Analysis of Ethernet-like protocols

1
Analysis of Ethernet-like protocols

• Andrey Lukyanenko
• University of Kuopio

2
History of Ethernet
Bob Metcalfe and David Boggs created Ethernet in
laboratory of Xerox Company in 1973 (1976
scientific paper).

• Idea
• Cheapness (just put wire in the building)
• Easiness (to add new station just buy a
  transceiver to it, and tap it into the network).
• Access to sources of local area network (printer,
  file server, etc)
• Robustness (if any number of station becomes
  unreachable, the network still working).
• Success of idea Today 95 of LANs are Ethernet
  LANs.

3
The Idea

• Shared medium (bus).
• all data simply broadcast over the medium.
• receivers listen to the network, if there is a
  message for them.
• Collisions.
• If two or more messages broadcast in the network
  then collision could happen.
• Backoff protocol from Aloha.
• The part of collision resolution protocol.
• Problem of algorithms with fixed retransmission
  time (Pure Aloha isnt stable).

4
Collision resolution

• Mechanisms to reduce probability and cost of
  losing packets
• Carrier detection
• Phase encoded (to remove silent spaces during
  packet transfer)
• If a station wants to transfer a packet it listen
  to the channel, deferring the packet if the
  channel busy.
• Collisions only if two or more stations find the
  Ether silent.
• Interference detection
• each transceiver has detector, which says if the
  channel has the same signal that it transmits. If
  the signal differ then collision.
• We define time slot from now as double time to
  propagate the signal over network (round trip
  time).
• Packet error detection (checksums)
• Truncated packet filtering (reduce processing
  load).
• Collision consensus enforcement
• When station find it message experenced
  interference it jams the network, to let all
  station know about it.

5
Backoff protocol in Ethernet

• Metcalfe and Boggs took binary exponential
  backoff protocol for their network.
• Difference that isnt anymore a constant, now
  it is a function from the number of successive
  collisions of a message (backoff counter ).
• In Ethernet this function have the following form
  .
• If backoff counter exceeds 16, then we discard
  the message and zero the counter.
• Time delay always is a random number that is
  taken uniformly from sector We
  work with time delay before next attempt to send
  instead of clear probability .

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Why do we continue study the Ethernet?

• Answer We can use backoff protocol in the
  future.
• Examples of use
• Wireless network (also took binary exponential
  backoff).
• OCPC (optical comunication parallel computer)
• h-relation problem currently studied in Kuopio.
• Collisions happen when two or more station
  transmit to the same station at some moment of
  time.
• Every station has h messages to send.
• The expected number of messages to some
• station is h (some kind of balanced situation).

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h-relation problem (closer view)

• Tasks
• In h-relation problem backoff protocol may be
  used.
• We need to choose the best one.
• In general we can take any kind of backoff
  function, backoff protocol wasnt studied quite
  well yet (though, but some results say that
  binary exponential isnt good choice).

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History of research

• Different authors got different results on
  backoff.
• Kelly
• mathematically formulation of problem (binary),
  criterion of instability with high input rate,
  for infinite model.
• Aldous
• Ultimate instability of all acknowledge-based
  protocols, for infinite model.
• Goodman et al
• stability for small incoming rate, for finite
  model.
• Håstad et al
• Instability of binary exponential backoff for big
  incoming rate (gt0.5)
• Stability of polynomial backoff.
• Instability of linear and sublinear protocols at
  all.
• Shenker
• Denies some results of Håstad et al (according
  polynomial backoff)

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Main Results by now

• For infinite model (when number of station is
  infinite) the protocol is unstable for all
  backoffs.
• For finite model polynomial backoff stable, and
  binary exponential unstable for big incoming rate
  (gt0.5) and stable for small incoming rate, which
  goes to zero as the number of station grows up.

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Our model

• Model was taken from Kwak et al paper.
• Its slightly differ from model in Bianchi.
• Assumptions of the model
• The model is under Saturation conditions.
• The model is in steady state (collision
  probability is the same, this state we could
  achieve if let the model work for a long period
  of time).
• Time slotted model (with slot equal to the double
  round trip time). Message broadcasts during one
  time slot and has exactly bounds of the slot
  (also synchronized).

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Calculus (1)

• Our first task for this model was to find the
  dependence
• between probability to transmit and probability
  to collide at
• any moment of time. We found that
• 
  where
• From Bianchi we have that
• so solution of this system gives us the exact
  value for
• probability of collision (unfortunately we
  couldnt solve it in
• general).
• Note that function F(z) has all the properties of
  backoff functions
• (combined together).

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Calculus (2)

• Solving the previous equations we
• have, that
• The condition to have exactly
• one intersection is

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Calculus (3)

• One of the most important characteristic of a
  network is the delay time
• of the system. Its time that message should wait
  until successful
• transmission
• Combining it with
  we can find the
• value of optimal probability of collision

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Calculus (4)

• Existing BEB
• Optimal EB

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Optimality for general function
16
Leaving saturation condition

• Using negative drift we can leave
• saturation conditions.
• New model is almost the same. New
• node which doesnt affect if number of
• messages in the queue greater than
• zero.

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Negative drift (idea).
Condition of drift
Current state
Q(t) gt C
Zero state
Negative drift
Q(t) lt C
The number of steps to return to zero is at most
(with positive probability)
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Repeat results.

• We found optimality conditions for backoff
  protocol (model with infinite backoff counter).
• Extended the development of backoff to general
  functionality.
• Showed the performance of known backoff functions.

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Future work.

• Make simulation (checking received results).
• Extend the theory on backoff function with finite
  model backoff counter.
• Check the formulas for small network preload
  (weakness of the assumption that model in steady
  state).

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Thanks.

• Questions?