Slotted Nonpersistent CSMA

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Slotted Nonpersistent CSMA

• Timeline divided into time slots, called mini
  slot, with length equal to maximum propagation
  delay t.
• Before attempting transmission, the user waits
  for the beginning of the next slot, and senses
  whether the channel is idle. If idle, he sends
  the packet for T time slots.
• If the channel is busy, the packet is rescheduled
  to some randomly chosen time in the future.

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Throughput analysis

• Idle period 1 gt arrival in first idle slot
• Idle period 2 gt no arrival in first and
  arrival in second

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Idle period

• Following the above reasoning we get
• Giving us

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Busy Period

• Both successful and unsuccessful transmissions
  last Tt
• A busy period will contain k transmission periods
  if there is at least one arrival in the last
  mini-slot of each of the first k-1 transmission
  periods, and no arrival in the last mini-slot of
  the kth transmission period
• And

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Useful time

• During the busy period, the number of
  transmission periods is
• When a transmission period is useful it carries
  information for T seconds
• The useful part of the busy-idle cycle is then
• Where Psuc denotes the success probability

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Success probability

• We divide by the probability of some arrivals
  because we know there was at least one arrival,
  since a transmission period has been initiated

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Throughput
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BTP collision resolution

• Given a MA channel with Trenary Feedback running
  BTP for collision resolution.
• A node perform the following algorithm upon
  waking up
• If collision, wait for resolution and then
  transmit
• Otherwise (if quiet or success), broadcast in the
  next time slot.
• At time t, n nodes collided. At time Tgtt a new
  node woke up wishing to send a packet. Which of
  the following is true?
• The node will transmit successfully only after
  all n nodes have successfully transmitted
• The node will transmit during the collision
  resolution, and the result will be as if the node
  had collided with the n nodes in the first place
• Either 1. or 2. depending on the place in the of
  the slot in the virtual tree
• Either 1. or 2. according to the type of slot
  the node sensed
• All the above answers are wrong

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Analysis
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BTP in a noisy channel

• Consider a MA channel where BTP is applied and
  noise is present. The impact of noise is that
  there is a probability p1 that a slot which
  contains a single transmission is interpreted as
  a collision.
• How will the CRIs (Collision Resolution
  Intervals) change?

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• How will the optimal probability p change

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