TCOM 540

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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 doesnt 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
• S Ni e Tj wi lt W
• STrees SL e LinksCost(end L1, endL2) is minimum

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Example
A
B
Y
X
C
D
3 backbone nodes 17 access locations
Z
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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 S ( ) 217-k partitions ..
• Computationally very large

17 k
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
6
2
7
1
5
4
10
9
8
3
Node 8 is closer to 1 than 2 But its cheaper to
home it to 2 via 9
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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) minjCost(Ni,Nj) Cost (Comp(Ni),N0)
• Computes cost of linking to neighbor vs. cost of
  going to center
• MCEW Tradeoff function is
• Tr(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
• lt 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

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Mesh Example
32
A
B
32
32
32
32
32
32
C
D
32
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Example Tree Design
64
A
B
64
64
64
64
64
C
D
Requires 6 x 64kbps links at 50 utilization
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Example Ring Design
32
A
B
32
32
32
32
32
32
C
D
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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 11)
• TCOM 541 starts following week