject to:

Jjsjj wXm Ss (2)

(1)Jj

jj Xc

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,

,

sJj

0jX integer, Jj (3)

“Fixed Charge and Routing”

• Fixed Charge and Routing (FCIP) 1. Generate a set of several possible routes for each demand.

2. Generate a set of ring candidates (topology and ring type) and2. Generate a set of ring candidates (topology and ring type) and calculate ring candidate costs.

Minimize:

FCRIP

Subject to:

Ii iJj

ijijJj

jj GbXc)(

(1)

)(kIi

ki dF , Kk (2)

G ( )

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)(sJj

iij FG Ii Ss, ,(3)

)(sIi

jjij XmG , Jj Ss, (4)

32

Understanding “Fixed Charge and Routing” approach

D

(3) amongst “stacked” ring spans allocation of

Key idea: Solver is free to choose rings and routing of flows jointly,to min cost of rings plus inter-ring add/ drop transition costs

O

D

ring

ring

j J

j J

three possible routes for demand pair k,

I(k)

route and flow

for otheradd/ drop

(“fixed” optical line cost)

each ring’s portion of flow sums to total on the given route

for that O-D pair

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(2) sum of flow F(i) to each route I(k) = dk

for other

demand pairs

(4) capacity greater thansum of flows crossing span

routing dependentadd/ drop costs

add/ dropcosts

Numerical Comparison

1

23

4

1415

0

2 3 4

5

9

10

11 1315 19

• Test Networks

1

1116

2122

26

27

28

29

30

5

6

7

8

9

10

11

1213

3

5

7

10

11

12

13

14

15

16

17

18

20

22 23

33

38

39

40

42

43

Net15 Net20

Metro

1

6

7

8

12

14

16

17

18

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2

34

56

7

8

9

10

12

13

14

15

17

18

192023

24

25

31

32

1

2

4

6

7

8

9

16 18

19

21

22 23

24

25

26

27

28

29

30

31

32

3435

36 37

41

Net32 Net43

Long-haul


33

Numerical Results

• Modeling Assumptions– Ring types: 12- OSPR and 48- OSPR.

Cost model: 4 times capacity for twice the cost– Cost model: 4 times capacity for twice the cost.

– No restrictions on inter-ring transition locations.

• Experimental Procedure1.Formulated each IP in AMPL mathematical

programming language.

2 Populated AMPL data sets

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2.Populated AMPL data sets.

3.Generated problem instances using AMPL and solved with CPLEX.

4.Entered solutions into SONET Planner (Nortel Networks) to obtain final detailed costing.

Results

Cost ($000s)

RingBuilder SCIP FCRIP

* - time limit exceeded, best feasible solution shown.


Net15 6,535 5,810 7,187*

Net20 9,886 10,083 8,953*

Net32 91,596 90,291 96,368*

Net45 116,674 130,100* -


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Net15 6.2 1.6 43,200

Net20 10.5 38.7 43200

Net32 8.5 361 43,200

Net45 1,233 43,200 -

43,200 sec = 12 hour run-time limit

34

MANs

• Discussed a few algorithms/approaches to MAN design– Graph theory based (e.g., MENTOR, MENTOUR)– Optimization based (focus largely on ring networks ) Op ( g y g )

• (e.g., SONET Toolkit from Telcordia – RingBuilder – TRLabs, etc.)

– Heuristics – routing based (will see some with WANs)

• MANs are evolving with newer technology– DWDM and multi-provisioning– Virtual Private LAN Service (VPLS) over service provider network

(GEthernet interconnect over MAN)– WiMAX for wireless last mile or MAN interconnect

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WiMAX for wireless last mile or MAN interconnect– SAN (Storage Area Networks)– Etc.

metro network design - university of pittsburghdtipper/2110/slides9.pdf · – graph theory based...

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