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TCOM 541. Session 2. Mesh Network Design. Algorithms for access are not suitable for backbone design Access designs generally are trees – sites connect to center Diverse access (redundancy) is another question, and only needed for special situations

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Tcom 541

TCOM 541

Session 2


Mesh network design

Mesh Network Design

  • Algorithms for access are not suitable for backbone design

    • Access designs generally are trees – sites connect to center

      • Diverse access (redundancy) is another question, and only needed for special situations

    • Backbone designs require many-many connectivity


Mentor algorithm

MENTOR Algorithm

  • “High quality, low complexity” algorithm

  • Originally developed for time division multiplexing

    • Works with other technologies


Mentor algorithm 2

MENTOR Algorithm (2)

  • Assume initially only a single link type of capacity C

  • Divide sites into backbone sites and end sites

    • Backbone sites are aggregation points

    • Several algorithms to do this

      • Threshold clustering is used


Threshold clustering

Threshold Clustering

  • Weight of a site is sum of all traffic into and out of the site

  • Normalized weight of site i is

    NW(i) = W(i)/C

  • Sites with NW(i) > W are made into backbone sites

    • Where W is a parameter


Threshold clustering 2

Threshold Clustering (2)

  • All sites that do not meet the weight criterion and are close to a backbone site are made into end sites

    • “Close” is defined as when the link cost from the end site e to the backbone site is less than a predefined fraction of the maximum link cost MAXCOST = maxi,jcost(Ni,Nj):

      cost(e,Ni) < MAXCOST*RPARM


Threshold clustering 3

Threshold Clustering (3)

  • If all sites that pass the weight limit as backbone sites have been chosen and there are still edge sites “too far” from any backbone site, we assign a “merit” to each site

    • Assign coordinates to each site (e.g., V&H)

    • Compute center of gravity of sites


Center of gravity cg

Center of Gravity (CG)

  • Defined as (xctr, yctr) where

    xctr = SnxnWn/SWn

    yctr = SnynWn/SWn

    Note: These coordinates need not correspond to any actual site


Distances to cg

Distances to CG

  • Define

    dcn = [(xn-xctr)2 + (yn-yctr)2]0.5

    maxdc = max(dcn)

    maxW = max(Wn)

  • Then

    meritn= 0.5(maxdc–dcn)/maxdc + 0.5(Wn/maxW)

  • That is, “merit” gives equal value to a node’s proximity to the center and to its weight


Mentor algorithm 3

MENTOR Algorithm (3)

  • From among remaining nodes, choose the one with the highest merit as a backbone node

  • Continue until all nodes are either backbone nodes or within RPARM*MAXCOST of a backbone node

  • Select backbone node with smallest moment to be center

    • Moment(n) = Sdist(n,n*)Wn*

  • Construct a Prim-Dijkstra tree, parameter a


Mentor example

MENTOR Example

Radius = RPARM*MAXCOST

C*G

Edge node

Backbone node


Mentor example 2

MENTOR Example (2)

Radius = RPARM*MAXCOST

C*G

Edge node

Backbone node


Mentor example 3

MENTOR Example (3)

Radius = RPARM*MAXCOST

C*G

Edge node

Backbone node


Mentor example 4

MENTOR Example (4)

Radius = RPARM*MAXCOST

C*G

Edge node

Backbone node


Mentor example 5

MENTOR Example (5)

Radius = RPARM*MAXCOST

C*G

Edge node

Backbone node


Need for improvement

Need for Improvement

  • As we know, tree designs have several drawbacks, especially for large networks

    • Lack of redundancy increases probability of failure

    • Chain-like network (low a)

      • Aggregation of traffic in “central” links raises costs

      • Large average hops in large networks

    • Star-like network network (high a)

      • May have low link utilization


Refining the design in mentor

Refining the Design in MENTOR

  • We introduce the concepts of sequencing and homing to add links so as to make a better design by adding direct links where the traffic justifies it

  • Use the Prim-Dijkstra tree to define a sequencing of the sites

    • A sequencing is an outside-in ordering

    • Do not sequence the pair (N1,N2) until all pairs (N1*,N2*) have been sequenced where N1 and N2 lie on the path between N1* and N2*

    • Roughly, the longest paths get sequenced first


Example of sequencing

Example of Sequencing

Sequence

AE

AF

BE

BF

CE

CF

DA

DB

AC

BC

DF

F

A

C

3 hops

D

E

B

2 hops

1 hop


Comments on sequences

Comments on Sequences

  • Sequences are not unique

  • Different (valid) sequences do not influence the design greatly


Homing

Homing

  • For each pair of nodes (N1, N2) that are not adjacent we select a home

    • If 2 hops separate N1 and N2, the home is the node between them

    • If they are more than 2 hops apart there are multiple candidates for their home


Homing 2

Homing (2)

N4

N1

N3

N2

Candidate for home (N1,N2)

Candidate for home (N1,N2)

Choose N3 as home(N1,N2) if:

Cost(N1,N3) + Cost(N3,N2) < Cost(N1,N4) + Cost(N4,N2)

Otherwise choose N4


Last step

Last Step

  • Consider each node pair only once, add a link if it will carry enough traffic to justify itself

  • Consider the traffic matrix T(Ni,Nj)

    • Assume it is symmetric

    • Recall that MENTOR was developed to design TDM networks, and muxes are bi-directional (usually)


Last step 2

Last Step (2)

  • For each pair (N1,N2), execute the following algorithm:

  • If capacity of a link is C, compute

  • n = ceil[T(N1,N2)/C]

  • Compute utilization

  • u = T(N1,N2)/(n*C)

  • Add link if u > umin, otherwise move traffic 1 hop through the network

  • I.e., add T(N1,N2) to both T(N1,H) and T(H,N2)

  • And do same for T(N2,N1)

  • Note – there is a special case when (N1,N2) belongs to the original tree

  • In this case just add the link (N1,N2) to the design


Comments

Comments

  • The link-adding algorithm aggregates traffic to justify links between nodes that are multiple hops apart

  • If traffic between N1 and N2 cannot justify a direct link, it is routed through their home node H

  • Eventually, in large networks, enough traffic is aggregated to justify a direct link


Comments 2

Comments (2)

  • Performance of MENTOR is governed by utilization parameter umin and the Prim-Dijkstra tree-building parameter a

  • How easy it is to add new links is controlled by umin

  • The shape of the initial tree is controlled by a

    • High a will build a star-like tree – then links will be added only between site pairs that have enough traffic without help from other nodes

    • Low a will build a more chain-like tree, so there will be more aggregation of traffic and likely addition of links


Performance of mentor

Performance of MENTOR

  • Low-cost algorithm

    • Three main steps

      • Backbone selection

      • Tree building

      • Link addition

    • All of O(n2)

    • Possible to re-run many times, varying parameters


Mentor example1

MENTOR Example

Based on mux1.inp on Cahn’s FTP site

15 sites, 60 256 kbps circuits

13

6

2

7

15

14

10

9

1

5

12

4

8

11

3


Initial choice of backbone nodes 5

Initial Choice of Backbone Nodes (5)

13

6

2

7

15

Backbone node

Backbone node

14

10

9

1

Backbone node

5

12

Backbone node

4

8

Backbone node

11

3


Initial design

Initial Design

a = 0

Cost = $269,785/month

13

6

2

7

15

5 x T1

2 x T1

14

10

9

1

5

5 x T1

12

5 x T1

4

8

11

3


Review of initial design

Review of Initial Design

  • Backbone links have multiple (5) T1 links

  • Probably not a good thing

  • Design Principle:

    • If a design has multiple parallel high-speed links there is usually a better, meshier design

      • Lower cost, greater diversity (= reliability)

  • Note this is not mathematically provable


Revised design

Revised Design

umin = 0.7

Cost = $221,590

13

6

2

7

15

3

1

2

14

10

9

1

1

2

5

12

1

4

8

1

11

3


Best 5 node backbone design

“Best” 5-Node Backbone Design

a = 0.1

umin = 0.9

Cost = 209,220

13

6

2

7

15

2

2

14

10

9

1

2

5

2

12

1

4

1

8

11

3


Comments1

Comments

  • Note that we produced multiple designs by varying some parameters and picking the best

  • Of course, there is no guarantee that this design really is “best”

  • In fact, changing number of backbone nodes yields much better designs

    • 13-node backbone yields design costing only $191,395

    • 12-node backbone costs $198,975


Routing

Routing

  • Now we have designed a good network, we consider how the traffic will actually flow across it

  • This introduces a whole new class of problems that center on the performance of the routing algorithms


Feasibility considerations

Feasibility Considerations

  • For any pair of nodes N0 and N1, define a route by

    (N0, N1, h,n)

    Where n = 0 if h is adjacent to N0 and n = 1 if h is adjacent to N1

  • If N0 and N1 are adjacent, we have a direct route

    • Else the route is the link (Nn,h) and the route (N1-n,h,h*,n*)

  • Continue until the full route is established


Feasibility considerations1

Feasibility Considerations

  • This process establishes a feasible routing pattern for the network

  • However, the muxes may not be smart enough to find this pattern

  • As an example, consider single-route, minimum-hop (SRMH) routing


An srmh disaster

An SRMH Disaster

A

H

  • Assume MENTOR adds link BF to carry traffic from B to F, G, H, I – but not traffic from F to ABC

  • SRMH insists on carrying all traffic from A, B, C to F, G, H, I – result is overload on BF

B

G

F

C

E

I

D


Feasibility and routing

Feasibility and Routing

  • In reality, few network-loading algorithms are as bad as SRMH

  • However, network-loading algorithms do add to the design constraints

    • In particular, minimum-hop routing algorithms are fragile with respect to network capacity changes

    • Effective algorithms for redesign are not available


A more realistic loading algorithm

A More Realistic Loading Algorithm

  • Flow-Sensitive, Minimum-Hop (FSMH) loader loads traffic onto a minimum-hop path, subject to using only links with enough free capacity to carry it

    • Allows overflow onto longer paths

    • If no path exists, traffic is blocked

  • However, there is no guarantee that FSMH will do better than SRMH!


Fsmh failure example

FSMH Failure Example

A

B

Each link has capacity 1

C

D

Traffic:

SRMH will block the second AB traffic

and load 4 out of 5 requirements

FSMH will load load both AB requirements,

but block all the rest

Note: order of loading traffic is significant!


Comments on fsmh

Comments on FSMH

  • In the earlier example (15 sites), FSMH fails on the best designs

    • 13-node, $191k design blocks 3.3% of traffic

    • 12-node, $199k design blocks 6.7% of traffic

  • Best design where FSMH does not block is 11-node, $201k


Approaches

Approaches

  • We cannot guarantee that a highly-optimized network design will work with a given routing algorithm

  • Approaches

    • Test the loading algorithm against best designs

      • Routing takes more computation than design Raises complexity to between O(n3) and O(n4)

    • Limit maximum link utilization to <100%

      • Also increases reliability, allows for growth


Router network design

Router Network Design

  • Common routing algorithm for IP is OSPF (Open Shortest Path First)

  • Implicit problem is design for minimum distance

    • Single-route, minimum distance loader (SRMD)

      • Computes single shortest path between site pairs

      • If traffic saturates the route, it’s discarded

      • Designer chooses link lengths appropriately


Srmd characteristics

SRMD Characteristics

  • Traffic not forced onto illogical paths if link lengths are chosen properly

  • Problems can still arise

    • Not dynamic

    • Cannot split traffic between different routes


Ospf example

OSPF Example

This link intended to carry traffic between A and H, and B to H

but not traffic between A and G

A

395

H

90

100

B

100

G

100

F

100

C

E

I

100

D

A-H traffic will take 1-hop path length 395

B-H traffic will take 2-hop path length 485

A-G traffic will take 5-hop path length 490


Important difference

Important Difference

  • Mux networks are designed for high utilization

  • Router networks are not designed for high utilization

    • Allows some margin for error by the routing algorithm


Comments2

Comments

  • Can encourage the traffic to use the MENTOR routing as we add edges by setting the length of each tree edge to 100, and the length of a direct edge between N1 and N2 to:

    100 + 90*(hops(N1,N2)-1)


Comments 21

Comments (2)

  • Any routing algorithm should work for a tree

  • Problems arise when design becomes more highly meshed

  • Can manipulate solution by

    • Increasing length of overloaded links

    • Shortening under-utilized links

    • Adding or deleting capacity


Homework assignment

Homework Assignment

  • Cahn Exercises 8.2, 8.6

  • Read Cahn Chapter 9


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