Models for Internet Cache Location

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Models for Internet Cache Location

• Adam Wierzbicki
• Institute of Telecommunications
• Warsaw University of Technology
• adamw_at_icm.edu.pl

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Introduction - 1

• Replica Location Problem (RLP)

• Cache Location Problem (CLP)

• Previous work on CLP
• oriented on complexity heuristics, special-case
  optimal solutions
• black-box approach to decision problem

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Introduction - 2

• Aim of this work

• design a Decision Support System (DSS) for cache
  location that allows the Decision Maker (DM) to
  find solutions that match his preferences

• secondary goal evaluate the practical complexity
  of using Mixed Integer Linear Programming for the
  CLP

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Modules of a DSS

• Information module could be integrated with other
  network management tools

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The Decision Maker (DM) of the CLP

• Who is the DM?
• manager of a Content Delivery Network (CDN)
• manager of a public caching infrastructure

• What other parties can influence DM preferences?
• content providers
• clients of content providers

• DM preferences
• can change over time
• are not known to the DM in advance

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The information module - 1

• Summary of input information

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The information module - 2

• Measurements

• due to traffic seasonality, choose one time of
  day during working days

• measure available TCP throughput using existing
  tools (treno), logs, approximations from RTT and
  loss

• Stabilized estimates

• exponential moving average

• discretize

• use histeresis when moving up a level

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Multicriteria models of the CLP - 1

• (Binary) Decision variables

• Constraints

• assignments must be a function

• assignment to a node implies location of cache at
  that node

• can constrain number of new caches or moved caches

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Allowing variable hit rates

• In reality, number of cache clients has influence
  on hit rate. This requires nonlinear models.

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Multicriteria models of the CLP - 2

• Criteria

• cost of new cache location

• cost of movement of old caches

• delay
• average delay of fetching a unit of data by a
  client
• average delay of sending a unit of data from a
  server

• network resource cost

• Find a common scale for all criteria

• define a scaling function

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Supporting the decision process - 1

• Objective functions that include DM preferences

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Supporting the decision process - 1

• Objective functions that allow the DM to express
  his preferences

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Supporting the decision process - 2

• Both the WS and RP methods always find a
  Pareto-optimal solution

• The new models allow the DM to
• change his preferences during a session with the
  DSS
• interactively explore the available optimal
  solutions by changing his preferences

• The DSS should graphically display solution
  quality with respect to each criterion

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Comparison of WS and RP methods - 1

• Locate cache in small example topology to
  minimize server delays

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Comparison of WS and RP methods - 2

• Delays of the two servers

• Pareto-optimal solutions
• Korhonen paradox

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Comparison of WS and RP methods - 3

• RP method is more precise in searching for
  solutions that best match DM preferences

• regardless of type of criteria

• regardless of type of DM preferences (fair, not
  fair)

• Expressing preferences using aspiration and
  reservation levels allows the DM to consider
  criteria separately (one at a time)

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Solving models of the CLP using MILP

• CLP of up to 100 nodes, 500 demands solvable by
  MILP solvers (cplex)

• Complexity depends on number of demands and
  number of potential cache locations

• MILP solvers can produce approximate solutions
  with controlled quality

• Practical limitation of MILP size of linear
  program

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Solving models of the CLP by heuristics

• Example greedy heuristic

• Modification for multiple criteria use objective
  function of RP method

• Greedy heuristic has similar drawback as WS
  method, but is suitable as a solver for the DSS

• Future work - test other heuristics (l-greedy)

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Conclusions

• Supporting DM preferences and the decision
  process requires different (multicriteria) models
  of the CLP

• Most model variants can be expressed using Mixed
  Integer Linear Programming

• Heuristics can be adapted to models that support
  DM preferences

Questions?