3. Randomization

1
3. Randomization

• randomization used in many protocols
• well study examples
• Ethernet multiple access protocol
• router (de)synchronization
• reliable multicast
• queue management

2
Ethernet

• single shared broadcast channel
• 2 simultaneous transmissions by nodes
  interference
• only one node can send successfully at a time
• multiple access protocol distributed algorithm
  that determines how nodes share channel, i.e.,
  determine when node can transmit

Metcalfes Ethernet sketch
3
Ethernet uses CSMA/CD

• A sense channel, if idle
• then
• transmit and monitor the channel
• If detect another transmission
• then
• abort and send jam signal
• update collisions
• delay as required by exponential backoff
  algorithm
• goto A
• else done with the frame set collisions to
  zero
• else wait until ongoing transmission is over and
  goto A

4
Ethernets CSMA/CD (more)

• Jam Signal make sure all other transmitters are
  aware of collision 48 bits
• Exponential Backoff
• first collision for given packet choose K
  randomly from 0,1 delay is K x 512 bit
  transmission times
• after second collision choose K randomly from
  0,1,2,3
• after next collision double K (and keep doubling
  on collisions until..)
• after ten or more collisions, choose K randomly
  from 0,1,2,3,4,,1023

5
Ethernets use of randomization

• resulting behavior probability of retransmission
  attempt (equivalently length of randomization
  interval) adapted to current load
• simple, load-adaptive, multiple access

randomize retransmissions over longer time
interval, to reduce collision probability
heavier Load (most likely), more nodes trying to
send
more collisions
6
Ethernet comments

• upper bounding at 1023 k limits max size
• could remember last value of K when we were
  succesful (analogy TCP remembers last values of
  congestion window size)
• Q why use binary backoff rather than something
  more sophisticated such as AIMD simplicity
• note ethernet does multiplicative-increase-comple
  te-decrease (why?)

7
Analyzing the CSMA/CD Protocol

• Goal quantitative understanding of performance
  of CSMA protocol
• fixed length pkts
• pkt transmission time is unit of time
• throughput S - number of pkts successfully
  (without collision) transmitted per unit time
• a end-to-end propagation time
• time during which collisions can occur

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• offered load G - number pkt transmissions
  attempted per unit time
• note SltG, but S depends on G
• Poisson model probability of k pkt transmission
  attempts in t time units
• Probk trans in t ((Gt)k
  )(e-Gt)/k!
• infinite population model
• capacity of multiple access protocol maximum
  value of S over all values of G

9
Analyzing CSMA/CD(cont)

• Focus on one transmission attempt
• S exp(- a G) /(1/Gexp(- a G)(1 a)1.5 a)

10
a .01
a .02
a .05
a .10
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The bottom line

• Why does ethernet use randomization to
  desynchronize a distributed adaptive algorithm
  to spread out load over time when there is
  contention for multiple access channel