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TCOM 540

Session 6

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Agenda

• Review Session 4 and 5 assignments

• Multicenter local access design

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Another Definition

• A Forest, F = (V,E) is a simple graph without cycles– Note it doesn’t say connected

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Multicenter Local Access (MCLA) Problem

• Given– A set of backbone sites (B0, …, Bm) = B

– A set of access nodes (N1, …, Nn) = N

– A set of weights (w1, …, wn) for each access node

– A cost matrix Cost(i,j) giving the costs between each backbone/access pair of sites

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Multicenter Local Access (MCLA) Problem (2)

• MCLA is to find a set of trees T1, …, Tk such that– Exactly one backbone site belongs to each tree

– Ni Tj wi < W

– Trees L LinksCost(end L1, endL2) is minimum

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Example

XY

Z

A

B

DC

3 backbone nodes17 access locations

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Solve by Enumeration?

• Each solution divides the 17 access locations into 3 sets (one to each backbone node) = 3 capacitated MST problems

• We can use E-W to solve these!

• But there are ( ) 217-k partitions …..

• Computationally very large …

17k

k = 0,…, 17

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A Simple Approach …

• Use nearest neighbor approach– For each backbone node B, let SB be the set of

access nodes that are closer to B than any other backbone node

– Run Esau-Williams on each SB

– Call this Nearest-Neighbor Esau-Williams (NNEW)

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… That is Not Very Good

• NNEW algorithm shows a failure rate of 30 to 60% on random problems with 2 or 3 backbone nodes and 10 to 150 total nodes

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An Example of How NNEW Fails

2

1

10

6

9

7

5

4

38Node 8 is closer to 1 than 2But it’s cheaper to home it to2 via 9

Lesson: Locationsof other accessnodes cannotbe ignored!

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Multicenter Esau-Williams (MCEW)

• Developed by Kerschenbaum and Chou (1974)

• Changes the tradeoff function

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MCEW (2)

• EW Tradeoff function is Tr() where

Tr(Ni) = minj[Cost(Ni,Nj)] –Cost (Comp(Ni),N0)

• Computes cost of linking to neighbor vs. cost of going to center

• MCEW Tradeoff function isTr(Ni) = minjCost(Ni,Nj) – dist(Comp(Ni), Center(Nj))

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MCEW (3)

• Initially, set Center(Ni) to be closest center

• If merge Ni with Nj, update Center(Ni) = Center(Nj)

• Note: Tradeoff function merges cost and distance functions

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MCEW (4)

• MCEW produces more creditable results than NNEW– Produces a better solution much more often– But cost advantage is surprisingly small

• < 1% for large numbers of sites

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Practical Issues

• Real problems often involve additional, sometimes quirky, constraints, such as– Limit on number of nodes in an access tree– Limit on number of hops– Limit on number of connections at a site– Unreliable links or sites

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More Highly-Connected Networks

• Best topology is not limited to a tree design– E.g., Four sites, full-duplex 64k lines, with

traffic matrix:

From/To A B C D

A 32 32

B 32 32

C 32 32

D 32 32

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Mesh Example

A B

CD

32

32

3232

32

32

3232

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Example – Tree Design

A B

CD

64

64

64646464

Requires 6 x 64kbps links at 50% utilization

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Example – Ring Design

A B

CD

32

32

3232

32

32

3232

Requires 4 x 64 kbps links

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Full vs. Partial Mesh

• Full mesh requires n(n-1)/2 links– Require n-1 connections at each site, imposes

heavily on site equipment– Likely to have many lower-speed links which

should be aggregated

• Partial mesh generally preferable– Increased number of hops

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Design Principles

• Have direct paths between origin and destination

• Have well-utilized (but not overloaded) components

• Have efficient high-speed links where possible

• Of course, these principles contradict each other ….

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How to Recognize a Good Design?

• For most designs, there is no known math that will prove they are optimal, or even close to optimal

• Most real designs will be produced by a computer program

• Good algorithms can yield bad designs– And vice-versa

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How to Recognize a Good Design? (2)

• Look for obvious problems

• Look for ways of changing a few links and saving costs

• Change design parameters (a little) and rerun algorithm

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Two Indicators of Possible Problems (1)

• High average nodal degree– I.e., lots of connections at each node– May indicate over-use of low-speed links– Unless most links are highest capacity available– Or there are stringent hop limitations

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Two Indicators of Possible Problems (2)

• High average number of hops– Hops act as traffic magnifiers– Introduce latency, reliability issues

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Routing Considerations

• Routing is generally irrelevant for access designs

• Can be important for backbone (mesh) designs

• Many algorithms

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Some Examples of Routing Algorithms

• Open Shortest Path First (OSPF)– Minimum distance routing

• Hierarchical (telephony)– Open alternate path when primary is busy (bifurcated)

• Systems Network Architecture (SNA)– Static, arbitrary, multiple, bifurcated

• Black box – e.g., PVCs– User generally has no information as to physical route

used

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Assignment and Schedule

• No homework this week

• Next session– TCOM540 papers due (where appropriate)– Interim TCOM540/541 annotated outlines due

• Must contain significant amount of information

– Finals for TCOM540• Open book exam, may deal with any topics covered

to date

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Assignment and Schedule (2)

• No class following week (March 9)

• TCOM 541 starts following week