A Study on the Efficacy of Regular Virtual Topology Design Heuristics for Optical Packet Switching

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• A Study on the Efficacy of Regular Virtual
  Topology Design Heuristics 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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REGULAR VIRTUAL TOPOLOGY DESIGN
Cost
INPUTS
SOLUTIONS
Optimisation techniques
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PROBLEM INPUTS
Cost
INPUTS
SOLUTIONS
Optimisation techniques
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Exemplar Regular Virtual Topology
Manhattan Street Network

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

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Arbitrary Physical Networks
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Arbitrary Physical Networks
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Arbitrary Physical Networks
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Arbitrary Physical Networks
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Arbitrary Physical Networks
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Arbitrary Physical Networks

• Unique if different values for any of
• maximum degree
• degree variance
• mean inter-nodal distance
• maximum inter-nodal distance
• diameter
• inter-nodal distance variance
• number of bridges
• link whose removal disconnects network

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COST
Cost
INPUTS
SOLUTIONS
Optimisation techniques
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Approach
Map MSN nodes onto physical topology
MSN
Physical topology
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Approach
Establish lightpaths between nodes
MSN
Physical topology
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Numerous different mappings
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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
Cost
INPUTS
SOLUTIONS
Optimisation techniques
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Optimisation Techniques

• NP-hard problem
• Use heuristics to find (near) optimal solutions
  expeditiously
• Use heuristics that work fundamentally
  differently
• confidence in results and trends

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Optimisation Techniques

• Simulated annealing
• modelled on cooling of molecules to form crystal
• uphill moves allowed with decreasing probability
• Genetic algorithms
• modelled on natural evolution
• 2 different implementations
• Cycle crossover (CX)
• Partially mapped crossover (PMX)
• Hill climbing
• Random search

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REGULAR VIRTUAL TOPOLOGY DESIGN
Cost
INPUTS
SOLUTIONS
Optimisation techniques
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REGULAR VIRTUAL TOPOLOGY DESIGN
Cost
INPUTS
SOLUTIONS
Optimisation techniques
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REGULAR VIRTUAL TOPOLOGY DESIGN
Cost
INPUTS
SOLUTIONS
Optimisation techniques
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REGULAR VIRTUAL TOPOLOGY DESIGN
Cost
INPUTS
SOLUTIONS
Optimisation techniques
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REGULAR VIRTUAL TOPOLOGY DESIGN
Cost
INPUTS
SOLUTIONS
Optimisation techniques
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PEERING INTO BLACK BOX
Cost
INPUTS
SOLUTIONS
Optimisation techniques
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Evaluation of Heuristics Efficacy

• 2 key metrics
• Quality of final solution
• final mean lightpath length obtained
• Efficiency associated with obtaining final
  solution
• number of solutions considered
• corresponds to area of search space explored
• indicative of time/computational effort
• generic and portable metric
• Monitor evolution in cost as optimisation
  heuristic progresses

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Experimental Approach

• Generate randomly connected physical networks
• mean degree 2, 5, 8
• Use heuristics to deploy MSN in each network
• monitor evolution in mean lightpath length
• Find average performance for each heuristic

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Sample Results SA (Mean degree 2)
Each line shows progress of SA when deploying MSN
in unique physical topology
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Sample Results SA (Mean degree 2)
Each line shows progress of SA when deploying MSN
in unique physical topology
Mean 3.345 STD 0.238 95 CI 0.079
Mean 5.721 STD 0.707 95 CI 0.234
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Randomly Connected Networks (Mean degree 2)
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Randomly Connected Networks (Mean degree 5)
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Randomly Connected Networks (Mean degree 8)
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General Observations
Significant reduction on initial cost
Converge to similar value
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Random Search
Worst performance
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Hill Climbing
Relatively good solutions
Short convergence time
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GA - Cycle Crossover
Relatively good solutions
Short convergence time
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GA - Partially Mapped Crossover
Very good solutions
Longer convergence time
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Simulated Annealing
Uphill moves
Longest convergence time
Best solutions
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Nature of Cost Function

• Determines performance of optimisation techniques
• Catch-22 scenario
• Must apply certain optimisation techniques to
  determine nature of cost function
• What insight do results provide about nature of
  cost function?

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Nature of Cost Function
Plateau with fissures?
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Meritocratic Ordering
Quality of Final Solution Simulated
Annealing Partially Mapped Crossover Hill
Climbing Cycle Crossover Random Search
of Solutions Considered Cycle Crossover Hill
Climbing Random Search Partially Mapped
Crossover Simulated Annealing
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Meritocratic Ordering
Quality of Final Solution Simulated
Annealing Partially Mapped Crossover Hill
Climbing Cycle Crossover Random Search
of Solutions Considered Cycle Crossover Hill
Climbing Random Search Partially Mapped
Crossover Simulated Annealing
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THANKS