1

TCOM 541

Session 2

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

– Backbone designs require many-many connectivity

3

MENTOR Algorithm

• “High quality, low complexity” algorithm

• Originally developed for time division multiplexing– Works with other technologies

4

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

5

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

6

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

7

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

8

Center of Gravity (CG)

• Defined as (xctr, yctr) where

xctr = nxnWn/Wn

yctr = nynWn/Wn

Note: These coordinates need not correspond to any actual site

9

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

10

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) = dist(n,n*)Wn*

• Construct a Prim-Dijkstra tree, parameter

11

MENTOR Example

Backbone node

Edge node

Radius = RPARM*MAXCOST

C*G

12

MENTOR Example (2)

Backbone node

Edge node

Radius = RPARM*MAXCOST

C*G

13

MENTOR Example (3)

Backbone node

Edge node

Radius = RPARM*MAXCOST

C*G

14

MENTOR Example (4)

Backbone node

Edge node

Radius = RPARM*MAXCOST

C*G

15

MENTOR Example (5)

Backbone node

Edge node

Radius = RPARM*MAXCOST

C*G

16

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 )

• Aggregation of traffic in “central” links raises costs• Large average hops in large networks

– Star-like network network (high ) • May have low link utilization

17

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

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Example of Sequencing

A

B

CD

E

SequenceAEAFBEBFCECFDADBACBC…DF

F

3 hops

2 hops

1 hop

19

Comments on Sequences

• Sequences are not unique

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

20

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

21

Homing (2)N1

N2N3

N4

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

22

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)

23

Last Step (2)For each pair (N1,N2), execute the following algorithm:

1. If capacity of a link is C, compute

n = ceil[T(N1,N2)/C]

2. Compute utilization

u = T(N1,N2)/(n*C)

3. 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

24

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

25

Comments (2)

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

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

he shape of the initial tree is controlled by – High 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 will build a more chain-like tree, so there will be more aggregation of traffic and likely addition of links

26

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

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MENTOR ExampleBased on mux1.inp on Cahn’s FTP site15 sites, 60 256 kbps circuits

15

109

8

311

4

125

1

13

14

2

7

6

28

Initial Choice of Backbone Nodes (5)

15

109

8

311

4

125

1

13

14

2

7

6

Backbone node

Backbone node

Backbone node

Backbone node

Backbone node

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Initial Design

15

109

8

311

4

125

1

13

14

2

7

6

5 x T1

5 x T1

5 x T1

= 0Cost = $269,785/month

2 x T1

30

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

31

Revised Design

15

109

8

311

4

125

1

13

14

2

7

6

umin = 0.7Cost = $221,590

1

1

2

3 1

1

2

32

“Best” 5-Node Backbone Design

15

109

8

311

4

125

1

13

14

2

7

6

22

22

1

1

= 0.1umin = 0.9Cost = 209,220

33

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

34

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

35

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,n*,n*)

• Continue until the full route is established

36

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

37

An SRMH Disaster

• 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

C

A

B

DE

F

H

I

G

38

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

39

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!

40

FSMH Failure ExampleA

C D

B

A B C D

A 2 1

B 1

C 1

D

Traffic:

SRMH will block the second AB trafficand load 4 out of 5 requirementsFSMH will load load both AB requirements,but block all the restNote: order of loading traffic is significant!

Each link has capacity 1

41

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

42

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

43

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

44

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

45

OSPF Example

C

A

B

DE

F

H

I

G90

100

100

100

100100

395

This link intended to carry traffic between A and H, and B to Hbut not traffic between A and G

A-H traffic will take 1-hop path length 395B-H traffic will take 2-hop path length 485A-G traffic will take 5-hop path length 490

46

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

47

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)

48

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

49

Homework Assignment

• Cahn Exercises 8.2, 8.6

• Read Cahn Chapter 9