Problems with Simulation of TCPIP Networks

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Problems with Simulation of TCP/IP Networks

• Ron Addie,
• Zhi Li,
• University of Southern Queensland

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Models of TCP/IP Traffic

• Poisson arrivals of flows/bursts
• Flows/bursts heavy tailed in size
• Flow delivery process determined by the network.

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Problems

• Duration of simulation
• How long should a simulation be?
• Initialization of simulation
• How long should the warm-up period be?
• Can we use Importance Sampling/Splitting to solve
  these problems?

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How Long?

• Congestion lasts a long time (because of
  long-range dependence)
• Therefore, the time between congestion periods is
  even longer (to keep the average congestion down).

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Correction Idle Times are short.

• The time to the next busy period in an M/Pareto
  queue is neg-exp distributed.
• Many short busy periods, and some very long ones.
• But, the time between long busy periods is very
  long.

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Intervals Between CongestionAlternative Method

• Since the average utilization must sum to ???Let
  ? be the av. length of a congestion interval and
  N the length of a non-congested interval. ThenN
  ??????????????) x ?????????
• Where ? is the proportion of bytes in
  congestion intervals.

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Simplified Case

• Consider a single link.
• All traffic streams will experience congestion in
  this link.
• (In reality, only some streams are limited in
  this link).

E.g. 1 Mbit/s
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How Long?

• In the simplest instance (one link only,
  end-to-end), congestion will be like the busy
  period in a M/Pareto/1 queue.
• So, congestion has a heavier tail than the queue
  distribution, which is heavy-tailed Veitch et
  al.
• Tacacs formula for the Busy period can be used
  also to estimate the busy period distribution and
  its tail properties. This provides numerical LT,
  which can be inverted.

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Takacs Formula for the Busy Period

• B(s) P(s?(1-B(s))
• This formula gives
• Mean busy period ??????????
• Tail shape ?
• Tail weight ????????????????? roughly
• Infinite variance

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Busy Period Distribut-ion
These distributions were calculated by numerical
LT inversion

• The busy period distn is similar to the flow
  distn, but heavier.

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How Long is ? ?

• ? 90 of all packets are in busy periods
  shorter than ?.
• We need the length-weighted dist of busy periods.

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How long is ? ?
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Start in a Busy State?

• Why not start the simulation loaded with
  pre-existing flows?
• Problem there is no formula for the statistics
  of sampled flows.
• Simulation is required to find out what these
  flows would typically look like!

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Simulations also get slower

• To make matters worse, when heavy tailed flow
  length's are simulated, congestion continues to
  build for a long time.
• So the simulation get's slower and slower the
  longer it goes.

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Measurements

• You might be thinking that simulation must work,
  because its just like the real thing, and we do
  measurements of real networks!
• Actually, measurements suffer from the same
  problem.
• Naïve measurements (e.g. of congestion) will be
  very inaccurate.

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Solutions

• Importance Sampling
• Half mathematical model / half simulation
• Requires better initialization OR
• Importance sampling which approaches a stationary
  state.

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Importance Sampling Paradox

• Importance sampling is faster by reaching
  interesting states more quickly.
• So, surely, estimates of duration must all be
  biased?
• Not necessarily such direct time estimates might
  just be inaccurate.

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More Problems

• Importance Sampling is not an easy solution
  because
• We need to work out the optimal distortion for
  this model not obvious
• The real system really does evolve slowly

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Does it matter?

• Not necessarily. We could just invent scenarios,
  or choose them from observed systems.
• However, there is a risk.
• We do need to understand what situations occur,
  and how frequently.

For some problems, it matters!
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Ideal Solution

• Pure simulation is best, so we can check the
  mathematics
• How
• Simulate low congestion periods very quickly (and
  inaccurately).
• Simulate in parallel (this effectively shortens
  the idle periods).
• Genetically select better simulations.

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Conclusions

• Simulating TCP/IP communication systems with an
  arbitrary configuration of traffic is currently
  the best we can do.
• However, we should also conduct simulations based
  on stationary models of TCP/IP traffic.

Next step simulate the // simulations.