network design with constraints

Prepared by Giray Birkan [email protected] by Giray Birkan [email protected]

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Network Design with ConstraintsNetwork Design with Constraints

Chapter 10 Chapter 10 Part 1Part 1


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OverviewOverview

Build a network connecting 75 stores to a Build a network connecting 75 stores to a HQHQ

Each store generates 500bps of traffic & Each store generates 500bps of traffic & receives about 1500bps of traffic.receives about 1500bps of traffic.

An MST or CMST will be the correct An MST or CMST will be the correct solutionsolution

But you are told that each store needs But you are told that each store needs 64Kbps access & 3 hops maximum.64Kbps access & 3 hops maximum.

Or the lowest cost network where the Or the lowest cost network where the average end-to-end delay is 300 ms or average end-to-end delay is 300 ms or less.less.


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Designs Constraints Designs Constraints

Cheapest design may not be Cheapest design may not be acceptable for reasons of acceptable for reasons of reliability, performance, … or reliability, performance, … or organizational or political organizational or political reasonsreasons

May have to modify algorithms May have to modify algorithms or write problem-specific code to or write problem-specific code to produce an acceptable design.produce an acceptable design.

Manual Design?Manual Design?


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Types of ConstraintsTypes of Constraints

Hop constraintsHop constraints Worst caseWorst case AverageAverage Node-pairNode-pair

Equipment Equipment constraintsconstraints DegreeDegree ThroughputThroughput

Link constraintsLink constraints Required or Required or

forbiddenforbidden

Performance constraintsPerformance constraints Worst caseWorst case AverageAverage Node-pairNode-pair

Reliability constraintsReliability constraints Entire networkEntire network BackboneBackbone Node-pairNode-pair

MiscellaneousMiscellaneous High & Low Security NodesHigh & Low Security Nodes


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Over-Constrained ProblemOver-Constrained Problem

It is possible to specify so many or It is possible to specify so many or so severe constraints that there is no so severe constraints that there is no feasible network designfeasible network design

War Story 10.1: each node must be War Story 10.1: each node must be of degree three, for example if n = 7. of degree three, for example if n = 7. There is no solutionThere is no solution

Suppose each site has equipment Suppose each site has equipment that can only terminate a LAN and that can only terminate a LAN and two leased lines - Can only build a two leased lines - Can only build a ring.ring.


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Over-Constrained ProblemOver-Constrained Problem

In any network, the total amount of In any network, the total amount of capacity used by all of the traffic is capacity used by all of the traffic is bounded from below bybounded from below by

Capacity of a leased line is C and Capacity of a leased line is C and capacity of the ring is (n-1)C.capacity of the ring is (n-1)C.

As network grows, link capacity will As network grows, link capacity will be overloaded at some pointbe overloaded at some point

jiji

ji hopsTrafS ,,

, Tnn

S8

)1( 2


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Hop-Limited DesignsHop-Limited Designs

Problem Statement 10.1: Given a set Problem Statement 10.1: Given a set of traffic Trafof traffic Traf i,j, i,j, find the lowest cost find the lowest cost

design such that if Trafdesign such that if Traf i,j i,j > 0> 0 then the then the

path chosen by the routing algorithm path chosen by the routing algorithm through the network has less than h through the network has less than h hops.hops.

If h is very large, first solve the If h is very large, first solve the unconstrained problem maybe a unconstrained problem maybe a cost-optimized network is sufficient.cost-optimized network is sufficient.


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AMPL and Hop-Limited DesignAMPL and Hop-Limited Design

Arc-Path ModelArc-Path Model Set P : set of pathsSet P : set of paths Only paths with 3 hops are in the data Only paths with 3 hops are in the data

modelmodel A-BA-B A-D-B A-D-E-B A-D-B A-D-E-B

A separate program can be written to A separate program can be written to find these pathsfind these paths

A

E

B

D

C


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AMPL and Hop-Limited DesignAMPL and Hop-Limited Design

Node-Arc ModelNode-Arc Model Only links and nodes no paths are Only links and nodes no paths are

givengiven The hop limit is 3 and each The hop limit is 3 and each

demand must be satisfied by a demand must be satisfied by a single path.single path.

Giray’s Solution:Giray’s Solution:Subject to HopLimit {c in N, n in {N diff {c}}:Subject to HopLimit {c in N, n in {N diff {c}}:

sum{e in E} (-yi[c,e,n] - xi[c,e,n]) >= 3 * rhs[c,n];sum{e in E} (-yi[c,e,n] - xi[c,e,n]) >= 3 * rhs[c,n];


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Badly Posed ExamplesBadly Posed Examples

1.1. MUX network : The path that a MUX network : The path that a requirement takes depends on requirement takes depends on the loading sequence.the loading sequence.

A B

DCAssume each link can load 2 circuits

Network appears to be a 2-hop designLoading pattern 1 : { AB, AB, CB}Loading pattern 2 : { AB, CB, AB}


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Badly Posed ExamplesBadly Posed Examples

2.2. Boundary of the NetworkBoundary of the Network 6 Hop Design:6 Hop Design:

NY - Philadelphia - Detroit - Chicago - Denver - LA - San DiegoNY - Philadelphia - Detroit - Chicago - Denver - LA - San Diego

6 Hops or 12 hops?6 Hops or 12 hops?

BBBBNY NY – Building – 14 Floor – Workstation– Building – 14 Floor – Workstation

Generally, we don’t cost optimize building Generally, we don’t cost optimize building networksnetworks


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Approach I : CullingApproach I : Culling

Generate a lot of designs with varying Generate a lot of designs with varying parametersparameters If Mentor is used try different values for alpha, If Mentor is used try different values for alpha,

slack, nclst, seedslack, nclst, seed Throw away all that do not meet hop Throw away all that do not meet hop

constraintsconstraints Select best remaining designSelect best remaining design Brute force method may be quite Brute force method may be quite

acceptable if it avoids writing problem-acceptable if it avoids writing problem-specific codespecific code

May not work if constraints are too severe May not work if constraints are too severe Frequency of feasible designs may be too low to Frequency of feasible designs may be too low to

be practicablebe practicable


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Culling ContinuedCulling Continued

Cost Optimized design with 11 hopsCost Optimized design with 11 hops


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The best 9-hop design culled from a runThe best 9-hop design culled from a run Out of 325 trial, only 28 of them had 9 hopsOut of 325 trial, only 28 of them had 9 hops


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More than 150 different networks only one More than 150 different networks only one of them had 7 hopsof them had 7 hops


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Culling ContinuedCulling Continued If Culling fails to find 6-hop designsIf Culling fails to find 6-hop designs

Reduce the diameter of the backboneReduce the diameter of the backbone Reduce the depth of the access treesReduce the depth of the access trees

A tree centered on N45


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Approach II : AugmentationApproach II : Augmentation

5 pairs of nodes 8 hops apart, 7 hop design 5 pairs of nodes 8 hops apart, 7 hop design requiredrequired


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An Algorithm To Compute Hops In The An Algorithm To Compute Hops In The Access TopologyAccess Topology

1.1. For each backbone node b compute la(b) : max For each backbone node b compute la(b) : max depth of the local access tree at b.depth of the local access tree at b.

2.2. Loop until done. Compute diameter of the network:Loop until done. Compute diameter of the network:

If d > h, return failIf d > h, return fail For each backbone site b, computeFor each backbone site b, compute

e(b) gives the number of extra hops we can expand e(b) gives the number of extra hops we can expand la(b) and still meet the h hop constraint la(b) and still meet the h hop constraint

If any e(b) greater than 0, select a node b and If any e(b) greater than 0, select a node b and increase la(b) by 1. Otherwise break loopincrease la(b) by 1. Otherwise break loop

3.3. Return the values la(b)Return the values la(b)

)()(),(max , blablabbhopsd Backbonebb

)()(),(max)( blablabbhopsdbe Backboneb


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Algorithm ContinuedAlgorithm Continued

)()(),(max , blablabbhopsd Backbonebb

)()(),(max)( blablabbhopsdbe Backboneb

SiteSite la(b)la(b) e(b)e(b)

N20N20 11 00

N41N41 11 11

N42N42 11 11

N43N43 11 00

N44N44 11 00

N45N45 11 22

N46N46 11 11

N47N47 11 00

N48N48 11 00

N49N49 11 11

N50N50 00 XX

h = 6


2020

Algorithm ContinuedAlgorithm Continued

SiteSite la(b)la(b) e(b)e(b)

N20N20 11 00

N41N41 11 11

N42N42 11 11

N43N43 11 00

N44N44 11 00

N45N45 33 00

N46N46 11 11

N47N47 11 00

N48N48 11 00

N49N49 11 11

N50N50 00 XXThe design with a 3 hop cluster at N45


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Average Hop ConstraintsAverage Hop Constraints

Average number of hops is a far easier Average number of hops is a far easier constraint to meet than a constraint on the constraint to meet than a constraint on the maximum number of hopsmaximum number of hops

Three approaches for MENTORThree approaches for MENTOR Increase alphaIncrease alpha

Builds more star-like networksBuilds more star-like networks Increase slackIncrease slack

Introduces more links Introduces more links If slack = 1, we will build a network where there is If slack = 1, we will build a network where there is

a link between any 2 sites that have traffica link between any 2 sites that have traffic

Use lower-speed linksUse lower-speed links Introduces more links – because of utilizationIntroduces more links – because of utilization

1hops


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Average Hop ConstraintsAverage Hop Constraints

trafTotalTrafvolTrafhopshops

meanSecond

tTrafhopshops

meanFirst

tkTraf

kk

k

kk

k

_/)()(

/)(

,...,1,

2

1

First mean tends to equalize performance among large & small sites

Second makes most people happy at the cost of a minority of users with lower grade of service


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Meeting hops ConstraintsMeeting hops Constraints

SlackSlack CostCost hopshops22

00 88,56088,560 3.6153.615

0.050.05 91,97591,975 3.3373.337

0.100.10 92,16192,161 3.3913.391

0.150.15 102,732102,732 2.8882.888

0.200.20 110,237110,237 2.7592.759

0.250.25 112,334112,334 2.7302.730

0.300.30 107,996107,996 2.8312.831

0.350.35 110,097110,097 2.7802.780

0.400.40 112,761112,761 2.6592.659

SlackSlack Cost/hopCost/hop

0.050.05 19,47819,478

0.150.15 22,24522,245

0.200.20 27,66027,660

0.250.25 29,12329,123

0.300.30 27,35427,354

0.350.35 26,59526,595

0.400.40 27,40627,406

Hops & cost for variousValues of slack

The cost of improving hopshops22

slackslack CostCost hopshops22

0.050.05 91,97591,975 3.3373.337

0.150.15 102,732102,732 2.8882.888

0.350.35 110,097110,097 2.7802.780

The interesting choices for slack


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Meeting hops ConstraintsMeeting hops Constraints


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Homework 12Homework 12

Using node-arc model from homework 8 Using node-arc model from homework 8 solve the following mesh design problem.solve the following mesh design problem.

Use one model fileUse one model file

First, Minimize the number of average hops First, Minimize the number of average hops Then, Minimize the total costThen, Minimize the total cost Trunk types:Trunk types:

96K bps - $50 per trunk96K bps - $50 per trunk 128K bps - $60 per trunk128K bps - $60 per trunk 256K bps - $105 per trunk256K bps - $105 per trunk

Each demand must be satisfied by a single path.Each demand must be satisfied by a single path. The utilization should be no more than 50%.The utilization should be no more than 50%.


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B

A

E

D

G

F

C


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A B C D E F G

A - 25 10 - 96 15 50

B 22 - 82 25 18 16 28

C 60 45 - - 15 - 32

D 70 56 88 - 20 27 -

E - - 86 96 - 81 25

F 20 28 15 45 - - 61

G - 36 23 - 32 85 -


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AMPL & Multiple Objective AMPL & Multiple Objective FunctionsFunctions

You can define several problems in one model fileYou can define several problems in one model file You can solve a problem then fix some variables and solve You can solve a problem then fix some variables and solve

another problemanother problem

#---first problem-----#---first problem-----problem DefineBIG:problem DefineBIG: # objective# objective segmentlength,segmentlength, # variables# variables X, Y, A, B, BIG,X, Y, A, B, BIG, # constraints# constraints flowbalance, flowbalance2 ,linkbetweenXandA, linkbetweenYandB, linkbetweenAandB,flowbalance, flowbalance2 ,linkbetweenXandA, linkbetweenYandB, linkbetweenAandB, linkbetweenBIGandX, lastAMP, firstAMP;linkbetweenBIGandX, lastAMP, firstAMP;

solve DefineBIG;solve DefineBIG;#---second problem-----#---second problem-----problem ReduceAMPS:problem ReduceAMPS: # objective# objective amps,amps, # variables# variables X, Y, A, B, BIG,X, Y, A, B, BIG, # constraints# constraints flowbalance, flowbalance2, linkbetweenXandA, linkbetweenYandB, linkbetweenAandB,flowbalance, flowbalance2, linkbetweenXandA, linkbetweenYandB, linkbetweenAandB, linkbetweenBIGandX, lastAMP, firstAMP, BIGfix;linkbetweenBIGandX, lastAMP, firstAMP, BIGfix;

solve ReduceAMPS;solve ReduceAMPS;


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GRINGRIN

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network design with constraints

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