Enterprise Network Design Methods

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Impact of Graph Theoretic Network Parameters on
the Design of Regular Virtual Topologies for
Optical Packet Switching
Olufemi Komolafe - University of Strathclyde,
Glasgow, UK David Harle - University of
Strathclyde, Glasgow, UK David Cotter - Corning
Research Centre, Ipswich, UK
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Introduction
ARBITRARY PHYSICAL TOPOLOGIES Contentions highly
probable Complex routing schemes needed
OPTICAL PACKET SWITCHING Minimise/avoid optical
buffering Minimise routing complexity
BUT
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Introduction
ARBITRARY PHYSICAL TOPOLOGIES Contentions highly
probable Complex routing schemes needed
OPTICAL PACKET SWITCHING Minimise/avoid optical
buffering Minimise routing complexity
Multiprocessor inter-connection architectures
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Approach
Map MIA nodes onto physical topology
Exemplar multi-processor interconnection
architecture (MIA)
Physical topology
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Approach
Establish lightpaths between nodes
Exemplar multi-processor interconnection
architecture (MIA)
Physical topology
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Numerous different mappings
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Previous Work

• Different architectures
• Manhattan Street Network, Hypercube, Shufflenet
• Different optimisation techniques
• AI techniques
• genetic algorithms, tabu search, simulated
  annealing
• heuristic algorithms
• hill climbing, random search
• Different costs
• number of wavelengths, inter-nodal distances,
  mean lightpath length

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BUT Most previous work of an ad hoc
nature Only specific physical topologies
considered No insight into parameters of
physical topology that affect optimisation results
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Motivation
What parameter(s) of a physical topology
determines the efficacy of regular virtual
topology design?
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Approach

• Generate large number of unique randomly
  connected networks
• calculate different parameters
• degree (mean, max, variance, STD, CV)
• inter-nodal distance (mean, max, variance, STD,
  CV)
• number of bridges
• bounds on cost
• Use heuristics to seek optimal solutions
• Investigate relationship between network
  parameters and optimisation result

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Exemplar MIA
Manhattan Street Network

• Clockwork Routing
• Simple packet routing
• No optical contentions
• Favourable performance
• No resequencing _at_ destinations

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Cost

• Mean lightpath length
• impacts number of hops packets traverse
• affects number of ? needed
• indicates number of optical cross-connects
  traversed between adjacent MSN nodes
• affects deployment of optical amplifiers
  consumption of other network resources

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Optimisation Techniques

• Simulated annealing (SA)
• modelled on cooling of molecules to form crystal
• uphill moves allowed with decreasing probability
• Genetic algorithms (GA)
• modelled on natural evolution
• synergistic combination of solutions to find
  optimum
• Use of these radically different optimisation
  techniques engenders confidence in findings

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Network Classification Degree

• Mean degree varied
• i.e. number of links varied
• uniform random distribution of links
• Distribution of nodal degree varied
• i.e. number of links constant BUT
• non-uniform random distribution of links
• existence of hub nodes

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Variation of Mean Degree
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Variation of Mean Degree
Exemplar 16-node networks
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Variation of Mean Degree
Exemplar 64-node networks
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Variation of Mean Degree

• Exemplar results statistically verified
• 3000 unique randomly connected networks
  considered

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Variation of Degree Distribution

• Achieved by varying number of hub nodes

No hub node
Single hub node
Mean degree 3 Max degree 5 CV degree 0.404
Mean degree 3 Max degree 10 CV degree 0.689
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Variation of Degree Distribution
Average results for 500 unique 36-node
networks Mean degree 3
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Variation of Degree Distribution
Average results for 500 unique 36-node
networks Mean degree 7
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Observations Initial Cost
Initial mean lightpath length falls with
increasing CV degree
Fall more pronounced for lower mean degree
Mean degree 3
Mean degree 7
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Explanation Initial Cost Fall

• Why does initial cost fall with rising degree CV?
• Counter-intuitive result
• expect uniform distribution of links to be
  better than having hub nodes
• Estimate for initial cost introduced to explain
  results
• What would be the resulting mean lightpath length
  for a typical random (un-optimised) embedding?

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Estimate for Initial Cost
Random Embedding Each MSN node mapped to
arbitrary physical topology node
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Estimate for Initial Cost
Random Embedding Each MSN node mapped to
arbitrary physical topology node Neighbours
mapped to arbitrary physical topology nodes
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Estimate for Initial Cost
Random Embedding Mean lightpath length Mean
distance to 4 arbitrary nodes i.e. Mean
inter-nodal distance
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Explanation Initial Cost Fall

• Mean inter-nodal distance found to be excellent
  estimate for initial mean lightpath length

Effect of CV degree on mean inter-nodal distance
Effect of CV degree on initial mean lightpath
length

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Explanation Initial Cost Fall
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Observations Final Cost
Final mean lightpath length rises with increasing
CV degree
Rise more pronounced for lower mean degree
Mean degree 3
Mean degree 7
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Explanation Final Cost Rise

• Why does final cost rise with rising degree CV?
• Estimate for improvement margin on initial cost
  introduced to explain results
• What parameter of a network determines the
  improvement obtainable on an random initial
  solution?

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Estimate for Improvement Margin
CV degree insufficient to characterise
improvement obtainable!
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Estimate for Improvement Margin
Spread in inter-nodal distances indicates margin
for improvement
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Explanation Final Cost Rise

• CV inter-nodal distances indicative of
  improvement obtainable on initial embedding
• Low spread in inter-nodal distance
• all mappings of MSN onto network produce similar
  results
• High spread in inter-nodal distance
• significant improvement obtainable if adjacent
  MSN nodes placed onto physical topology nodes
  near each other

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Explanation Final Cost Rise
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Conclusions

• Addressing ad hoc approach to regular virtual
  topology design
• What parameters of physical topologies affect the
  optimisation results?
• Mean inter-nodal distance ? initial embedding
  cost
• Spread in inter-nodal distance ? margin of
  improvement
• Suggest principles applicable to other areas in
  telecommunication network design

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THANKS