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802.11e EDCA

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  1. 802.11e EDCA WLN 2005 Sydney, Nov. 15 2005 Paal E. Engelstad (presenter) UniK / Telenor R&D Olav N. Østerbø Telenor R&D 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) • AC[0] (AC_BK) • AC[1] (AC_BE) • AC[2] (AC_VI) • AC[3] (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 ρ 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 • ρ, p, p*, q and q*

  8. The collision probability • The probability of a busy slot: • The collision probability of AC[i]: • (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, ρ:

  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. AC[3] AC[2] AC[1] AC[0] AIFSN 2 2 3 7 CWmin 3 7 15 15 CWmax 15 31 1023 1023 Retry Limit (long/short) 7/4 7/4 7/4 7/4 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 (n=5)

  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 s=1 s=0

  19. z-transform of the medium access delay (cntd.) • The mean medium access delay is found by derivation of the z-transform and by letting z=1 • 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 (n=5)

  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 z=1:

  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 AC[i]: • 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 n=1 • 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, AC[3]. • 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 AC[3]:

  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