TCOM 541

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) gt 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) lt MAXCOSTRPARM

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., VH)
• Compute center of gravity of sites

8
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

9
Distances to CG

• Define
• dcn (xn-xctr)2 (yn-yctr)20.5
• maxdc max(dcn)
• maxW max(Wn)
• Then
• meritn 0.5(maxdcdcn)/maxdc 0.5(Wn/maxW)
• That is, merit gives equal value to a nodes
  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 RPARMMAXCOST 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

11
MENTOR Example
Radius RPARMMAXCOST
CG
Edge node
Backbone node
12
MENTOR Example (2)
Radius RPARMMAXCOST
CG
Edge node
Backbone node
13
MENTOR Example (3)
Radius RPARMMAXCOST
CG
Edge node
Backbone node
14
MENTOR Example (4)
Radius RPARMMAXCOST
CG
Edge node
Backbone node
15
MENTOR Example (5)
Radius RPARMMAXCOST
CG
Edge node
Backbone node
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 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

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

18
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
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)
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) lt 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
• If capacity of a link is C, compute
• n ceilT(N1,N2)/C
• Compute utilization
• u T(N1,N2)/(nC)
• Add link if u gt 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 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

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

27
MENTOR Example
Based on mux1.inp on Cahns FTP site 15 sites, 60
256 kbps circuits
13
6
2
7
15
14
10
9
1
5
12
4
8
11
3
28
Initial Choice of Backbone Nodes (5)
13
6
2
7
15
Backbone node
14
Backbone node
10
9
1
5
Backbone node
12
Backbone node
4
8
Backbone node
11
3
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Initial Design
a 0 Cost 269,785/month
13
6
2
7
15
5 x T1
2 x T1
14
10
9
1
5
12
5 x T1
5 x T1
4
8
11
3
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
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
32
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
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,h,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
A
H
B
G
F
C
E
I
D

• 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

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 Example
A
B
Each link has capacity 1
C
D
Traffic
A B C D
A 2 1
B 1
C 1
D
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!
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 lt100
• 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, its 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
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
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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

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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)

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