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TCOM 541

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TCOM 541

Session 2

- 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

- Access designs generally are trees – sites connect to center

- “High quality, low complexity” algorithm
- Originally developed for time division multiplexing
- Works with other technologies

- 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

- 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

- 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

- “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):

- 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

- Defined as (xctr, yctr) where
xctr = SnxnWn/SWn

yctr = SnynWn/SWn

Note: These coordinates need not correspond to any actual site

- 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

- 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

Radius = RPARM*MAXCOST

C*G

Edge node

Backbone node

Radius = RPARM*MAXCOST

C*G

Edge node

Backbone node

Radius = RPARM*MAXCOST

C*G

Edge node

Backbone node

Radius = RPARM*MAXCOST

C*G

Edge node

Backbone node

Radius = RPARM*MAXCOST

C*G

Edge node

Backbone node

- 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

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

- 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

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

- 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)

- 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

- Low-cost algorithm
- Three main steps
- Backbone selection
- Tree building
- Link addition

- All of O(n2)
- Possible to re-run many times, varying parameters

- Three main steps

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

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

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

- 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)

- If a design has multiple parallel high-speed links there is usually a better, meshier design
- Note this is not mathematically provable

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

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

- 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

- 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

- 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

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

- 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!

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

- 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

- Test the loading algorithm against best designs

- 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

- Single-route, minimum distance loader (SRMD)

- Traffic not forced onto illogical paths if link lengths are chosen properly
- Problems can still arise
- Not dynamic
- Cannot split traffic between different routes

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

- 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)

- 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

- Cahn Exercises 8.2, 8.6
- Read Cahn Chapter 9