TCOM 541

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# TCOM 541 - PowerPoint PPT Presentation

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

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
• Backbone designs require many-many connectivity
MENTOR Algorithm
• “High quality, low complexity” algorithm
• Originally developed for time division multiplexing
• Works with other technologies
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
• 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)
• 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)
• 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)
• Defined as (xctr, yctr) where

xctr = SnxnWn/SWn

yctr = SnynWn/SWn

Note: These coordinates need not correspond to any actual site

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)
• 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

C*G

Edge node

Backbone node

MENTOR Example (2)

C*G

Edge node

Backbone node

MENTOR Example (3)

C*G

Edge node

Backbone node

MENTOR Example (4)

C*G

Edge node

Backbone node

MENTOR Example (5)

C*G

Edge node

Backbone node

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
• 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

Sequence

AE

AF

BE

BF

CE

CF

DA

DB

AC

BC

DF

F

A

C

3 hops

D

E

B

2 hops

1 hop

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

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
• 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)
• 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
• 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
• 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
• Low-cost algorithm
• Three main steps
• Backbone selection
• Tree building
• All of O(n2)
• Possible to re-run many times, varying parameters
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)

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

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
• 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

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

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

• 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
• 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
• 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 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

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
• 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
• 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

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!

• 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
• 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
• 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
• 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

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
• Mux networks are designed for high utilization
• Router networks are not designed for high utilization
• Allows some margin for error by the routing algorithm
• 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)