802'11e EDCA

1
802.11e EDCA

• WLN 2005
• Sydney, Nov. 15 2005
• Paal E. Engelstad (presenter)
• UniK / Telenor RD
• Olav N. Østerbø
• Telenor RD
• http//www.unik.no/paalee/research.htm

2
Agenda

• Delay and Throughput Analysis of IEEE 802.11e
  EDCA with Starvation Prediction
• Non-saturation analysis
• AIFS differentiation and Starvation prediction
• Z-tranform of the delay
• Virtual collision handling
• Differentiation of Downlink 802.11e Traffic in
  the Virtual Collision Handler
• Downlink UDP scenario
• Virtual collision handling (demonstration)
• Closed-form solution to this scenario
• Follow-up work
• The queueing delay (WONS 2006 - Accepted)
• The full delay distribution (IPCCC 2006 -
  Pending)

3
Recap EDCA 4 Access Categories (AC)

• AC0 (AC_BK)
• AC1 (AC_BE)
• AC2 (AC_VI)
• AC3 (AC_VO)
• 4 queues on each station
• ... and Virtual Collision Handling (VCH) between
  the queues

4
EDCA channel Access

• Differentiation parameters
• Contention Windows
• Arbitration IFS (AIFS)
• (TXOP lengths)

5
Markov Chain

• The utilization factor ? balances between
  saturation and non-saturation
• Collision prob. p
• Other parameters
• p, q and q
• Drop probability
• Transmission in (i,j,0) states, with distribution

6
... some calculations ...

• The transmission probablity
• From chain regularities...
• ... and after normalization

7
The transmission probability
Non-Saturation part

• Before solving the equations, we first need to
  determine the remaining parameters
• ?, p, p, q and q

8
The collision probability

• The probability of a busy slot
• The collision probability of ACi
• (Here Without Virtual Collisions)
• The probability of blocking of the countdown, p,
  is distinguished from the collision probablity,
  p.
• Gives much flexibility
• p 0 (similar to the original Bianchi model)
• p p (similar to the model of Xiao / Ziouva)
• In this paper, we propose to incorporate AIFS
  differentiation into p...

9
AIFS Differentiation

• We scale down the collision probability during
  countdown, depending on the AIFS setting
• Starvation is thus predicted to occur when

where
10
Determining the remaining parameters

• The pdf of the length of a slot
• Thus, assuming Poisson traffic
• And from the general result regarding
  the utilization factor, ?

11
Throughput

• We have shown that this expression is valid also
  under non-saturation

12
Preliminary Throughput Validations Setup I

• 802.11b with long preamble and without RTS/CTS
• Poisson distributed traffic 1024B packets

13
Preliminary Throughput Validations Setup II

• We use the recommended (default) parameter
  settings of 802.11e EDCA
• Simulations
• ns-2
• with TKN implementation of 802.11e from TUB
• Numerical computations
• Mathematica

14
Preliminary Throughput Validation The
non-saturation analysis
15
Preliminary Throughput Validation The starvation
predictions
16
Fixed number of nodes (n5)
17
The delay analysis

• The major contribution of this paper is probably
  that the Medium Access Delay (MAC delay) is
  expressed in terms of the z-transform...

18
z-tranform of the MAC delay
s1
s0
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z-transform of the medium access delay (cntd.)

• The mean medium access delay is found by
  derivation of the z-transform and by letting z1
• Obtain a delay expression that can easily be
  verified directly...

20
Mean Medium Access Delay I
21
Mean Medium Access Delay II

• ... and the mean medium access delay is finally
  found as

22
Validation of Mean delay (n5)
23
Conclusion - 1

• An analytical model is found that also describes
  non-saturation conditions
• We propose a new model, leading to a relatively
  simple set of equations
• AIFS differentiation is incorporated into the
  model
• We propose a new approach
• Starvation prediction follows
• Virtual collision handling is incorporated
• Demonstrated in our downlink work (next paper)
• Most importantly The z-transform of the medium
  access delay was found
• Our analytical findings seem to be supported by
  simulation results

24
The z-transform is an important contribution...

• ...because it encompasses a full description of
  the delay in the system
• The medium access delay
• Given by the first order moment
• Demonstrated in the presented paper
• The queuing delay
• Given by the second order moment
• Variation of the queuing delay
• Given by the third order moment
• The full delay distribution
• The transform can be inverted numerically
• All desirable delay percentiles follow

... and so forth ....
25
Agenda

• Delay and Throughput Analysis of IEEE 802.11e
  EDCA with Starvation Prediction
• Non-saturation analysis
• AIFS differentiation and Starvation prediction
• Z-tranform of the delay
• Virtual collision handling
• Differentiation of Downlink 802.11e Traffic in
  the Virtual Collision Handler
• Downlink UDP scenario
• Virtual collision handling (demonstration)
• Closed-form solution to this scenario
• Follow-up work
• The queueing delay (WONS 2006 - Accepted)
• The full delay distribution (IPCCC 2006 -
  Pending)

A small side-step
26
Queueing Delay

• Assuming a M/G/1 system the queueing delay is
  expressed as
• The second order of the delay is found by double
  derivation of the z-transform and by letting z1

27
Double derivation of the z-transform
28
Example of queueing delay results
29
The full delay distribution

• The z-transform of the delay
• For the tail probabilities
• then
• and can be expressed by the Cauchy
  contour integral

30
Approximation Trapezodial Rule

• The Cauchy contour integral can be approximated
  using the trapezodial rule with stepsize
• Hence
• It can be shown that the accuracy is bounded by

31
Same method to find distribution of the queueing
delay

• Pollaczek-Khinchin formula (discrete time)
• Thus, the tail probability of the
• Queueing Delay
• Total Delay

32
Distribution of Medium Access Delay
33
Distribution of Queueing Delay
34
Conclusion - 2

• The z-transform of the delay was found
• Derived the mean medium access delay (as before)
• It is so important because, it can be used to
  find
• the mean medium access delay, its variation,
  etc...
• the mean queueing delay, its variation and so
  forth
• the full delay distribution
• all desirable delay percentiles
• Our analytical findings seem to be supported by
  simulation results

35
Agenda

• Delay and Throughput Analysis of IEEE 802.11e
  EDCA with Starvation Prediction
• Non-saturation analysis
• AIFS differentiation and Starvation prediction
• Z-tranform of the delay
• Virtual collision handling
• Differentiation of Downlink 802.11e Traffic in
  the Virtual Collision Handler
• Downlink UDP scenario
• Virtual collision handling (demonstration)
• Closed-form solution to this scenario
• Follow-up work
• The queueing delay (WONS 2006 - Accepted)
• The full delay distribution (IPCCC 2006 -
  Pending)

36
Background Downlink Analysis

• Unlike most related work, we also put focus on
  the downlink scenario

37
Assumption

• All traffic are downlink!
• E.g. downlink video streaming over UDP
• The AP has full control over the wireless medium
• Collision primarily happens in the virtual
  collision handler

38
Core idea of Downlink Analysis

• Treat the Virtual Collision Handler as a virtual
  channel and disregard the wireless medium as a
  channel
• Re-use the Markov model
• Introduce Virtual Collision Handling into the
  model
• Set the number of nodes to 1

39
Virtual Collision Handling 1 node

• The probability of a busy slot
• The collision probability of ACi
• Without Virtual Collisions
• With Virtual Collisions

40
Throughput 1 node

• Generally
• But for 1 node
• Using the above, we have quite interestingly -
  proved by induction that
• Hence, the throughput becomes

41
Validations
42
Conclusion - 3

• We have shown that the Bianchi model can be
  extended to also cover downlink traffic
• All collisions in the virtual collision handler
  of the AP. It is treated as a virtual channel.
• Need a model that incoporates virtual collision
  handling.
• Set n1
• The approach was validated, and numerical results
  matched well with simulations.

43
Closed-form solution under saturation conditions

• We show that the downlink model can be expressed
  ON CLOSED FORM...
• ...under saturation conditions

44
Recursive solution method

• Start with the highest priority ACs
• For lower priority ACs
• etc....
• Use , ,
  or (starvation)

45
Example of solution for the second highest
priority AC

• Note that it is expressed in terms of the
  transmission probability of the highest priority
  AC, AC3.
• This is why a recursive solution method is
  required.

46
Closed form delay expression

• Using these expressions, the delay can be found
  on closed form, e.g. for AC3

47
Validation Scenarios
48
Throughput validations of closed form solution
(Scenario 1)
49
Throughput validations of closed form solution
(Scenario 2)
50
Validations with other scenarios
51
Conclusion - 4

• We have also derived a closed form solution for
  the downlink scenario
• Analytical results were validated and matched
  well with simulation results

52
Backup slides...
53
The effect of AIFS differentiation during
countdown
Slots that AC3 can use for countdown
AC3s perspective
Packet
Packet
AC0s perspective
Packet
Packet
Slots that AC0 can use for countdown

• A higher AIFS value translates into a lower
  average countdown rate

54
Medium Access Starvation
Slots that AC3 can use for countdown
AC3s perspective
Packet
Packet
Packet
AC0s perspective
Packet
Packet
Packet
No slots for AC0s countdown

• AIFS differentiation leads to starvation at high
  traffic loads

55
How to incorporate this effect into the
analytical model?
AIFSN0
Packet
Packet
Ai AIFSNi - AIFSN0 (i.e. defined such that
always A0 0)
unblocked empty slots
one busy slot
Packet
Packet
Ai blocked slots