Bianchis Model: Topology and Parameters

1
Mobile Networks
Module C- Part 1WLAN Performance Aspects
Mohammad Hossein Manshaei Jean-Pierre Hubaux
http//mobnet.epfl.ch
2
Performance Evaluation of IEEE 802.11(DCF)

• Real Experimentations
• HoE on IEEE 802.11b
• Analytical Models
• Bianchis Model
• Simulations
• HoE on ns-2

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Bianchis Model Topology and Parameters

• N links with the same physical condition
  (single-collision domain)

3
2
4
1
2
3
N
1
AP
N-2
N
N-1
We want to calculate the throughput of this
network.
Probability of Transmission
Probability of Collision More than one
transmission at the same time 1 (1- p)N-1
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802.11 - CSMA/CA unicast (Review)

• Sending unicast packets
• station has to wait for DIFS before sending data
• receiver acknowledges at once (after waiting for
  SIFS) if the packet was received correctly (CRC)
• automatic retransmission of data packets in case
  of transmission errors

DIFS
data
sender
SIFS
ACK
receiver
DIFS
data
other stations
t
waiting time
Contentionwindow
The ACK is sent right at the end of SIFS(no
contention)
5
802.11 DCF with RTS/CTS (Review)

• Sending unicast packets
• station can send RTS with reservation parameter
  after waiting for DIFS (reservation determines
  amount of time the data packet needs the medium)
• acknowledgement via CTS after SIFS by receiver
  (if ready to receive)
• sender can now send data at once, acknowledgement
  via ACK
• other stations store medium reservations
  distributed via RTS and CTS

DIFS
data
RTS
sender
SIFS
SIFS
SIFS
ACK
CTS
receiver
DIFS
NAV (RTS)
data
other stations
NAV (CTS)
t
defer access
Contentionwindow
RTS/CTS can be present forsome packets and not
for other
NAV Net Allocation Vector
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Bianchis Model Two Dimensional Markov chain
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Bianchis Model Two Dimensional Markov chain
Stationary distribution
Probability of transmission
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Bianchis Model Two Dimensional Markov chain
Successful Transmission
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Bianchis Model Two Dimensional Markov chain
Collision
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Bianchis Model Stationary Distribution of Chain
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Bianchis Model Solution for p and p

• After some derivations ? system of two nonlinear
  equations with two variables p and p

? Can be solved numerically to obtain p and p
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Bianchis model Throughput Calculation

• Throughput of node i
• Ptr Probability of at least one transmission in
  slot time
• Ps Probability of successful transmission of
  during a random time slot
• L Average packet payload size
  
• Ts Average time to transmit a packet of size L
• Tc Average time of collision
• Tid Duration of the idle period
• ACK ACK transmission time
• H Header transmission time

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Numerical Results